Pat'sBlog

On This Day in Math - Jan 28

2012-01-28T00:10:00.000Z

Mathematical discoveries, like springtime violets in the woods, have their season which no human can hasten or retard.
~Janos Bolyai

The 28th day of the year; 28 is the second perfect number; the sum of its proper factors.

EVENTS

1699 Leibniz elected the ﬁrst foreign member of the French Academy. *VFR

1902 "It is proposed to found in the city of Washington, an institution which...shall in the broadest and most liberal manner encourage investigation, research, and discovery [and] show the application of knowledge to the improvement of mankind..." — Andrew Carnegie, January 28, 1902
Established to support scientific research, today the CIW directs its efforts in six main areas: plant molecular biology at the Department of Plant Biology (Stanford, California), developmental biology at the Department of Embryology (Baltimore, Maryland), global ecology at the Department of Global Ecology (Stanford, CA), Earth science, materials science, and astrobiology at the Geophysical Laboratory (Washington, DC); Earth and planetary sciences as well as astronomy at the Department of Terrestrial Magnetism (Washington, DC), and (at the Observatories of the Carnegie Institution of Washington (OCIW; Pasadena, CA and Las Campanas, Chile)).*Wik

1977 According to the Guinness Book of World Records, the most freakish rise in temperature ever recorded was on this date in Spearﬁsh, South Dakota. At 7:30 a.m. it was −4 degrees Fahrenheit; at 7:32 a.m. it was +45 degrees Fahrenheit. What was the average rate of change in temperature per minute? [NCTM Sourcebook of Applications of School Mathematics, p. 125] *VFR
Some other temp changes from around the net show:

1972 The greatest temperature change in 24 hours occurred in Loma, MT. on January 15. The temperature rose exactly 103 degrees, from -54 degrees Fahrenheit to 49 degrees. This is the world record for a 24—hour temperature change.
1911 Fastest temperature drop: 27.2 °C (49 °F) in 15 minutes on Jan 10 in Rapid City, South Dakota,

BIRTHS

1540 Ludolph van Ceulen, a German mathematician who is famed for his calculation of π to 35 places. In Germany π used to be called the Ludolphine number. Because van Ceulen could not read Greek, Jan Cornets de Groot, the burgomaster of Delft and father of the jurist, scholar, statesman and diplomat, Hugo Grotius, translated Archimedes' approximation to π for Van Ceulen. This proved a significant point in Van Ceulen's life for he spent the rest of his life obtaining better approximations to π using Archimedes' method with regular polygons with many sides.*SAU He has Pi on his memorial stone.

1608 Giovanni Alfonso Borelli (28 Jan 1608; 31 Dec 1679) Italian mathematician, physiologist and physicist sometimes called “father of biomechanics.” He was the first to apply the laws of mechanics to the muscular action of the human body. In De motu animalium (Concerning Animal Motion, 1680), he correctly described the skeleton and muscles as a system of levers, and explained the mechanism of bird flight. He calculated the forces required for equilibrium in various joints of the body well before the mechanics of Isaac Newton. In 1649, he published a work on malignant fevers. He repudiated astrological causes of diseases and believed in chemical cures. In 1658, he published Euclidus restitutus. He made anatomical dissections, drew a diver's rebreather, investiged volcanoes, was first to suggest a parabolic path for comets, and considered Jupiter had an attractive influence on its moons.*TIS

1611 Johannes Hevelius (28 Jan 1611; 28 Jan 1687) German astronomer, who studying in Leiden and established his own observatory on the rooftops of several houses. From four years' telescopic study of the Moon, using telescopes of long focal power, Hevelius compiled Selenographia ("Pictures of the Moon", 1647), an atlas of the Moon with some of the earliest detailed maps. A few of his names for lunar mountains (e.g., the Alps) are still in use, and a lunar crater is named for him. Hevelius is today best remembered for his use of "aerial" telescopes of enormous focal length and his rejection of telescopic sights for stellar observation and positional measurement. He catalogued 1564 stars in Prodromus Astronomiae (1690), discovered four comets, and was one of the first to observe the transit of Mercury. He died on his birthday. *TIS

1622 Adrien Auzout (28 January 1622 – 23 May 1691) was a French astronomer.
In 1664–1665 he made observations of comets, and argued in favor of their following elliptical or parabolic orbits. (In this he was opposed by his rival Johannes Hevelius.) Adrien was briefly a member of the Académie Royale des Sciences from 1666 to 1668, and a founding member of the French Royal Obseratory. (He may have left the academy due to a dispute.) He was elected a Fellow of the Royal Society of London in 1666. He then left for Italy and spent the next 20 years in that region, finally dying in Rome in 1691. Little is known about his activities during this last period.
Auzout made contributions in telescope observations, including perfecting the use of the micrometer. He made many observations with large aerial telescopes and he is noted for briefly considering the construction of a huge aerial telescope 1,000 feet in length that he would use to observe animals on the Moon. In 1647 he performed an experiment that demonstrated the role of air pressure in function of the mercury barometer. In 1667–68, Adrien and Jean Picard attached a telescopic sight to a 38-inch quadrant, and used it to accurately determine positions on the Earth. The crater Auzout on the Moon is named after him. *Wik

1701 Charles Marie de La Condamine (28 January 1701 – 13 February 1774) was a French explorer, geographer, and mathematician. He spent ten years in present-day Ecuador measuring the length of a degree latitude at the equator and preparing the first map of the Amazon region based on astronomical observations. *Wik

1855 William Seward Burroughs (28 Jan 1855, 5 Sep 1898) American inventor who invented the world's first commercially viable recording adding machine and pioneer of its manufacture. He was inspired by his experience in his beginning career as a bank clerk. On 10 Jan 1885 he submitted his first patent (issued 399,116 on 21 Aug 1888) for his mechanical “calculating machine.” Burroughs co-founded the American Arithmometer Co in 1886 to develop and market the machine. The manufacture of the first machines was contracted out, and their durability was unsatisfactory. He continued to refine his design for accuracy and reliability, receiving more patents in 1892, and began selling the much-improved model for $475 each. By 1895, 284 machines had been sold, mostly to banks, and 1500 by 1900. The company later became Burroughs Corporation (1905) and eventually Unisys. *TIS

1855 Karl Friedrich Wilhelm Rohn (January 25 1855 in Schwanheim - August 4 1920 in Leipzig ) was a German mathematician working mainly in geometry.
He studied under Alexander von Brill , who led him away from an initial engineering studies for mathematics; and in 1878 he received his doctorate in Munich under Felix Klein. His doctoral was on the Kummer surface of fourth Order and its relationship with hyperelliptic functions (with Riemann surfaces of genus 2). Besides his work on the Kummer surface, and other algebraic surfaces , he also examined algebraic space curves, and there completed the classification work of Georges Halphen and Max Noether. In 1913 he was president of the German Mathematical Society. *Wik His love of geometry is also illustrated by his beautiful thread models which were especially produced to excite the curiosity of the uninitiated. Rohn constructed models of surfaces and space curves that he was studying, particularly in the early part of his career. In 1884 the Jablonowski Society proposed as prize problem asking for essays on the general surface of order 4, extending the work of Schläfli, Klein and Zeuthen on cubic surfaces; they awarded the prize to Rohn for his essay in 1886. He made important contributions to the theory of quartic surfaces, in particular of ruled quartics and quartics with a triple point.*SAU

1888 Louis Joel Mordell (28 January 1888 – 12 March 1972) was a British mathematician, known for pioneering research in number theory. He was born in Philadelphia, USA, in a Jewish family of Lithuanian extraction. He came in 1906 to Cambridge to take the scholarship examination for entrance to St John's College, and was successful in gaining a place and support.
Having taken third place in the Mathematical Tripos, he began independent research into particular diophantine equations: the question of integer points on the cubic curve, and special case of what is now called a Thue equation, the Mordell equation

y² = x² + k.

During World War I he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Ramanujan's tau-function. The proof was by means, in effect, of the Hecke operators, which had not yet been named after Erich Hecke; it was, in retrospect, one of the major advances in modular form theory, beyond its status as an odd corner of the theory of special functions.
In 1920 he took a teaching position in Manchester College of Technology, becoming the Fielden Reader in Pure Mathematics at the Victoria University of Manchester in 1922 and Professor in 1923. There he developed a third area of interest within number theory, geometry of numbers. His basic work on Mordell's theorem is from 1921/2, as is the formulation of the Mordell conjecture.
In 1945 he returned to Cambridge as a Fellow of St. John's, when elected to the Sadleirian Chair, and became Head of Department. He officially retired in 1953. It was at this time that he had his only formal research students, of whom J. W. S. Cassels was one. His idea of supervising research was said to involve the suggestion that a proof of the transcendence of the Euler–Mascheroni constant was probably worth a doctorate. *Wik

1892 Carlo Emilio Bonferroni (28 Jan 1892 in Bergamo, Italy - 18 Aug 1960 in Florence, Italy) His articles are more of a contribution to probability theory than to simultaneous statistical inference. He also had interests in the foundations of probability. He developed a strongly frequentist view of probability denying that subjectivist views can even be the subject of mathematical probability. *SAU He is best known for the Bonferroni inequalities, and gives his name to (but did not devise) the Bonferroni correction in statistics. *Wik

1903 Dame Kathleen Lonsdale (28 Jan 1903; 1 Apr 1971) British crystallographer (née Yardley) who developed several X-ray techniques for the study of crystal structure. Her experimental determination of the structure of the benzene ring by x-ray diffraction, which showed that all the ring C-C bonds were of the same length and all the internal C-C-C bond angles were 120 degrees, had an enormous impact on organic chemistry. She was the first woman to be elected (1945) to the Royal Society of London. *TIS

1911 Robert Schatten (January 28, 1911 – August 26, 1977) principal mathematical achievement was that of initiating the study of tensor products of Banach spaces. The concepts of crossnorm, associate norm, greatest crossnorm, least crossnorm, and uniform crossnorm, all either originated with him or at least first received careful study in his papers. He was mainly interested in the applications of this subject to linear transformations on Hilbert space. In this subject, the Schatten Classes perpetuate his name. Schatten had his own way of making abstract concepts memorable to his elementary classes. Who could forget what a sequence was after hearing Schatten describe a long corridor, stretching as far as the eye could see, with hooks regularly spaced on the wall and numbered 1, 2, 3, ...? "Then," Schatten would say, "I come along with a big bag of numbers over my shoulder, and hang one number on each hook." This of course was accompanied by suitable gestures for emphasis. *SAU

1924 Wilhelm Paul Albert Klingenberg (28 January 1924 Rostock, Mecklenburg, Germany – 14 October 2010 Röttgen, Bonn) was a German mathematician who worked on differential geometry and in particular on closed geodesics. One of his major achievements is the proof of the sphere theorem in joint work with Marcel Berger in 1960: The sphere theorem states that a simply connected manifold with sectional curvature between 1 and 4 is homeomorphic to the sphere. *Wik

DEATHS

1687 Johannes Hevelius (28 Jan 1611; 28 Jan 1687) German astronomer, who studying in Leiden and established his own observatory on the rooftops of several houses. From four years' telescopic study of the Moon, using telescopes of long focal power, Hevelius compiled Selenographia ("Pictures of the Moon", 1647), an atlas of the Moon with some of the earliest detailed maps. A few of his names for lunar mountains (e.g., the Alps) are still in use, and a lunar crater is named for him. Hevelius is today best remembered for his use of "aerial" telescopes of enormous focal length and his rejection of telescopic sights for stellar observation and positional measurement. He catalogued 1564 stars in Prodromus Astronomiae (1690), discovered four comets, and was one of the first to observe the transit of Mercury. He died on his birthday. *TIS

1864 Benoit Clapeyron (26 Feb 1799, 28 Jan 1864) French engineer who expressed Sadi Carnot's ideas on heat analytically, with the help of graphical representations. While investigating the operation of steam engines, Clapeyron found there was a relationship (1834) between the heat of vaporization of a fluid, its temperature and the increase in its volume upon vaporization. Made more general by Clausius, it is now known as the Clausius-Clapeyron formula. It provided the basis of the second law of thermodynamics. In engineering, Clayeyron designed and built locomotives and metal bridges. He also served on a committee investigating the construction of the Suez Canal and on a committee which considered how steam engines could be used in the navy.*TIS

1889 Joseph Émile Barbier (18 March 1839 in St Hilaire-Cottes, Pas-de-Calais, France - 28 Jan 1889 in St Genest, Loire, France)
He was offered a post at the Paris Observatory by Le Verrier and Barbier left Nice to begin work as an assistant astronomer. For a few years he applied his undoubted genius to problems of astronomy. He proved a skilled observer, a talented calculator and he used his brilliant ideas to devise a new type of thermometer. He made many contributions to astronomy while at the observatory but his talents in mathematics were also to the fore and he looked at problems in a wide range of mathematical topics in addition to his astronomy work.
As time went by, however, Barbier's behaviour became more and more peculiar. He was clearly becoming unstable and exhibited the fine line between genius and mental problems which are relatively common. He left the Paris Observatory in 1865 after only a few years of working there. He tried to join a religious order but then severed all contacts with his friends and associates. Nothing more was heard of him for the next fifteen years until he was discovered by Bertrand in an asylum in Charenton-St-Maurice in 1880.
Bertrand discovered that although Barbier was clearly unstable mentally, he was still able to make superb original contributions to mathematics. He encouraged Barbier to return to scientific writing and, although he never recovered his sanity, he wrote many excellent and original mathematical papers. Bertrand, as Secretary to the Académie des Sciences, was able to find a small source of income for Barbier from a foundation which was associated with the Académie. Barbier, although mentally unstable, was a gentle person and it was seen that, with his small income, it was possible for him to live in the community. This was arranged and Barbier spent his last few years in much more pleasant surroundings.
Barbier's early work, while at the Observatory, consists of over twenty memoirs and reports. These cover topics such as spherical geometry and spherical trigonometry. We mentioned above his work with devising a new type of thermometer and Barbier wrote on this as well as on other aspects of instruments. He also wrote on probability and calculus.
After he was encouraged to undertake research in mathematics again by Bertrand, Barbier wrote over ten articles between the years 1882 and 1887. These were entirely on mathematical topics and he made worthwhile contributions to the study of polyhedra, integral calculus and number theory. He is remembered for Barbier's theorem, nicely explained here by Alex Bogomolny.*SAU

1910 Alfredo Capelli (5 Aug 1855, Milan, Italy – 28 Jan 1910, Naples, Italy) was an Italian mathematician who discovered Capelli's identity.
Capelli graduated from the University of Rome in 1877, and moved to the University of Pavia where he worked as an assistant for Felice Casorati. In 1881 he became a professor at the University of Palermo, replacing Cesare Arzelà who had recently moved to Bologna. In 1886, he moved again to the University of Naples, where he held the chair in algebra. He remained at Naples until his death in 1910. As well as being a professor there, he was editor of the Giornale di Matematiche di Battaglini from 1894 to 1910, and was elected to the Accademia dei Lincei.*Wik

1946 Dmitrii Matveevich Sintsov (21 November 1867 – 28 January 1946) was a Russian mathematician known for his work in the theory of conic sections and non-holonomic geometry.
He took a leading role in the development of mathematics at Kharkov University, serving as chairman of the Kharkov Mathematical Society for forty years, from 1906 until his death at the age of 78.*Wik

1954 Ernest Benjamin Esclangon (March 17, 1876 – January 28, 1954) was a French astronomer and mathematician.
Born in Mison, Alpes-de-Haute-Provence, in 1895 he started to study mathematics at the École Normale Supérieure, graduating in 1898. Looking for some means of financial support while he completed his doctorate on quasi-periodic functions, he took a post at the Bordeaux Observatory, teaching some mathematics at the university.
During World War I, he worked on ballistics and developed a novel method for precisely locating enemy artillery. When a gun is fired, it initiates a spherical shock wave but the projectile also generates a conical wave. By using the sound of distant guns to compare the two waves, Escaglon was able to make accurate predictions of gun locations.
After the armistice, Esclangon became director of the Strasbourg Observatory and professor of astronomy at the university the following year. In 1929, he was appointed director of the Paris Observatory and of the International Time Bureau, and elected to the Bureau des Longitudes in 1932. In 1933, he initiated the talking clock telephone service in France. He was elected to the Académie des Sciences in 1939.
Serving as director of the Paris Observatory throughout World War II and the German occupation of Paris, he retired in 1944. He died in Eyrenville, France.
The binary asteroid 1509 Esclangona and the lunar crater Esclangon are named after him.*Wik

1988 (Emil) Klaus (Julius) Fuchs (29 Dec 1911; 28 Jan 1988) was a German-born physicist who was convicted as a spy on 1 Mar 1950, for passing nuclear research secrets to Russia. He fled from Nazi Germany to Britain. He was interned on the outbreak of WW II, but Prof. Max Born intervened on his behalf. Fuchs was released in 1942, naturalized in 1942 and joined the British atomic bomb research project. From 1943 he worked on the atom bomb with the Manhattan Project at Los Alamos, U.S. By 1945, he was sending secrets to Russia. In 1946, he became head of theoretical physics at Harwell, UK. He was caught, confessed, tried, imprisoned for nine of a 14 year sentence, released on 23 Jun 1959, and moved to East Germany and resumed nuclear research until 1979. *TIS

1993 Helen Battles (Sawyer) Hogg (1 Aug 1905, 28 Jan 1993) was a Canadian astronomer who located, cataloged and measured the distances to variable stars in globular clusters (stars with cyclical changes of brightness found within huge, dense conglomerations of stars located in the outer halo of the Milky Way galaxy). Her interest in astronomy was spurred when she witnessed a total eclipse of the sun in 1925. Alongside her career work, she was also foremost in Canada in popularizing astronomy, about which she wrote a column in the Toronto Star for thirty years. She was the first woman to become president of the Royal Canadian Institute. In 1989, the observatory at the National Museum of Science and Technology in Ottawa was dedicated in her name.*TIS

2009 William Moser (5 Sep 1927;28 Jan 2009) My mathematical interests are: presentations for finite groups; combinatorial enumerations (e.g., counting restricted permutations and combinations); problems in discrete and combinatorial geometry. *From his page at McGill Univ.
In March 2003 Moser was interviewed by Siobhan Roberts who was working on her major work on Coxeter King of Infinite space. He recounted the following story

"Donald made many great contributions to mathematics. I made one great contribution," recounted Moser. Moser's opportunity came at the end of Coxeter's 1955 summer of roving lectures, after his session in Stillwater, at Oklahoma State University. Moser drove down to meet Coxeter and serve as his assistant, taking detailed notes of the well-polished lectures. "At the end of the summer we drove north, to civilisation," said Moser wryly. "We were in my car and Donald asked me if he could drive. It was a new car. Indeed it was the first car I had ever purchased, a green 1955 Plymouth 2-door. I paid $2,000 for it and drove it to Oklahoma. But I agreed. I was surprised to see that he was an aggressive driver. At one point he was trying to pass a car while driving up a hill on a 2-lane highway. I immediately perceived that this was not a prudent thing to do. He tried to coax the car to go faster but it wouldn't respond. At the last moment I shrieked at him, 'Pull back, pull back'. I was probably his only student to shriek at him. He began to pull back and at that moment a truck came over the hill. He managed to get back in the right lane just in time. I HAD SAVED HIS LIFE! And mine. But saving Coxeter's life was my greatest contribution to mathematics." *SAU

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

Before There Were Four-Fours, There Were Four-Threes

2012-01-27T23:20:00.000Z

*Eyegate Gallery

EVERYONE has encountered the four-fours problem, using four fours and whatever mathematical operations that were allowed to make a number, or a set of numbers. You may even have read that it originated in the famous book of recreations by W. W. Rouse Ball; Wikipedia still has, "The first printed occurrence of this activity is in 'Mathematical Recreations and Essays' by W. W. Rouse Ball published in 1892. In this book it is described as a 'traditional recreation'. "

I know you've heard it before, but here we go again, "Wikipedia is wrong about that."

The first record I have found of a puzzle like these was in an 1818 edition of The schoolmaster's assistant: being a compendium of arithmetic both practical and theoretical : in five parts, and early American Arithmetic by Thomas Dilworth.

This image is from page 189 and part of a collection of "Short and Diverting Questions". As is typical of many of the early such problems, there were no specifications for the operations that might be employed.
In the same collection of problems, Dilworth poses a problem requesting the use of three threes...

Ok, even I can do that one, and the dd+d/d format becomes a regular problem through the years with different digits; the most common being in the form of "use four nines to make 100."

Professor Singmaster says the both the Dilworth problems appear in a 1743 edition of this book.
By 1788 similar problems show up in another classic American Arithmetic by Nicolas Pike,"Said Harry to Edmund, I can place four 1's so that, when added, they shall make precisely 12. Can you do so too?"

The first printed version I can find of a question like this that asks about using three of four of the same number to find a set of integers appears in 1881 in a U.K. magazine called, Knowledge: an Illustrated Magazine of Science. It was founded and edited by Richard A Proctor, the English astronomer who is remembered for his maps of Mars (and has a crater there named for him). It may be that the Cupidus Scientiae who submitted the question is, in fact, the editor.

The next edition (Jan 6, 1882) did indeed carry the solutions, as well as correspondence from an H. Snell who provides that 19 = 4! - 4 - 4/4 (he uses the Jarret symbol for factorial which looks like a right angle symbol with the number on the horizontal line)
The editor felt that factorials were inappropriate for the problem as posed. The following week (Jan 13,1882) there were several solutions for 19 from contributors, including (4+4-.4)/.4.

When W. W. Rouse Ball got into the act, it was in the third edition of his MRE 1896 and it was a long step away from the four-fours as we have come to know it. He repeated a problem previously used by Sam Loyd in 1893 which became popular in the United Kingdom; "Make 82 with the seven digits 9, 8, 7, 6, 5, 4, 0." Loyd offered a prize of 100 pounds for the solution. The solution, involving the use of repeating fractions, was given as 80.5 + .97 + .46 = 82 with all the decimal values repeating. This was indicated in the period by using a single dot above the values which repeated.

It was not until the fifth edition of 1911 of MRE that Ball gives the more common version, and describes it as, "An arithmetical amusement, said to have been first propounded in 1881,...) which seems to refer to the posting in Knowledge. By the sixth edition (1914) he has extended the problem to four nines and four threes. This one is significant because it seems to be the first that discusses what values can be achieved by what set of operations.

After a while it even caught on with higher level mathematicians. In 1991 Clifford A. Pickover asked for good approximations to Phi using four fours.
In 1999 it became popular to ask for integers created using the digits 1, 9, 9, 9.
And it seems I saw a few of those floating around the internet at the beginning of 2012.
But remember, it all started with Jack and Harry, and four-threes.

On This Day in Math - Jan 27

2012-01-27T00:10:00.003Z

*Starship Asterisk web site

It troubles me that we are so easily pressured by purveyors of technology into permitting so-called ‘progress’ to alter our lives without attempting to control it—as if technology were an irrepressible force of nature to which we must meekly submit.
~Hyman G. Rickover

The 27th day of the year; 27³ = 19,683 which has a digit sum of 27. There is no larger number for which the sum of the digits of the cube is equal to the number .

EVENTS

1520 Oﬀ the Patagonian coast near a small peninsula called Punta Tombo, during Ferdinand Magellan’s voyage around the world, a crewman espied strange creatures swimming in the bay. He called them ﬂightless geese, but scientists believe they were penguins of a sort classiﬁed as Spheniscus magellanicus.*VFR

1613 Galileo observed Neptune, but did not recognize it as a planet. Galileo's drawings show that he first observed Neptune on December 28, 1612, and again on January 27, 1613. On both occasions, Galileo mistook Neptune for a fixed star when it appeared very close—in conjunction—to Jupiter in the night sky; hence, he is not credited with Neptune's discovery. (The official discovery is usually cited as September 23, 1846, Neptune was discovered within 1° of where Le Verrier had predicted it to be.) During the period of his first observation in December 1612, Neptune was stationary in the sky because it had just turned retrograde that very day. This apparent backward motion is created when the orbit of the Earth takes it past an outer planet. Since Neptune was only beginning its yearly retrograde cycle, the motion of the planet was far too slight to be detected with Galileo's small telescope.*Wik A new theory says he may have known it was a planet. Professor David Jamieson, Head of the School of Physics at University of Melbourne is investigating the notebooks of Galileo from 400 years ago and believes that buried in the notations is the evidence that he discovered a new planet that we now know as Neptune. Galileo was observing the moons of Jupiter in the years 1612 and 1613 and recorded his observations in his notebooks. Over several nights he also recorded the position of a nearby star which does not appear in any modern star catalogue. "It has been known for several decades that this unknown star was actually the planet Neptune. Computer simulations show the precision of his observations revealing that Neptune would have looked just like a faint star almost exactly where Galileo observed it," Professor Jamieson says.
In one of his notebooks he noticed the movement of a background star (Neptune) on January 28 and a dot (in Neptune's position) drawn in a different ink suggests that he found it on an earlier sketch, drawn on the night of January 6, suggesting a systematic search among his earlier observations. However, any notification about the discovery hasn't been found. *onOrbit.com

In 1921, Albert Einstein suggested the possibility of measuring the universe, which startled the audience, with his address Geometry and Expansion given at the Prussian Academy of Sciences in Berlin. Applying certain results of the relativity theory, he came to the conclusion that if the real velocities of the stars (as could be actually measured) were less than the calculated velocities, then it would prove that real gravitations' great distances were smaller than the gravitational distances demanded by the law of Newton. From such divergence, the finiteness of the universe could be proved indirectly, and it would even permit the estimation of its size. *TIS

1994 Silicon Graphics Inc. co-founder Jim Clark leaves the company to start Mosaic Communications, the operation that later became Netscape Communications Corp. With Netscape cofounder Marc Andreesen, Clark helped popularize the World Wide Web by distributing the company's browser for free.*CHM

2012 An asteroid, 2012 BX34, passed within about 60,000km of Earth - less than a fifth of the distance to the Moon.The asteroid's path made it the closest space-rock to pass by the Earth since June 2011. The asteroid, estimated to be about 11m (36ft) in diameter, was first detected on Jan 25.*BBC website

BIRTHS

1701 Charles-Marie de La Condamine (27 Jan 1701; 4 Feb 1774) French naturalist and mathematician who became particularly interested in geodesy (earth measurement). He was put in charge by the King of France of an expedition to Equador to measure a meridional arc at the equator (1735-43). It was wished to determine whether the Earth was either flattened or elongated at its poles. He then accomplished the first scientific exploration of the Amazon River (1743) on a raft, studying the region, and brought the drug curare to Europe. He also worked on establishment of a universal unit of length, and is credited with developing the idea of vaccination against smallpox, later perfected by Edward Jenner. However, he was almost constantly ill and died in 1773, deaf and completely paralyzed. *TIS

1829 Isaac Roberts (27 Jan 1829; 17 Jul 1904) British astronomer who was a pioneer in photography of nebulae. In 1885 he had built an observatory with a 20 inch reflector. Using this instrument Roberts was to make considerable progress in the newly developing science of Astro-photography. He photographed numerous celestial objects including Orion Nebula on 15 Jan 1986 (90 minute exposure) and Pleiades. Undoubtedly his finest work was a photograph showing the spiral structure of the Great Nebula in Andromeda, M31 on 29 Dec 1888. In addition to his contribution to astro-photography, Roberts also devised a machine to be used to engrave stellar positions on copper plates, known as the Stellar Pantograver. He was also a geologist of some considerable note.*TIS

1831 Charles Lutwidge Dodgson, pen-name Lewis Carroll (27 Jan 1832, 14 Jan 1898), was an English logician, mathematician, photographer, and novelist, remembered for Alice's Adventures in Wonderland (1865) and its sequel. After graduating from Christ Church College, Oxford in 1854, Dodgson remained there, lecturing on mathematics and writing treatises until 1881. As a mathematician, Dodgson was conservative. He was the author of a fair number of mathematics books, for instance A syllabus of plane algebraical geometry (1860). His mathematics books have not proved of enduring importance except Euclid and his modern rivals (1879) which is of historical interest. As a logician, he was more interested in logic as a game than as an instrument for testing reason.*TIS (I once read that if Dodgson had not written "Alice", he would be remembered today for his photography, and if he had not done either of those, then, if he was remembered at all, it would be for his logic book. One of my favorite Lewis Carroll stories is about his gift of a book to Queen Victoria. Here is the version as it is told on the Mathworld page):

Several accounts state that Lewis Carroll (Charles Dodgson ) sent Queen Victoria a copy of one of his mathematical works, in one account, An Elementary Treatise on Determinants. Heath (1974) states, "A well-known story tells how Queen Victoria, charmed by Alice in Wonderland, expressed a desire to receive the author's next work, and was presented, in due course, with a loyally inscribed copy of An Elementary Treatise on Determinants," while Gattegno (1974) asserts "Queen Victoria, having enjoyed Alice so much, made known her wish to receive the author's other books, and was sent one of Dodgson's mathematical works." However, in Symbolic Logic (1896), Carroll stated, "I take this opportunity of giving what publicity I can to my contradiction of a silly story, which has been going the round of the papers, about my having presented certain books to Her Majesty the Queen. It is so constantly repeated, and is such absolute fiction, that I think it worth while to state, once for all, that it is utterly false in every particular: nothing even resembling it has occurred" (Mikkelson and Mikkelson)

And then, I learned that "Lewis Carroll coined 'chortle' in Through the Looking-Glass, in 1871." @OEDonline, Twitter

1900 Hyman George Rickover (27 Jan 1900; 8 Jul 1986) was a Polish-American naval officer who immigrated to the US (1906) and graduated from the Naval Academy in 1922. He eventually became an Admiral. He is known as the “Father of the Nuclear Navy” for his leadership to build the atomic-powered submarine, USS Nautilus (1954). He served on active duty with the United States Navy for more than 63 years, receiving exemptions from the mandatory retirement age due to his critical service in the building of the United States Navy's nuclear surface and submarine force. *TIS

1903 Howard Percy Robertson (27 Jan 1903 in Hoquiam, Washington, USA - 26 Aug 1961) made outstanding contributions to differential geometry, quantum theory, the theory of general relativity, and cosmology. He was interested in the foundations of physical theories, differential geometry, the theory of continuous groups, and group representations. He was particularly interested in the application of the latter three subjects to physical problems.
His contributions to differential geometry came in papers such as: The absolute differential calculus of a non-Pythagorean non-Riemannian space (1924); Transformation of Einstein space (1925); Dynamical space-times which contain a conformal Euclidean 3-space (1927); Note on projective coordinates (1928); (with H Weyl) On a problem in the theory of groups arising in the foundations of differential geometry (1929); Hypertensors (1930); and Groups of motion in space admitting absolute parallelism (1932). *SAU

1936 Samuel C.C. Ting(27 Jan 1936, ) Samuel Chao Chung Ting is an American physicist who shared, with Burton Richter, the Nobel Prize for Physics in 1976 for his discovery of a new subatomic particle, the J/psi particle.*TIS

DEATHS

1667 Gregorius Saint Vincent (8 Sept 1584 in Bruges, Belgium - 27 Jan 1667 in Ghent, Belgium). His Opus geometricum (1647) contains the most beautiful frontispiece of any mathematics text. In this work, Gregorius was the ﬁrst to develop the theory of the geometric series and also the ﬁrst to show that the area under a hyperbola is a logarithm. *VFR (in the frontispiece he claims to have squared the circle) The engraved frontispiece shows sunrays inscribed in a square frame being arranged by graceful angels to produce a circle on the ground: 'mutat quadrata rotundis'. There was uneasiness in the learned world because no one in that world still believed that under the specific Greek rules the quadrature of a circle could possibly be effected, and few relished the thought of trying to locate an error, or errors, in 1200 pages of text. Four years later, in 1651, Christiaan Huygens found a serious defect in the last book of 'Opus geometricum', namely in Proposition 39 of Book X, on page 1121. This gave the book a bad reputation.*SAU

1823 Charles Hutton (14 Aug 1737 in Newcastle-upon-Tyne, England - 27 Jan 1823 in London, England) was an English mathematician who wrote arithmetic textbooks. A textbook he wrote while at the Royal Military Academy, Woolwich was later adopted as the first math text by the USMA in West Point, NY and served as the principal math text for two decades. *Wik

1860 János Bolyai (15 Dec 1802; 27 Jan 1860) Hungarian mathematician and one of the founders of non-Euclidean geometry - geometry that does not include Euclid's axiom that only one line can be drawn parallel to a given line through a point not on the given line. His father, Farkas Bolyai, had devoted his life to trying to prove Euclid's famous parallel postulate. Despite his father's warnings that it would ruin his health and peace of mind, János followed in working on this axiom until, in about 1820, he came to the conclusion that it could not be proved. He went on to develop a consistent geometry (published 1882) in which the parallel postulate is not used, thus establishing the independence of this axiom from the others. He also did valuable work in the theory of complex numbers. *TIS

1860 Sir Thomas Makdougall Brisbane, Baronet (23 Jul 1773, 27 Jan 1860) British soldier and astronomical observer for whom the city of Brisbane, Australia, is named. He was Governor of NSW (1821-25). Mainly remembered as a patron of science, he built an astronomical observatory at Parramatta, Australia, made the first extensive observations of the southern stars since Lacaille in (1751-52) and built a combined observatory and magnetic station at Makerstoun, Roxburghshire, Scotland. He also conducted (largely unsuccessful) experiments in growing Virginian tobacco, Georgian cotton, Brazilian coffee and New Zealand flax.*TIS

1895 James Cockle (14 Jan 1819 in Great Oakley, Essex, England - 27 Jan 1895 in Bayswater, London, England) Cockle was remarkably productive as a mathematician publishing over 100 papers. He wrote papers on both pure and applied mathematics, as well as on the history of science. On the former topic he wrote on fluid dynamics and magnetism. Most of his work, however, was in pure mathematics where he studied algebra, the theory of equations, and differential equations. He had a collaborator on mathematical work, a Congregationalist minister named Robert Harley. *SAU

1947 Alexander Brown (5 May 1877 in Dalkeith, near Edinburgh, Scotland - 27 Jan 1947 in Cape Town, South Africa) In 1903 Brown was appointed as Professor of Applied Mathematics in the South African College. In 1911 he married Mary Graham; they had a son and a daughter. He remained in Cape Town until his death in 1947, but his status changed in 1918 when the South African College became the University of Cape Town.
He was a member of the Edinburgh Mathematical Society, joining the Society in December 1898. He contributed papers to meetings of the Society such as On the Ratio of Incommensurables in Geometry to the meeting on Friday 9 June 1905 and Relation between the distances of a point from three vertices of a regular polygon, at the meeting on Friday 11 June 1909, communicated by D C McIntosh.
Brown was elected a Fellow of the Royal Society of South Africa in 1918, was on its Council from 1931 to 1935 and again in 1941, was its Honorary Treasurer from 1936 to 1940, and President from 1942 to 1945. Alexander Brown was elected to the Royal Society of Edinburgh on 20 May 1907. *SAU

1965 Philip Franklin (October 5, 1898 in New York — January 27, 1965 in Belmont, Massachusetts) was an American mathematician and professor whose work was primarily focused in analysis.
His dissertation, The Four Color Problem, was supervised by Oswald Veblen. After teaching for one year at Princeton and two years at Harvard (as the Benjamin Peirce Instructor), Franklin joined the MIT Department of Mathematics, where he stayed until his 1964 retirement.
In 1922, Franklin gave the first proof that all planar graphs with at most 25 vertices can be four-colored.
In 1928, Franklin gave the first description of an orthonormal basis for L²([0,1]) consisting of continuous functions (now known as "Franklin's system").
In 1934, Franklin published a counterexample to the Heawood conjecture, this 12-vertex cubic graph is now known as the Franklin graph.
He was married to Norbert Wiener's sister Constance. *Wik

1972 Richard Courant (8 Jan 1888, 27 Jan 1972) German-American mathematician who, upon joining the faculty of New York University in 1934, began to build the nucleus of a small research group based on the Göttingen model he had experienced as a student of David Hilbert in Germany. Courant's published papers were in variational problems, finite difference methods, minimal surfaces, and partial differential equations. He encouraged the publication of mathematical texts and high quality monographs, such as Methods of Mathematical Physics by Courant and Hilbert. His leadership was commemorated in 1964 when the institute he founded was named the Courant Institute of Mathematical Sciences at New York University *TIS He died at age 84 of a stroke in New Rochelle, NY. Today it is named after him: The Courant Institute. *VFR

1995 Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) was an American mathematician.
In 1941, Robinson married his former student Julia Bowman. She became his Berkeley colleague and the first woman president of the American Mathematical Society.
He worked on mathematical logic, set theory, geometry, number theory, and combinatorics. Robinson (1937) set out a simpler and more conventional version of John Von Neumann's 1923 axiomatic set theory. Soon after Alfred Tarski joined Berkeley's mathematics department in 1942, Robinson began to do major work on the foundations of mathematics, building on Tarski's concept of "essential undecidability," by proving a number of mathematical theories undecidable. Robinson (1950) proved that an essentially undecidable theory need not have an infinite number of axioms by coming up with a counterexample Robinson's work on undecidability culminated in his coauthoring Tarski et al. (1953), which established, among other things, the undecidability of group theory, lattice theory, abstract projective geometry, and closure algebras.
Robinson worked in number theory, even employing very early computers to obtain results. For example, he coded the Lucas-Lehmer primality test to determine whether 2n − 1 was prime for all prime n less than 2304 on a SWAC. In 1952, he showed that these Mersenne numbers were all composite except for 17 values of n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281. He discovered the last 5 of these Mersenne primes, the largest ones known at the time.
Robinson wrote several papers on tilings of the plane, in particular a clear and remarkable 1971 paper "Undecidability and nonperiodicity for tilings of the plane" simplifying what had been a tangled theory.*Wik

2001 Robert Alexander Rankin (27 Oct 1915 in Garlieston, Wigtownshire, Scotland - 27 Jan 2001 in Glasgow, Scotland) At Cambridge Rankin began to undertake research in number theory on the difference between two successive primes which won him the Rayleigh Prize in 1939. He published four papers on The difference between consecutive prime numbers between this time and 1950. in 1939 he began to work with G H Hardy on the results of Ramanujan. Although Ramanujan had died nearly twenty years earlier, he had left a number of unpublished notebooks filled with theorems that Hardy and other mathematicians continued to study.
After an interruption during WWII, Rankin wrote over 100 research papers, mostly on the theory of numbers and the theory of functions. He wrote The modular group and its subgroups published in 1969 and Modular forms and functions which was published in 1977. The former of these is described by Rankin himself in the Preface, "This short course of lectures was given at the Ramanujan Institute for Advanced Study in Mathematics, in the University of Madras, in September 1968. The object of the course was to study the modular group and some of its subgroups, with help of algebraic rather than analytic or topological methods." He made a number of remarkable contributions to the theory of numbers have played a major part in the modern development of the topic. *SAU

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 26

2012-01-26T01:10:00.000Z

As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

~Arthur Cayley

The 26th day of the year; 26 is the smallest non-palindrome with a palindromic square. (676). (What's the next smallest?)

EVENTS

1126 Adelard of Bath translates Muhammad ibn Mˆusˆa al-Khwˆarizmˆı’s Astronomical Tables into Latin. *VFR

1678 Phillipe de LaHire nominated to the Academy of Sciences. This geometer was so adept at synthetic techniques that he, together with Rolle, was hostile to the inﬁnitesimal calculus when discussions of its value were raised in the Academy beginning in 1701*VFR

In 1697, Isaac Newton received and solved Jean Bernoulli's brachistochrone problem. The swiss mathematician Bernouilli had challenged his colleagues to solve it within six months. Newton not only solved the problem before going to bed that same night, but in doing so, invented a new branch of mathematics called the calculus of variations. He had resolved the issue of specifying the curve connecting two points displayed from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time. Newton, age 55, sent the solution to be published, at his request, anonymously. But the brilliant originality of the work betrayed his identity, for when Bernoulli saw the solution he commented, "We recognize the lion by his claw." *TIS

1738 Frederick the Great wrote Voltaire of his plan of study, “to take up again philosophy, history, poetry, music. As for mathematics, I confess to you that I dislike it; it dries up the mind. We Germans have it only too dry; it is a sterile ﬁeld which must be cultivated and watered constantly, that it may produce”. Nonetheless, Frederick supported Euler at the Berlin Academy from 1741 to 1766.*VFR

1750 Danial Bernoulli writes to Euler to complain that d'Alembert's work on the wind had no experimental basis and ..his abstract speculations brought more shame than honor to mathematics. "After one has read his paper, one knows no more about the wind than he did before." * Thomas L. Hankins, Jean d'Alembert: science and the Englightenment; pg 3

1784 The idea that Benjamin Franklin preferred the turkey as the national bird of the United States comes from a letter he wrote to his daughter Sarah Bache on January 26, 1784, criticizing the choice of the Bald Eagle as the national bird and suggesting that a turkey would have made a better alternative. This letter to Franklin's daughter was written after Congress had spent six years choosing the eagle as the emblem of the newly formed country. Franklin's disapproval of the choice of the Bald Eagle appears evident, but may have been made with mock indignation, since it is not apparent that he ever officially advocated the use of the turkey as a national emblem. *Wik

1802 Congress passed an act calling for a library to be established within the U. S. Capitol. The collection was the forerunner of the Library of Congress. *VFR

1952 EDVAC demonstrated. John Von Neumann was instrumental in designing this machine, which used the stored program concept. *VFR

1963 France issued a stamp picturing the bathyscaph “Archimede.” Do you know why this name is appropriate? [Scott #1052] *VFR (image at top) On 15 July 1962, Archimede descended to 31,350 feet (9,560 m) into the Kurile-Kamchatcha Trench, making it the second deepest dive ever, at that point in time.

1984 The Fredkin Foundation announced it will award a prize of $100,000 for the ﬁrst major mathematical discovery made by a computer. [News release at the Louisville AMS meeting] *VFR (Fredkin Foundation was established by Edward Fredkin, an artificial-intelligence expert at MIT. They offered another large prize for the first computer program which could defeat a Chess Grand Master)

1997 Electronic vs. Paper Books in S.F. Library
The New York Times chronicles the debate between electronic and paper books in an article about the new San Francisco public library. Critics complained that the library sacrificed too much book space for computer terminals and too many books for online information, lamenting as well the end of the traditional card catalogue that has marked a move to the information age for many libraries.*CHM (Twenty-five years later such discussions continue as Kindle and on-line texts start to replace traditional paper.)

BIRTHS

1862 Eliakim Hastings Moore (January 26, 1862 – December 30, 1932) was an American mathematician. He discovered mathematics through a summer job at the Cincinnati Observatory while in high school. When the University of Chicago opened its doors in 1892, Moore was the first head of its mathematics department, a position he retained until his death in 1931. His first two colleagues were Bolza and Maschke. The resulting department was the second research-oriented mathematics department in American history, after Johns Hopkins University.
Moore first worked in abstract algebra, proving in 1893 the classification of the structure of finite fields (also called Galois fields). Around 1900, he began working on the foundations of geometry. He reformulated Hilbert's axioms for geometry so that points were the only primitive notion, thus turning Hilbert's primitive lines and planes into defined notions. In 1902, he further showed that one of Hilbert's axioms for geometry was redundant. Independently, the twenty year old R.L. Moore (no relation) also proved this, but in a more elegant fashion than E. H. Moore used. When E. H. Moore heard of the feat, he arranged for a scholarship that would allow R.L. Moore to study for a doctorate at Chicago. E.H. Moore's work on axiom systems is considered one of the starting points for metamathematics and model theory. After 1906, he turned to the foundations of analysis. The concept of closure operator first appeared in his 1910 Introduction to a form of general analysis. He also wrote on algebraic geometry, number theory, and integral equations.
At Chicago, Moore supervised 31 doctoral dissertations, including those of George Birkhoff, Leonard Dickson, Robert Lee Moore (no relation), and Oswald Veblen. Birkhoff and Veblen went on to forge and lead the first-rate departments at Harvard and Princeton, respectively. Dickson became the first great American algebraist and number theorist. Robert Moore founded American topology. According to the Mathematics Genealogy Project, as of January 2011, E. H. Moore had over 14,900 known "descendants."
Moore convinced the New York Mathematical Society to change its name to the American Mathematical Society, whose Chicago branch he led. He presided over the AMS, 1901–02, and edited the Transactions of the American Mathematical Society, 1899–1907. He was elected to the National Academy of Sciences, the American Academy of Arts and Sciences, and the American Philosophical Society.
The American Mathematical Society established a prize in his honor in 2002. *Wik

1911 Polykarp Kusch (26 Jan 1911; 20 Mar 1993) German-American physicist who shared the Nobel Prize for Physics in 1955 for his accurate determination that the magnetic moment of the electron is greater than its theoretical value. This he deduced from researching the hyperfine structure of the energy levels in certain elements, and in 1947 found a discrepancy of about 0.1% between the observed value and that predicted by theory. Although minute, this anomaly was of great significance and led to revised theories about the interactions of electrons with electromagnetic radiation, now known as quantum electrodynamics. (He shared the prize with Willis E. Lamb, Jr. who performed independent but related experiments at Columbia University on the hyperfine structure of the hydrogen atom.)*TIS

1945 John Henry Coates, FRS (born 26 January 1945) is a mathematician who holds (since 1986) the position of Sadleirian Professor of Pure Mathematics at the University of Cambridge in the United Kingdom. He was elected a fellow of the Royal Society of London in 1985, and was President of the London Mathematical Society from 1988 to 1990. The latter organisation awarded him the Senior Whitehead Prize in 1997, for "his fundamental research in number theory and for his many contributions to mathematical life both in the UK and internationally".
Since 1986 Coates has worked in the Department of Pure Mathematics and Mathematical Statistics (DPMMS) of the University of Cambridge. In the last ten years he has focused on the study of various aspects of non-commutative Iwasawa theory, for instance, the study of the arithmetic of elliptic curves in nonabelian infinite extensions.*Wik

DEATHS

1630 Henry Briggs (Feb ? 1561, 26 Jan 1630) English mathematician who constructed the decimal-based common (Briggsian) logarithms that use base 10, and popularized them in Europe. John Napier had already introduced “natural” logarithms (1614) that use the base e (2.71...) [I think this is an error. Napier's log tables were not base e, nor any other particular base as they produced smaller log values for larger numbers, with log(10⁷=0.]. Briggs visited Napier in 1616, and they agreed on the merit of using base 10. By 1624, Briggs had calculated logarithm tables to 14 decimal places, published in Arithmetica Logarithmica. These tables vastly simplified the task of mathematicians, astronomers and other scientists making otherwise long and tedious calculations. Briggs was professor of astronomy at Oxford from 1619. He is also credited with developing the modern method of long division. Briggs was strongly opposed to astrology, at a time when it was otherwise widely accepted by many scholars, including Napier. *TIS A story is told that when Briggs first journeyed to Scotland to meet Napier, after he was shown into the room they stood in silence for almost a quarter of an hour, "each beholding the other with admiration".

1697 1640 – Georg Mohr, (April 1, 1640 – January 26, 1697) (also Jorgen)Danish mathematician His only original contribution to geometry was the proof that any geometric construction which can be done with compass and straightedge can also be done with compasses alone, a result now known as the ohr–Mascheroni theorem. He published his proof in the book Euclides Danicus, Amsterdam, 1672.

1721 Pierre-Daniel Huet (8 Feb 1630, 26 Jan 1721) French scholar, antiquary, scientist, and bishop whose incisive skepticism, particularly as embodied in his cogent attacks on René Descartes, greatly influenced contemporary philosophers. Huet wrote a number of philosophical works that asserted the fallibility of human reason in addition to scientific work in the fields of astronomy, anatomy, and mathematics. *TIS

1895 Arthur Cayley (16 Aug 1821, 26 Jan 1895)English mathematician who played a leading role in founding the modern British school of pure mathematics. He trained first as a lawyer, and from 1849, spent 14 years at the bar, during which time he maintained an interest in mathematics and published about 250 mathematical papers. In 1863, Cayley followed his passion and commenced a new career as professor of Pure Mathematics at Cambridge and during his tenure published 900 papers and notes covering nearly every aspect of modern mathematics. The legacy of his work in n-dimensional geometry was later applied in physics to the study of the space-time continuum. His work on matrices served as a foundation for quantum mechanics developed by Werner Heisenberg in 1925.*TIS Cayley died, at age 74, after a long illness that he bore with courage and resignation. He continued his creative activity up to the week of his death. *VFR

1929 Constantin Marie Le Paige (9 March 1852 in Liège, Belgium - 26 Jan 1929 in Liège, Belgium) worked on the theory of algebraic forms, a topic whose study was initiated by Boole in 1841 and then developed by Cayley, Sylvester, Hermite, Clebsch and Aronhold. In particular Le Paige studied the geometry of algebraic curves and surfaces, building on this earlier work. He is best known for his construction of a cubic surface given by 19 points.
Le Paige studied the generation of plane cubic and quartic curves, developing further Chasles's work on plane algebraic curves and Steiner's results on the intersection of two projective pencils.
The history of mathematics was another topic which interested Le Paige. He published Sluze's correspondence with Pascal, Huygens, Oldenburg and Wallis. *SAU

1942 Felix Hausdorff (8 Nov 1868 in Breslau, Germany (now Wrocław, Poland)
- 26 Jan 1942 in Bonn, Germany) worked in topology creating a theory of topological and metric spaces. He also worked in set theory and introduced the concept of a partially ordered set.
As a Jew his position became more and more difficult. In 1941 he was scheduled to go to an internment camp but managed to avoid being sent.
Bonn University requested that the Hausdorffs be allowed to remain in their home and this was granted. By October 1941 they were forced to wear the "yellow star" and around the end of the year they were informed that they would be sent to Cologne.
They were not sent to Cologne but in January 1942 they were informed that they were to be interned in Endenich. Together with his wife and his wife's sister, he committed suicide on 26 January. He wrote to a friend on Sunday 25 January:

Dear Friend Wollstein
By the time you receive these lines, we three will have solved the problem in another way - in the way which you have continually attempted to dissuade us. ...
What has been done against the Jews in recent months arouses well-founded anxiety that we will no longer be allowed to experience a bearable situation. ...
Forgive us, that we still cause you trouble beyond death; I am convinced that you will do what you are able to do (and which perhaps is not very much). Forgive us also our desertion! We wish you and all our friends will experience better times
Yours faithfully
Felix Hausdorff

On the night of Sunday 25 January all three took barbiturates. Both Hausdorff and his wife Charlotte were dead by the morning of the 26 January. Edith, Charlotte's sister, survived for a few days in a coma before dying. *SAU

1952 James Ireland Craig (24 Feb 1868 in Buckhaven, Fife, Scotland - 26 Jan 1952 in Cairo, Egypt) graduated from Edinburgh and Cambridge. He taught at Eton and Winchester and then went to work on the Nile Survey for the Egyptian government. He made some significant inventions in map projections. He was killed when a mob attacked the Turf Club in Cairo.*SAU

2007 Gregory Maxwell Kelly (5 June 1930 in Bondi, New South Wales, Australia - 26 Jan 2007 in Sydney, Australia) founded the thriving Australian school of category theory. With Samuel Eilenberg he formalized and developed the notion of an enriched category based on intuitions then in the air about making the homsets of a category just as abstract as the objects themselves. He subsequently developed the notion in considerably more detail in his 1981 monograph Basic Concepts of Enriched Category Theory. The explicitly foundational role of the category Set in his treatment is noteworthy in view of the folk intuition that enriched categories liberate category theory from the last vestiges of Set as the codomain of the ordinary external hom-functor.
In 1967 Kelly was appointed Professor of Pure Mathematics at the University of New South Wales. In 1972 he was elected a Fellow of the Australian Academy of Science. He returned to the University of Sydney in 1973, serving as Professor of Mathematics until his retirement in 1994. In 2001 he was awarded the Australian government's Centenary Medal. He continued to participate in the department as Professorial Fellow and Professor Emeritus until his death at age 76.
Kelly worked on many other aspects of category theory besides enriched categories, both individually and in a number of fruitful collaborations. His Ph.D. student Ross Street is himself a noted category theorist and early contributor to the Australian category theory school.*Wik

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 25

2012-01-25T00:10:00.000Z

*Wik

Only a moment to cut off that head and a hundred years may not give us another like it.

~Count Joseph-Louis de Lagrange,
a Comment to Delambre on Lavoisier's execution, 8 May 1794.

The 25th day of the year; 25 is the smallest square that can be written as a sum of 2 squares. (What's the next?)

EVENTS

1635 Cardinal Richelieu widens the scope of the Paris literary union (established 1625) to the Academie francaise. *VFR

In 1798, Benjamin Thompson (Count Rumford) presented a paper to the Royal Society, Enquiry concerning the Source of Heat which is excited by Friction, in which he presented the idea that heat represents a form of motion, as opposed to the prevailing idea of being a fluid. He had come to this conclusion from observation that the boring of cannon barrels produces heat from friction. *TIS

In 1839, Michael Faraday publicly announced for the first time the existence of photography as the subject of his Friday Evening Discourse at the Royal Institution. Faraday announced the "Daguerreotype" and Fox Talbot's "photogenic drawings" at the same time, and invited the audience to inspect the specimens displayed in the library. Fox Talbot returned the following week to read a more detailed paper describing his process. Faraday had been instrumental in founding and sustaining (1826) the Friday Evening Discourse series of lectures which continue to this day.*TIS

1931 Max Planck, Quoted in The Observer on this date, "I regard consciousness as fundamental. I regard matter as derivative from consciousness. We cannot get behind consciousness. Everything that we talk about, everything that we regard as existing, postulates consciousness. "

In 1955, Columbia University scientists developed an atomic clock accurate to within one second in 300 years. *TIS

1962 Professor Mina Reese, dean of graduate studies at CUNY, is named recipient of the MAA’s ﬁrst Award for Distinguished Service to Mathematics. This award was made "for outstanding service to mathematics, other than mathematical research" and for "contributions [that] influence significantly the field of mathematics or mathematical education on a national scale." *Agnes Scott College Web page

1979 Robot violates Asimov's First Law, "A robot may not injure a human being or, through inaction, allow a human being to come to harm." Robert Williams of Michigan was the first human to be killed by a robot. He was 25 years old. The accident at the Ford Motor Company resulted in a $10 million dollar lawsuit. The jury deliberated for two-and-a-half hours before announcing the decision against Unit Handling Systems, a division of Litton Industries. It ordered the manufacturer of the one-ton robot that killed Williams to pay his family $10 million. The robot was designed to retrieve parts from storage, but its work was deemed too slow. Williams was retrieving a part from a storage bin when the robot's arm hit him in the head, killing him instantly. In the suit, the family claimed the robot had no safety mechanisms, lacking even a warning noise to alert workers that it was nearby. *CHM

BIRTHS

1627 Robert Boyle (25 Jan 1627; 30 Dec 1691) Irish-English chemist and natural philosopher noted for his pioneering experiments on the properties of gases and his espousal of a corpuscular view of matter that was a forerunner of the modern theory of chemical elements. He was a founding member of the Royal Society of London. From 1656-68, he resided at Oxford where Robert Hooke, who helped him to construct the air pump. With this invention, Boyle demonstrated the physical characteristics of air and the necessity of air for combustion, respiration, and the transmission of sound, published in New Experiments Physio-Mechanical, Touching the Spring of the Air and its Effects (1660). In 1661, he reported to the Royal Society on the relationship of the volume of gases and pressure (Boyle's Law)*TIS

1736 Count Joseph-Louis de Lagrange (25 Jan 1736; 10 Apr 1813)Italian-French mathematician who made great contributions to the theory of numbers and to analytic and celestial mechanics. His most important book is Mécanique analytique (1788; "Analytic Mechanics"), the textbook on which all later work in this field is based.*TIS Lagrange died in his 76th year. He excelled in all fields of analysis and number theory and analytical and celestial mechanics. *SAU

1774 George Dollond (25 Jan 1774; 13 May 1852) British optician who invented a number of precision instruments used in astronomy, geodesy, and navigation. *TIS

1812 William Shanks (25 Jan 1812; June ? ,1882) English mathematician who spent numerous years manually calculating the value of pi. Shanks kept a boarding school at Houghton-le-Spring in a coal mining area near Durham. His calculation of pi reached 707 places by 1873, a feat unchallenged until the use of electronic computers. He used the formula:
pi/4 = 4 tan^-1(1/5) - tan^-1(1/239).
In 1944, Ferguson's new computation of pi showed Shanks had made a mistake in the 528th decimal place, invalidating the digits calculated beyond. Shanks had omitted two terms which caused his error. By the end of the twentieth century, computers could easily extend the results to over 2 billion places.*TIS

1843 Karl Hermann Amandus Schwarz (25 Jan 1843 in Hermsdorf, Silesia (now Poland)
- 30 Nov 1921 in Berlin, Germany) Schwarz worked on the conformal mapping of polyhedral surfaces onto the spherical surface and on a problem of the calculus of variation, namely surfaces of least area. In 1870 he produced work related to the Riemann mapping theorem. Although Riemann had given a proof of the theorem that any simply connected region of the plane can be mapped conformally onto a disc, his proof involved using the Dirichlet problem. Weierstrass had shown that Dirichlet's solution to this was not rigorous, see for details. Schwarz's gave a method to conformally map polygonal regions to the circle. Then, by approximating an arbitrary simply connected region by polygons he was able to give a rigorous proof of the Riemann mapping theorem. Schwarz also gave the alternating method for solving the Dirichlet problem which soon became a standard technique.
His most important work is a Festschrift for Weierstrass's 70th birthday. Schwarz answered the question of whether a given minimal surface really yields a minimal area. An idea from this work, in which he constructed a function using successive approximations, led Émile Picard to his existence proof for solutions of differential equations. It also contains the inequality for integrals now known as the 'Schwarz inequality', *SAU He was married to Marie Kummer, a daughter of the mathematician Ernst Eduard Kummer *Wik

1855 Gyula Vályi (5 January 1855 - 13 October 1913) was a Hungarian mathematician and theoretical physicist, a member of the Hungarian Academy of Sciences, known for his work on mathematical analysis, geometry, and number theory.*Wik

1870 Niels Fabian Helge von Koch (Stockholm, January 25, 1870 – ibidem, March 11, 1924) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake(at top), one of the earliest fractal curves to be described. Von Koch wrote several papers on number theory. One of his results was a 1901 theorem proving that the Riemann hypothesis is equivalent to a stronger form of the prime number theorem. He described the Koch curve in a 1904 paper entitled "On a continuous curve without tangents constructible from elementary geometry" (original French title: "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire"). *Wik

1917 Ilya Prigogine (25 Jan 1917; 28 May 2003) Russian-born Belgian physical chemist who received the Nobel Prize for Chemistry in 1977 for contributions to nonequilibrium thermodynamics, or how life could continue indefinitely in apparent defiance of the classical laws of physics. The main theme of Prigogine's work was the search for a better understanding of the role of time in the physical sciences and in biology. He attempted to reconcile a tendency in nature for disorder to increase (for statues to crumble or ice cubes to melt, as described in the second law of thermodynamics) with so-called "self-organisation", a countervailing tendency to create order from disorder (as seen in, for example, the formation of the complex proteins in a living creature from a mixture of simple molecules). *TIS

1924 Jack Carl Kiefer;(25 Jan 1924 in Cincinnati, Ohio, USA - 10 Aug 1981 in Berkeley, California, USA) Kiefer's main research area was the optimal design of experiments, and about half his 100 publications dealt with that topic. However he also wrote papers on a whole variety of topics in mathematical statistics including decision theory, inventory theory, stochastic approximation, queuing theory, nonparametric inference, estimation, sequential analysis, and conditional inference. His first paper Almost subminimax and biased minimax procedures written jointly with his fellow graduate student at Columbia, Peter Frank, was published in 1951. A paper Sequential minimax search for a maximum which Kiefer published in the Proceedings of the American Mathematical Society in 1953 was based on his master's thesis. The method of search proposed in the paper, namely the Fibonacci Search, became a widely used tool. *SAU

DEATHS

1894 Emil Weyr (1 July 1848 in Prague, Bohemia (now Czech Republic) - 25 Jan 1894 in Vienna, Austria) His father Frantisek Weyr, was a professor of mathematics at a realschule (secondary school) in Prague from 1855. Emil was four years older than his brother Eduard Weyr who also became a famous mathematician. Emil attended the realschule in Prague where his father taught, then studied at the Prague Polytechnic from 1865 to 1868 where he was taught geometry by Vilém Fiedler.
He studied in Italy with Cremona and Casorati during the academic year 1870-71 returning to Prague where he continued to teach. In 1872 he was elected to be Head of the Union of Czech Mathematicians and Physicists. In 1875 he was appointed as professor of mathematics at the University of Vienna. He, together with his brother Eduard Weyr, were the main members of the Austrian geometric school. They were interested in descriptive geometry, then in projective geometry and their interests turned towards algebraic and synthetic methods in geometry. Among many works Emil Weyr published were Die Elemente der projectivischen Geometrie and Über die Geometrie der alten Aegypter.
Emil Weyr led the geometry school in Vienna throughout the 1880's up until his death. Together with Gustav von Escherich, Emil Weyr founded the important mathematical journal Monatshefte fuer Mathematik und Physik in 1890. The first volumes of the journal contain papers written by his brother Eduard. In 1891 Emil Weyr became one of the first 19 founder members of the Royal Czech Academy of Sciences. *SAU

1935 Alfred Loewy (20 June 1873, 25 Jan 1935) was a German mathematician who worked on representation theory. Loewy rings, Loewy length, and Loewy series are named after him.*Wik

1960 Beno Gutenberg (4 Jun 1889, 25 Jan 1960) American seismologist noted for his analyses of earthquake waves and the information they furnish about the physical properties of the Earth's interior. With Charles Richter, he developed a method of determining the intensity of earthquakes. Calculating the energy released by present-day shallow earthquakes, they showed that three-quarters of that energy occurs in the Circum-Pacific belt. *TIS

1973 Wilhelm Ljunggren (7 Oct 1905 in Oslo, Norway - 25 Jan 1973 in Oslo, Norway) was a Norwegian mathematician, specializing in number theory.
and in particular Diophantine equations. He showed that Ljunggren's equation,

X² = 2Y⁴ − 1

has only the two integer solutions (1,1) and (239,13)
Ljunggren also posed the question of finding the integer solutions to the Ramanujan–Nagell equation

2ⁿ − 7 = x²

(or equivalently, of finding triangular Mersenne numbers) in 1943, independently of Srinivasa Ramanujan who had asked the same question in 1913. Ljunggren's publications are collected in a book edited by Paulo Ribenboim.*Wik

1994 Stephen Cole Kleene (5 Jan 1909, 25 Jan 1994)American mathematician and logician whose research was on the theory of algorithms and recursive functions. He developed the field of recursion theory with Church, Gödel, Turing and others. He contributed to mathematical Intuitionism which had been founded by Brouwer. His work on recursion theory helped to provide the foundations of theoretical computer science. By providing methods of determining which problems are soluble, Kleene's work led to the study of which functions can be computed.*TIS

1995 Albert William Tucker (28 November 1905 – 25 January 1995) was a Canadian-born American mathematician who made important contributions in topology, game theory, and non-linear programming.In the 1960s, he was heavily involved in mathematics education, as chair of the AP Calculus committee for the College Board (1960–1963), through work with the Committee on the Undergraduate Program in Mathematics (CUPM) of the MAA (he was president of the MAA in 1961–1962), and through many NSF summer workshops for high school and college teachers.
In the early 1980s, Tucker recruited Princeton history professor Charles Gillispie to help him set up an oral history project to preserve stories about the Princeton mathematical community in the 1930s. With funding from the Sloan Foundation, this project later expanded its scope. Among those who shared their memories of such figures as Einstein, von Neumann, and Gödel were computer pioneer Herman Goldstine and Nobel laureates John Bardeen and Eugene Wigner.
Albert Tucker noticed the leadership ability and talent of a young mathematics graduate student named John G. Kemeny, whose hiring Tucker suggested to Dartmouth College. Following Tucker's advice, Dartmouth recruited Kemeny, who became Chair of the Mathematics Department and later College President. Years later, Darthmouth College recognized Albert Tucker with an honorary degree. Tucker died in Highstown, N.J. in 1995 at age 89. *Wik

2000 Herta Taussig Freitag (December 6, 1908 - January 25, 2000) Herta obtained a job at a private high school, the Greer School, in upstate New York. There she met Arthur H. Freitag and they were married in 1950. Herta started teaching at Hollins College (now University) in Roanoke, VA in 1948. She received a Ph.D. degree from Columbia University in 1953 and the title of her dissertation was "The Use of the History of Mathematics in its Teaching and Learning on the Secondary Level."
During Herta's years at Hollins she was a frequent guest speaker at local schools and gave lectures at both Virginia and North Carolina Governor's Schools. She published numerous articles in The Mathematics Teacher, The Arithmetic Teacher, and The Mathematics Magazine. At the request of the National Council of Teachers of Mathematics, Professor Freitag wrote the monograph, The Number Story, with her husband. In 1962 she was the first woman to be President of the Maryland-District of Columbia-Virginia Section of the Mathematical Association of America (MAA). Professor Freitag received the Hollins' Algernon Sydney Sullivan Award, which is awarded for recognition of "extraordinary humane and scholarly achievement." She officially retired from Hollins in 1971 to spend time with her husband, who was ill. After his death in 1978, Hollins welcomed her back to the classroom as a leave replacement in 1979-1980 and as a teacher in the Master of Arts in Liberal Studies (MALS) program for several years. Professor Herta Freitag was the first faculty member to receive the Hollins Medal (1979) and the first recipient of the Virginia College Mathematics Teacher of the Year award (1980).
Professor Freitag was very proud of her perfect attendance at the International Conferences of the Fibonacci Association. Most of her work with Fibonacci numbers occurred after she retired, which demonstrates the fallacy of a commonly held belief that mathematicians complete their best work before the age of 40. Professor Freitag published more than thirty articles in the Fibonacci Quarterly after 1985. The November 1996 issue of the Fibonacci Quarterly was dedicated to "Herta Taussig Freitag as she enters her 89th year, in recognition of her years of outstanding service and achievement in the mathematics community through excellence in teaching, problem solving, lecturing and research." This award was given to celebrate her 89th birthday, since 89 is a Fibonacci number. *Biographies of Women Mathematicians, Agnes Scott College web site

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

Flipping Pennies

2012-01-24T19:55:00.001Z

The Jan 1, 2012 issue of The College Mathematics Journal featured articles inspired by the late-great Martin Gardner. One by Ian Stewart begins with the Three Penny Puzzle invented by Gardner and Karl Fulves:

Gardner’s three-penny trick:
The trick is performed by a blindfolded magician. A volunteer places three pennies
in a row, and chooses at will whether each coin shows heads or tails. However, both heads and tails must appear, otherwise the trick ends before it begins. The magician announces that even though she cannot see the coins, she will give instructions to turn coins over so that all three coins show the same face, heads or tails.
The instructions are:
1. Flip the left-hand coin.
2. Flip the middle coin.
3. Flip the left-hand coin.
After steps 1 and 2 the magician asks whether all three coins show the same face,
and if the answer is ‘yes’, the trick stops, otherwise the magician requests the third flip.
Although it is plausible that enough flips will eventually
get all coins the same way up, it is a little surprising that at most three flips are needed.

Not being very good at card tricks and such, I would sometimes perform this trick in study hall or odd class moments to amuse my students, and then challenge them to duplicate the trick. I avoided doing it more than once in order not to have them catch on to the fact that the same pattern always works (why children). In all the many times I did it, and sometimes had students discover the logic, I don't think I ever asked them if they could do the same with four pennies, or five, or n. That is, for n Pennies, what is the minimal number of blind-flips f(n) to get them all alike, and what is the sequence of flips.

I assume that the questions from the solver can only be "are all coins alike now?"

On This Day in Math - Jan 24

2012-01-24T00:10:00.001Z

* The art of photography

A mathematician's reputation rests on the number of bad proofs he has given.
~Abram S Besicovitch

The 24th day of the year; 24! (6.2044840173323943936 10²³)is almost equal to Avogadro's Number, (6.022141×10^23). Also 1² + 2² +...+ 24² = 70² the only pyramidal number that is a square.

EVENTS

In 1544, a solar eclipse was viewed at Louvain, which was later depicted in the first published book illustration of the camera obscura in use. Dutch mathematician and astronomer Reinerus Gemma-Frisius viewed a solar eclipse using a hole in one wall of a pavillion to project the sun's image upside down onto the opposite wall. He published the first illustrationof a camera obscura, depicting his method of observation of the eclipse in De Radio Astronomica et Geometrica (1545). Several astronomers made use of such a device in the early part of the 16th century. Both Johannes Kepler and Christopher Scheiner used a camera obscura to study the activity of sunspots. The technique was known to Aristotle (Problems, ca 330 BC). *TIS

In 1925, a motion picture of a solar eclipse was taken by the U.S. Navy from the dirigible Los Angeles. The craft was at an elevation of about 4,500-ft and positioned about 19 miles east of Montauk Point, Long Island, NY. This give a view of a total eclipse of the sun that lasted just over 2-min. Four astronomical cameras and a spectrograph were used as well as two moving picture cameras. This was the first time in the U.S. that a dirigible had been used as a platform for observation of a total eclipse of the sun. The first U.S. attempt to photograph one from an aircraft 10 Sep 1923 was unsuccessful due to cloudy conditions, but on 28 Apr 1930, a flight over California sponsored by the U.S. Naval Observatory recorded a total solar eclipse. *TIS

1948 IBM dedicates the Selective Sequence Electronic Calculator (SSEC). Later the SSEC was put on public display near the company's Manhattan headquarters so passers-by could watch its operational speed. Before its decommissioning in 1952, the SSEC produced the moon-position tables used for plotting the course of the 1969 Apollo flight to the moon. *CHM

BIRTHS

1679 Christian Freiherr von Wolff (24 Jan 1679; 9 Apr 1754) (baron) German philosopher, mathematician, and scientist who worked in many subjects but who is best known as the German spokesman of the Enlightenment, the 18th-century philosophical movement characterized by Rationalism. Wolff's first interest was mathematics. Though he made no original contribution to the discipline, he was important in the teaching of mathematics and instrumental in introducing the new mathematics into German universities. Later, as a philosopher, he developed the most impressive coherent system of his century. Thoroughly eclectic, influenced by Leibniz and Descartes, yet he continued fundamental themes of Aristotle. His system was important in making the discoveries of modern science known in Germany.
*TIS

1798 Karl George Christian von Staudt (24 Jan 1798; 1 Jun 1867)German mathematician who developed the first complete theory of imaginary points, lines, and planes in projective geometry. His early work was on determining the orbit of a comet and, based on this work, he received his doctorate. He showed how to construct a regular inscribed polygon of 17 sides using only compasses. He turned to projective geometry and Bernoulli numbers (discovered by Jacob Bernoulli). An important work on projective geometry, Geometrie der Lage was published in 1847. It was the first work to completely free projective geometry from any metrical basis. He also gave a geometric solution to quadratic equations. *TIS (*Wik gives birthdate as Jan 23)

1863 August Adler (24 Jan 1863 in Opava, Austrian Silesia (now Czech Republic)-17 Oct 1923 in Vienna, Austria) In 1906 Adler applied the theory of inversion to solve Mascheroni construction problems in his book Theorie der geometrischen Konstruktionen published in Leipzig. In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.
Since he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses. However Adler did not simplify Mascheroni proof. On the contrary, his new methods were not as elegant, either in simplicity or length, as the original proof by Mascheroni.
This 1906 publication was not the first by Adler studying this problem. He had published a paper on the theory of Mascheroni's constructions in 1890, another on the theory of geometrical constructions in 1895, and one on the theory of drawing instruments in 1902. As well as his interest in descriptive geometry, Adler was also interested in mathematical education, particularly in teaching mathematics in secondary schools. His publications on this topic began around 1901 and by the end of his career he was publishing more on mathematical education than on geometry. Most of his papers on mathematical education were directed towards teaching geometry in schools, but in 1907 he wrote on modern methods in mathematical instruction in Austrian middle schools. He produced various teaching materials for teaching geometry in the sixth-form in Austrian schools such as an exercise book which he published in 1908. *SAU

1872 Morris William Travers (24 Jan 1872; 25 Aug 1961)
English chemist who, while working with Sir Willam Ramsay in London, discovered the element krypton (30 May 1898). The name derives from the Greek word for "hidden." It was a fraction separated from liquified air, which when placed in a Plücker tube connected to an induction coil yielded a spectrum with a bright yellow line with a greener tint than the known helium line and a brilliant green line that corresponded to nothing seen before.*TIS

1882 Harold Delos Babcock (24 Jan 1882(Edgerton,Wisconsin) - 8 Apr 1968) American astronomer who with his son, Horace, invented the solar magnetograph (1951), for detailed observation of the Sun's magnetic field. With their magnetograph the Babcocks measured the distribution of magnetic fields over the solar surface to unprecedented precision and discovered magnetically variable stars. In 1959 Harold Babcock announced that the Sun reverses its magnetic polarity periodically. Babcock's precise laboratory studies of atomic spectra allowed others to identify the first "forbidden" lines in the laboratory and to discover the rare isotopes of oxygen. With C.E. St. John he greatly improved the precision of the wavelengths of some 22,000 lines in the solar spectrum, referring them to newly-determined standards.*TIS

1891 Abram Samoilovitch Besicovitch (24 Jan 1891 in Berdyansk, Russia -2 Nov 1970 in Cambridge, Cambridgeshire, England) Besicovitch left Petrograd for Copenhagen in 1924 and there worked with Harald Bohr. He had been awarded a Rockefeller Fellowship but his applications for permission to work abroad had been refused. He escaped across the border with a colleague J D Tamarkin under the cover of darkness. He managed to reach Copenhagen where he was supported financially for a year with the Rockefeller Fellowship. His interest in almost periodic functions came about through this year spent working with Harald Bohr. After he visited Oxford in 1925 Hardy, who quickly saw the mathematical genius in Besicovitch, found a post for him in Liverpool. At Cambridge Besicovitch lectured on analysis in most years but he also gave an advanced course on a topic which was directly connected with his research interests such as almost periodic functions, Hausdorff measure, or the geometry of plane sets. Besicovitch was famous for his work on almost periodic functions, his interest in which, as we mentioned above, came from his time in Copenhagen with Harald Bohr. In 1932 he wrote an influential text Almost periodic functions covering his work in this area.
One of the achievements, with which he will always be associated, was his solution of the Kakeya problem on minimising areas. The problem had been posed in 1917 by a Japanese mathematician S Kakeya and asked what was the smallest area in which a line segment of unit length could be rotated through 2p. Besicovitch proved in 1925 that given any e, an area of less than e could be found in which the rotation was possible. The figures that resulted from Besicovitch's construction were highly complicated, unbounded figures.
Other areas on which Besicovitch worked included geometric measure theory, Hausdorff measure, real function theory, and complex function theory. In addition to this work on deep mathematical theories, Besicovitch loved problems, particularly those which could be stated in elementary terms but which proved resistant to attack. Often he showed that the "obvious solution" to certain problems is false. An example of such a problem is the Lion and the Man problem posed by Richard Rado in the mid 1920s. *SAU

1902 Oskar Morgenstern (24 Jan 1902; 26 Jul 1977) German-American economist and mathematician who popularized "game theory" which mathematically analyzes behaviour of man or animals in terms of strategies to maximize gains and minimize losses. He coauthored Theory of Games and Economic Behavior (1944), with John von Neumann, which extended Neumann's 1928 theory of games of strategy to competitive business situations. They suggested that often in a business situation ("game'), the outcome depends on several parties ("players"), each estimating what all of the others will do before determining their own strategy. Morgenstern was a professor at Vienna University, Austria, from 1931 until the Nazi occupation in 1938), when he fled to America and joined the faculty at Princeton University. His later publications included works on economic prediction and aspects of U.S. defence.*TIS

1914 Vladimir Petrovich Potapov (24 Jan 1914 in Odessa, Ukraine - 21 Dec 1980 in Kharkov, Russia) In 1948 Potapov was invited to the Pedagogical Institute at Odessa. He soon became Head of Mathematics and, from 1952, Dean of the Faculty of Physics and Mathematics. He used his position to invite Livsic and others to the Institute.
During the 1950s Potapov worked on the theory of J-contractive matrix functions and the analysis of matrix functions became his main work. He published papers on the multiplicative theory of analytic matrix functions in the years 1950-55 which contain work from his doctoral thesis. He also worked on interpolation problems.
From 1974 Potapov lectured at Odessa Institute of National Economy, then he went to Kharkov to head the Department of Applied Mathematics at the Institute for low temperature physics. *SAU

1931 Lars V. Hörmander (24 Jan 1931 - ) Swedish mathematician who was awarded the Fields Medal in 1962 for his work on partial differential equations. Spending five years in writing, he produced a text The analysis of linear partial differential operators, in four volumes (1983-85). Between 1987 and 1990 he served as a vice president of the International Mathematical Union. In 1988 Hörmander was awarded the Wolf Prize. Hörmander's text, An Introduction to Complex Analysis in Several Variables, has become a classic dealing with the theory of functions of several complex variables. It developed from lecture notes of a course which he gave in Stanford in 1964 and published in book form two years later, with updates in 1973 and 1990.*TIS

1947 Michio Kaku (January 24, 1947 - ) is an American theoretical physicist, the Henry Semat Professor of Theoretical Physics in the City College of New York of City University of New York, the co-founder of string field theory, and a "communicator" and "popularizer" of science. He has written several books about physics and related topics; he has made frequent appearances on radio, television, and film; and he writes extensive online blogs and articles.*Wik

DEATHS

1860 James Pollard Espy (9 May 1785, 24 Jan 1860) American meteorologist who was one of the first to collect meteorological observations by telegraph. He gave apparently the first essentially correct explanation of the thermodynamics of cloud formation and growth. Every great atmospheric disturbance begins with a rising mass of heated, thus less dense air. While rising, the air mass dilates and cools. Then, as water vapour precipitates as clouds, latent heat is liberated so the dilation and rising continues until the moisture of the air forming the upward current is practically exhausted. The heavier air flows in beneath, and, finding a diminished pressure above it, rushes upward with constantly increasing violence. Water vapour precipitated during this atmospheric disturbance results in heavy rains.*TIS

1914 Sir David Gill (12 Jun 1843, 24 Jan 1914) Scottish astronomer known for his measurements of solar and stellar parallax, showing the distances of the Sun and other stars from Earth, and for his early use of photography in mapping the heavens. His early training in timekeeping as a watchmaker led to astronomy and he designed, equipped, and operated a private observatory near Aberdeen. To determine parallaxes, he perfected the use of the heliometer, a telescope that uses a split image to measure the angular separation of celestial bodies. In 1877, Gill and his wife measured the solar parallax by observing Mars from Ascension Island. He was appointed Her Majesty's Astronomer at the Cape of Good Hope (1879-1906). Gill also made geodetic surveys of South Africa. In fact he carried out all of the observations to measure the distances to stars in terms of the standard meter. His precise redetermination of the solar parallax was used for almanacs until 1968. *TIS

1930 Adolf Kneser was a German mathematician who wrote on integral equations.*SAU

1955 Percy John Heawood (8 September 1861 Newport, Shropshire, England[1] - 24 January 1955 Durham, England) was a British mathematician. He devoted essentially his whole working life to the four color theorem and in 1890 he exposed a flaw in Alfred Kempe's proof, that had been considered as valid for 11 years. With the four color theorem being open again he established the five color theorem instead. The four color theorem itself was finally established by a computer-based proof in 1976. *Wik

1961 Albert Carlton Gilbert (15 Feb 1884, 24 Jan 1961) was an American inventor who patented the Erector set after he founded the A.C. Gilbert Co. New Haven, Connecticut (1908) to manufacture boxed magic sets. In 1913, he introduced Erector Sets. Similar construction toys then existed, such as Hornby's Meccano set made in England. Meccano sets included pulleys, gears, and several 1/2" wide strips of varying length with holes evenly spaced on them. Gilbert needed something unique for his Erector sets, so he created the square girder, made using several 1" wide strips with triangles cut in them. These had their edges bent over so 4 strips could be screwed together to form a very sturdy square girder. Over the next 40 years, some 30 million Erector Sets were sold.*TIS

1982 Karol Borsuk (8 May 1905 in Warsaw, - 24 Jan 1982 in Warsaw) Borsuk introduced the important concept of absolute neighbourhood retracts in his doctoral dissertation, published in 1931, which was to lead to new and fruitful ideas in metric differential geometry. In 1936 he introduced the notion of cohomotopy groups, which could be said to mark the beginning of stable homotopy theory. Shape theory grew up at the same time as infinite-dimensional topology and the interaction between the two fields was of great mutual benefit. He was important for the many deep questions which Borsuk posed which stimulated most of the top mathematicians working in the area. *SAU

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 23

2012-01-23T00:10:00.002Z

Nature creates curved lines while humans create straight lines.

~Hideki Yukawa

The 23rd day of the year; 23 is the only number, n, such that n! is n digits long (decimal). 23 is also the answer to the classic Birthday Problem. (How many randomly selected people in a group makes the probability greater than 50% that two share a commmon birthdate.)

EVENTS

1656 Blaise Pascal wrote the ﬁrst of his eighteen Provincial Letters.

1640 John Pell wrote Mersenne that Thomas Harriot (1560–1621) had found the law of refraction, now known as Snell’s law.*VFR

1675 Christiaan Huygens drew a sketch in his notebook of a watch mechanism with a coiled spring regulator and then, “Eureka – I have found it”. He believed he had found a method of regulating a clock that would keep accurate time and not be affected by motion for use in attacking the problem of longitude. (Hooke had presented a watch regulated by a spring in the early 1660’s to the Royal Society for exactly the same goal in response to Huygen’s first pendulum clock. ) *Lisa Jardine, Ingenious Pursuits, pg 148

1764 Fire gutted Harvard Hall, the last of Harvard’s original buildings. The job of replacing the valuable scientiﬁc instruments housed in the building fell to John Winthrop, the second Hollis professor of mathematics and natural philosophy at Harvard. He was also friend and advisor of George Washington. *VFR

1848 Gold discovered in California. Jonas Clark soon was on hand with a wagon load of shovels and so made a wagon load of money. He used it to found Clark University in Worcester, MA, which,in the early 1890’s, had the strongest mathematics department in the country. *VFR

In 1896, Wilhelm Roentgen first made a public lecture-demonstration of his X-ray device, in Würzburg, Germany. *TIS

In 1911, Marie Curie's nomination to the French Academy of Sciences, having already won one Nobel Prize, is nevertheless voted down by the Academy's all-male membership. She went on to win a second Nobel Prize. *TIS

1930 Clyde Tombaugh photographed the planet Pluto, the only planet discovered in the twentieth century, after a systematic search instigated by the predictions of other astronomers. Tombaugh was 24 years of age when he made this discovery at Lowell Observatory in Flagstaff, Ariz. *TIS

*Northwestern University

1986 Science reported that a statistical analysis of word frequencies on a newly discovered poem attributed to Shakespeare concluded “There is no convincing evidence for rejecting the hypothesis that Shakespeare wrote it.” Otherwise said, the poem “ﬁts Shakespeare as well as Shakespeare ﬁts Shakespeare.” [Mathematics Magazine 59 (1986), p 183]. *VFR

1959 Robert Noyce Conceives the Idea for a Practical Integrated Circuit:
Robert Noyce, as a co-founder and research director of Fairchild Semiconductor, was responsible for the initial development of silicon mesa and planar transistors, which led to a commercially applicable integrated circuit. In 1968 Noyce went on to found Intel Corp. with Gordon Moore and Andy Grove.*CHM

BIRTHS

1693 Georg Bernhard Bilfinger (23 Jan 1693; 18 Feb 1750) German philosopher, mathematician, statesman, and author of treatises in astronomy, physics, botany, and theology. He is best known for his Leibniz-Wolffian philosophy, a term he coined to refer to his own position midway between those of the philosophers Gottfried Wilhelm Leibniz and Christian Wolff.*TIS

1719 John Landen (23 Jan 1719; died 15 Jan 1790) British mathematician who made important contributions on elliptic integrals. As a trained surveyor and land agent (1762-88), Landen's interest in mathematics was for leisure. He sent his results on making the differential calculus into a purely algebraic theory to the Royal Society, and also wrote on dynamics, and summation of series. Landen devised an important transformation, known by his name, giving a relation between elliptic functions which expresses a hyperbolic arc in terms of two elliptic ones. He also solved the problem of the spinning top and explained Newton's error in calculating the precession. Landen was elected a Fellow of the Royal Society in 1766. He corrected Stewart's result on the Sun-Earth distance (1771).*TIS

1785 Matthew Stewart (15 Jan 1717 in Rothesay, Isle of Bute, Scotland - 23 Jan 1785 in Catrine, Ayrshire, Scotland)was a Scottish geometer who wrote on geometry and planetary motion. Stewart's fame is based on General theorems of considerable use in the higher parts of mathematics (1746), described by Playfair as, "... among the most beautiful, as well as most general, propositions known in the whole compass of geometry." *SAU

1798 Karl Georg Christian von Staudt (January 24, 1798 – June 1, 1867) was a German mathematician born in the Free Imperial City of Rothenburg, which is now called Rothenburg ob der Tauber in Germany. From 1814 he studied in Gymnasium in Ausbach. He attended the University of Göttingen from 1818 to 1822 where he studied with Gauss who was director of the observatory. Staudt provided an ephemeris for the orbits of Mars and the asteroid Pallas. When in 1821 Comet Nicollet-Pons was observed, he provided the elements of its orbit. These accomplishments in astronomy earned him his doctorate from University of Erlangen in 1822.
The book Geometrie der Lage (1847) was a landmark in projective geometry. As Burau (1976) wrote, "Staudt was the first to adopt a fully rigorous approach. Without exception his predecessors still spoke of distances, perpendiculars, angles and other entities that play no role in projective geometry."
Furthermore, this book uses the complete quadrangle to "construct the fourth harmonic associated with three points on a straight line", the projective harmonic conjugate. *Wik (TIS gives birthdate as Jan 23)

1806 Ernst Ferdinand Adolf Minding (23 Jan 1806 in Kalisz,Russian Empire (now Poland) - 3 May 1885 in Dorpat, Russia (now Tartu, Estonia))His work, which continued Gauss's study of 1828 on the differential geometry of surfaces, greatly influenced Peterson. In 1830 Minding published on the problem of the shortest closed curve on a given surface enclosing a given area. He introduced the geodesic curvature although he did not use the term which was due to Bonnet who discovered it independently in 1848. In fact Gauss had proved these results, before either Minding of Bonnet, in 1825 but he had not published them.
Minding also studied the bending of surfaces proving what is today called Minding's theorem in 1839. The following year he published in Crelle's Journal a paper giving results about trigonometric formulae on surfaces of constant curvature. Lobachevsky had published, also in Crelle's Journal, related results three years earlier and these results by Lobachevsky and Minding formed the basis of Beltrami's interpretation of hyperbolic geometry in 1868.
Minding also worked on differential equations, algebraic functions, continued fractions and analytic mechanics. In differential equations he used integrating factor methods. This work won Minding the Demidov prize of the St Petersburg Academy in 1861. It was further developed by A N Korkin. Darboux and Émile Picard pushed these results still further in 1878. *SAU

1840 Ernst Abbe (23 Jan 1840, 14 Jan 1905) German physicist who made theoretical and technical innovations in optical theory. He improved microscope design, such as the use of a condenser lens to provide strong, even illumination (1870). His optical formula, now called the Abbe sine condition, applies to a lens to form a sharp, distortion-free image He invented the Abbe refractometer for determining the refractive index of substances. In 1866, he joined Carl Zeiss' optical works, later became his partner in the company, and in 1888 became the owner of the company upon Zeiss' death. Concurrently, he was appointed professor at the Univ. of Jena in 1870 and director of its astronomical and meteorological observatories in 1878.*TIS

1853 Kazimierz Żorawski (June 22, 1866 – January 23, 1953) was a Polish mathematician. His work earned him an honored place in mathematics alongside such Polish mathematicians as Wojciech Brudzewski, Jan Brożek (Broscius), Nicolas Copernicus, Samuel Dickstein, Stefan Banach, Stefan Bergman, Marian Rejewski, Wacław Sierpiński, Stanisław Zaremba and Witold Hurewicz.[citation needed]
Żorawski's main interests were invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics. His work in these disciplines was to prove important in other fields of mathematics and science, such as differential equations, geometry and physics (especially astrophysics and cosmology).*Wik

1857 Andrija Mohorovicic (23 Jan 1857; 18 Dec 1936) Croatian meteorologist and geophysicist who discovered the boundary between the Earth's crust and mantle, a boundary now named the Mohorovicic discontinuity. In 1901 he was appointed head of the complete meteorological service of Croatia and Slavonia, he gradually extended the activities of the observatory to other fields of geophysics: seismology, geomagnetism and gravitation. After the Pokuplje (Kupa Valley) earthquake of 8 Oct 1909, he analyzed the spreading of seismic waves with shallow depths through the Earth. From these, he was the first to establish, on the basis of seismic waves, a surface of velocity discontinuity separating the crust of the Earth from the mantle, now known as the Mohorovicic discontinuity.
*TIS

1862 David Hilbert (23 Jan 1862; 14 Feb 1943) German mathematician who reduced geometry to a series of axioms and contributed substantially to the establishment of the formalistic foundations of mathematics. In his book, Foundations of Geometry, he presented the first complete set of axioms since Euclid. His work in 1909 on integral equations led to 20th-century research in functional analysis (in which functions are studied as groups.) Today Hilbert's name is often best remembered through the concept of Hilbert space in quantum physics, a space of infinite dimensions.*TIS
He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of Hilbert spaces, one of the foundations of functional analysis.
Hilbert adopted and warmly defended Georg Cantor's set theory and transfinite numbers. A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century.
Hilbert and his students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. Hilbert is known as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.*Wik

1872 Paul Langevin (23 Jan 1872; 19 Dec 1946) French physicist who was the first to explain (1905) the effects of paramagnetism and diamagnetism (the weak attraction or repulsion of substances in a magnetic field) using statistical mechanics. He further theorized how the effects could be explained by how electron charges behaved within the atom. He popularized Einstein's theories for the French public. During WW I, he began developing a source for high intensity ultrasonic waves, which made sonar detection of submarines possible. He created the ultrasound from piezoelectric crystals vibrated by high-frequency radio circuits. In WW II, he spoke out against the Nazis, for which he was arrested and imprisoned, though he managed to escaped and fled to Switzerland.*TIS

1878 Edwin Plimpton Adams (23 Jan 1878 in Prague - 31 Dec 1956 in Princeton, USA) studied at Harvard, Göttingen and Cambridge and became Physics Professor at Princeton. He is best known for his translations of some of Einstein's lectures. *SAU

1907 Hideki Yukawa (23 Jan 1907; 8 Sep 1981) Japanese physician and physicist who shared the 1949 Nobel Prize for Physics for “his prediction of the existence of mesons on the basis of theoretical work on nuclear forces.” In his 1935 paper, On the Interaction of Elementary Particles*, he proposed a new field theory of nuclear forces that predicted the existence of the previously unknown meson. Mesons are particles heavier than electrons but lighter than protons. One type of meson was subsequently discovered in cosmic rays in 1937 by American physicists, encouraging him to further develop meson theory. From 1947, he worked mainly on the general theory of elementary particles in connection with the concept of the “non-local” field. He was the first Japanese Nobel Prize winner. *TIS (Yukawa donated a bronze crane that works as a wind chime when pushed against a traditional peace bell from which it is suspended at the Children's Peace Museum in Hiroshima. On the bell in his handwriting is the wish, "A Thousand Paper Cranes. Peace on Earth and in the Heavens."

1924 Sir Michael James Lighthill (23 Jan 1924, 17 Jul 1998) was a British mathematician who contributed to supersonic aerofoil theory and, aeroacoustics which became relevant in the design of the Concorde supersonic jet, and reduction of jet engine noise. Lighthill's eighth power law which states that the acoustic power radiated by a jet is proportional to the eighth power of the jet speed. His work in nonlinear acoutics found application in the lithotripsy machine used to break up kidney stones, the study of flood waves in rivers and road traffic flow. Lighthill also introduced the field of mathematical biofluiddynamics. Lighthill followed Paul Dirac as Lucasian professor of Mathematics (1969) and was succeeded by Stephen Hawking (1989) *TIS

DEATHS

1805 Claude Chappe (25 Dec 1763, 23 Jan 1805)French engineer who invented the semaphore visual telegraph. He began experimenting in 1790, trying various types of telegraph. An early trial used telescopes, synchronised pendulum clocks and a large white board, painted black on the back, with which he succeeded in sending a message a few sentences long across a 16km (10mi) distance. To simplify construction, yet still easily visible to read from far away, he changed to using his semaphore telegraph in 1793. Smaller indicators were pivoted at each end of large horizontal member. The two indicators could each be rotated to stand in any of eight equally spaced positions. By setting them at different orientations, a set of corresponding codes was used to send a message.*TIS

1810 Johann Wilhelm Ritter (16 Dec 1776, 23 Jan 1810) German physicist who discovered the ultraviolet region of the spectrum (1801) and thus helped broaden man's view beyond the narrow region of visible light to encompass the entire electromagnetic spectrum from the shortest gamma rays to the longest radio waves. After studying Herschel's discovery of infrared radiation, he observed the effects of solar radiation on silver salts and deduced the existence of radiation outside the visible spectrum. He also made contributions to spectroscopy and the study of electricity. *TIS

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 22

2012-01-22T00:10:00.000Z

Prudens interrogatio quasi dimidium sapientiae.

A prudent question is, as it were, one half of wisdom.

~Sir Francis Bacon

The 22nd day of the year; 22 is the smallest Hoax number (the sum of its digits is equal to the sum of the digits of its distinct prime factors). Can you find the next? [these sums that Hoax numbers add up to are an interesting study also]

EVENTS
1779 The parish register of Madron (the parish church) records ‘Humphry Davy, son of Robert Davy, baptized at Penzance, January 22nd, 1779. Davy was born in Penzance in Cornwall, United Kingdom, on 17 December 1778.

1876 The Johns Hopkins University Founded commonly referred to as Johns Hopkins, JHU, or simply Hopkins, is a private research university based in Baltimore, Maryland, United States. Johns Hopkins maintains campuses in Maryland, Washington, D.C., Italy, China, and Singapore.
The university was founded on January 22, 1876 and named for its benefactor, the philanthropist Johns Hopkins. Daniel Coit Gilman was inaugurated as first president on February 22, 1876. On his death in 1873, Johns Hopkins, a Quaker entrepreneur and childless bachelor, bequeathed $7 million to fund a hospital and university in Baltimore, Maryland. At that time this fortune, generated primarily from the Baltimore and Ohio Railroad, was the largest philanthropic gift in the history of the United States.*JHU Web page

1889 Oskar Bolza gave his ﬁrst lecture to a non-German audience. At Johns Hopkins University he gave twenty lectures “on the theory of substitution groups and its application to algebraic equations.” This was the ﬁrst course on Galois theory in this country. It was published in 1891 in the American Journal of Mathematics.*VFR

1919 Richard Courant married Nina Runge in G¨ottingen. She was the daughter of the mathematician Carl Runge and granddaughter of the physiologist and philosopher of science Emil DuBois-Reymond. This provides another example of mathematical talent being passed from father to son-in-law. [Constance Reid, Courant in G¨ottingen and New York. The Story of an Improbable Mathematician (Springer 1976), p. 75–76] *VFR

In 1980, Soviet dissident physicist Dr. Andrei Sakharov was arrested, stripped of his honors and exiled to Gorky from Moscow. *TIS

1984 Apple Computer Launches the Macintosh, the first successful mouse-driven computer with a graphic user interface, with a single $1.5 million commercial during the Super Bowl. Apple's commercial played on the theme of George Orwell's 1984 and featured the destruction of Big Brother -- a veiled reference to IBM -- with the power of personal computing found in a Macintosh.*CHM

In 1997, American Lottie Williams was reportedly the first human to be struck by a remnant of a space vehicle after re-entering the earth's atmosphere. At 3 a.m., while walking in a park in Tulsa, Oklahoma, she saw a light pass over her head. “It looked like a meteor,” she said. Minutes later, she was hit on the shoulder by a six-inch piece of blackened metallic material. The debris that struck Ms. Williams has not been examined to confirm its origin, but a used Delta II rocket, launched nine months earlier, had crashed into the Earth's atmosphere half an hour earlier. NASA scientists believe that Williams was hit by a part of it, making her the only person in the world known to have been hit by man-made space debris. *TIS

BIRTHS
1561 Sir Francis Bacon (22 Jan 1561; 9 Apr 1626) English philosopher remembered for his influence promoting a scientific method. He held that the aim of scientific investigation is practical application of the understanding of nature to improve man's condition. He wrote that scientists should concentrate on certain important kinds of experimentally reproducible situations, (which he called "prerogative instances"). After tabulating such phenomena, the investigator should also aim to make a gradual ascent to more and more comprehensive laws, and will acquire greater and greater certainty as he or she moves up the pyramid of laws. At the same time each law that is reached should lead him to new kinds of experiment, that is, to kinds of experiment over and above those that led to the discovery of the law. *TIS He died a month after performing his ﬁrst scientific experiment. He stuﬀed a chicken with snow to see if this would cause it to spoil less rapidly. The chill he caught during this experiment led to his death. [A. Hellemans and B. Bunch. The Timetables of Science, p . 32]. *VFR

1592 Pierre Gassendi (22 Jan 1592; 24 Oct 1655) French scientist, mathematician, and philosopher who revived Epicureanism as a substitute for Aristotelianism, attempting in the process to reconcile Atomism's mechanistic explanation of nature with Christian belief in immortality, free will, an infinite God, and creation. Johannes Kepler had predicted a transit of Mercury would occur in 1631. Gassendi used a Galilean telescope to observed the transit, by projecting the sun's image on a screen of paper. He wrote on astronomy, his own astronomical observations and on falling bodies.*TIS

1775 André-Marie Ampère (22 Jan 1775; 10 Jun 1836) French mathematician, physicist and chemist who founded and named the science of electrodynamics, now known as electromagnetism. His interests included mathematics, metaphysics, physics and chemistry. In mathematics he worked on partial differential equations. Ampère made significant contributions to chemistry. In 1811 he suggested that an anhydrous acid prepared two years earlier was a compound of hydrogen with an unknown element, analogous to chlorine, for which he suggested the name fluorine. He produced a classification of elements in 1816. Ampère also worked on the wave theory of light. By the early 1820's, Ampère was working on a combined theory of electricity and magnetism, after hearing about Oersted's experiments. *TIS (It is said that Ampere was capable of intense concentration leading to absent-mindedness. Once walking in Paris he had an insight and pulled a piece of chalk out of his pocket and finding the back of a cab he began to cover the back of the cab with equations, and was then shocked to see his solution begin to pull away and disappear down the street.)

1865 Louis Carl Heinrich Friedrich Paschen (22 Jan 1865; 25 Feb 1947) was a German physicist who was an outstanding experimental spectroscopist. In 1895, in a detailed study of the spectral series of helium, an element then newly discovered on earth, he showed the identical match with the spectral lines of helium as originally found in the solar spectrum by Janssen and Lockyer nearly 40 years earlier. He is remembered for the Paschen Series of spectral lines of hydrogen which he elucidated in 1908. *TIS

1866 Gustav de Vries (22 Jan 1866 in Amsterdam, The Netherlands
- 16 Dec 1934 in Haarlem, The Netherlands) was a Dutch mathematician who introduced the famous Korteweg-de Vries equation which characterizes traveling waves. *SAU

1874 Leonard Eugene Dickson (22 Jan 1874,Independence, Iowa, 17 Jan 1954, Harlingen, Texas)American mathematician who made important contributions to the theory of numbers and the theory of groups. He published 18 books including Linear groups with an exposition of the Galois field theory. The 3-volume History of the Theory of Numbers (1919-23) is another famous work still much consulted today. *TIS

1880 Frigyes Riesz (22 Jan 1880; 28 Feb 1956) Hungarian mathematician and pioneer of functional analysis, which has found important applications to mathematical physics. His theorem, now called the Riesz-Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space. It was the mathematical basis for proving that matrix mechanics and wave mechanics were equivalent. This is of fundamental importance in early quantum theory. His book Leçon's d'analyse fonctionnelle (written jointly with his student B Szökefalvi-Nagy) is one of the most readable accounts of functional analysis ever written. Beyond any mere abstraction for the sake of a structure theory, he was always turning back to the applications in some concrete and substantial situation. *TIS

1908 Lev Davidovich Landau (22 Jan 1908; 1 Apr 1968) Soviet physicist who worked in such fields as low-temperature physics, atomic and nuclear physics, and solid-state, stellar-energy, and plasma physics. Several physics terms bear his name. He was awarded the 1962 Nobel Prize for Physics for his theory to explain the peculiar superfluid behaviour of liquid helium at very low temperature (2.18 K). Landau's further contributions are partly reflected in such terms as Landau diamagnetism and Landau levels in solid-state physics, Landau damping in plasma physics, the Landau energy spectrum in low-temperature physics, or Landau cuts in high-energy physics. *TIS

1929 Walter Volodymyr Petryshyn (Vladimir Petryshin) (22 January 1929, Liashky Murovani, Lviv - ) is a famous Ukrainian mathematician. He had commenced his studies in Lviv during World War II, but he became a displaced person at the end of the war and continued his schooling in Germany. In 1950 he emigrated from Germany to the United States and completed his education there, living in Paterson, New Jersey. He studied at Columbia University and was awarded a B.A. in 1953, an M.S. in 1954, and a Ph.D. in 1961. Petryshyn's main achievements are in functional analysis. His major results include the development of the theory of iterative and projective methods for the constructive solution of linear and nonlinear abstract and differential equations.*Wik

DEATHS
1904 The Reverend George Salmon (25 September 1819 - 22 January 1904) was, firstly, a mathematician whose publications in algebraic geometry were widely read in the second half of the 19th century. He was also an Anglican theologian who devoted himself mostly to theology for the last forty years of his life. His publications in theology were widely read, too. He spent his entire career at Trinity College Dublin. In 1848 Salmon had published an undergraduate textbook entitled A Treatise on Conic Sections. This text remained in print for over fifty years, going though five updated editions in English, and was translated into German, French and Italian. In the late 1840s and the 1850s Salmon was in regular and frequent communication with Arthur Cayley and J.J. Sylvester. The three of them together with a small number of other mathematicians (including Charles Hermite) were developing a system for dealing with n-dimensional algebra and geometry. During this period Salmon published about 36 papers in journals. In these papers for the most part he solved narrowly defined, concrete problems in algebraic geometry, as opposed to more broadly systematic or foundational questions. But he was an early adopter of the foundational innovations of Cayley and the others. In 1859 he published the book Lessons Introductory to the Modern Higher Algebra (where the word "higher" means n-dimensional). This was for a while simultaneously the state-of-the-art and the standard presentation of the subject, and went through updated and expanded editions in 1866, 1876 and 1885, and was translated into German and French. *Wik

1951 Harald August Bohr (22 Apr 1887, 22 Jan 1951) Danish mathematician who devised a theory that concerned generalizations of functions with periodic properties, the theory of almost periodic functions. His brother was noted physicist Niels Bohr.*TIS Harald was an excellent football(soccer) player in his youth and played for the National team. Niels played also, but not at the same high level. An interesting anecdote about Niels Bohr as an athlete is here.

1921 Marie Georges Humbert (7 Jan 1859 in Paris, France - 22 Jan 1921 in Paris, France) His doctorate extended Clebsch's work on curves. He then studied Abel's work which he developed and put into a geometric setting. It was as a direct consequence of his work on using abelian functions in geometry which won for him the 1892 Académie des Sciences prize for work on Kummer surfaces. As Costabel writes, "He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication. "
He also extended work of Hermite considering applications to number theory throughout his life.
Humbert would be better known today if the area of mathematics in which he worked had remained in favor. Since it has now become merely something of an historical curiosity rather than mainstream mathematics, his contribution is less well known. It does, however, indicate the quality of his mathematics that, despite this, his name and results are known today. To some extent this is a consequence of the fact that although he worked in a specialized area he had a remarkably broad knowledge of mathematics and his results form links between areas. *SAU

1922 Camille Jordan (5 Jan 1838, 22 Jan 1922) French mathematician and engineer who prepared a foundation for group theory and built on the prior work of Évariste Galois. As a mathematician, Jordan's interests were diverse, covering topics throughout the aspects of mathematics being studied in his era. The topics in his published works include finite groups, linear and multilinear algebra, the theory of numbers, topology of polyhedra, differential equations, and mechanics.*TIS (His date of death is listed as 22 Jan by *SAU & *Wik but 20 Jan by *TIS)

1936 V Ramaswami Aiyar (1871 in Coimbatore district, India - 22 Jan 1936 in Chittoor, India) was an enthusiastic amateur mathematician who worked as a civil servant in India. He was a founder of the Indian Mathematical Society. *SAU

1981 Rudolf Oskar Robert Williams Geiger (24 Aug 1894, 22 Jan 1981) German meteorologist, one of the founders of microclimatology, the study of the climatic conditions within a few metres of the ground surface. His observations, made above grassy fields or areas of crops and below forest canopies, elucidated the complex and subtle interactions between vegetation and the heat, radiation, and water balances of the air and soil.*TIS

1987 Patrick du Val (March 26, 1903–January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named after him. Du Val's early work before becoming a research student was on relativity, including a paper on the De Sitter model of the universe and Grassmann's tensor calculus. His doctorate was on algebraic geometry and in his thesis he generalised a result of Schoute. He worked on algebraic surfaces and later in his career became interested in elliptic functions.*Wik

1989 Sydney Goldstein (3 Dec 1903 in Hull, England - 22 Jan 1989 in Belmont, Massachusetts, USA) Goldstein's work in fluid dynamics is of major importance. He is described as, "... one of those who most influenced progress in fluid dynamics during the 20th century." He studied numerical solutions to steady-flow laminar boundary-layer equations in 1930. In 1935 he published work on the turbulent resistance to rotation of a disk in a fluid. His work was important in aerodynamics, a subject in which Goldstein was extremely knowledgeable. *SAU

1990 Bill Ferrar graduated from Oxford after an undergraduate career interrupted by World War I. He lectured at Bangor and Edinburgh before moving back to Oxford. He worked in college administration and eventually became Principal of Hertford College. He worked on the convergence of series. *SAU

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Jan 21

2012-01-21T00:10:00.001Z

*Wik

The whole of the developments and operations of analysis are now capable of being executed by machinery. ... As soon as an Analytical Engine exists, it will necessarily guide the future course of science.
C. Babbage

The 21st day of the year; To tile a square out of integer sided squares requires a minimum of 21 squares. (technically, this is true for what are called "simple" squared squares, one where no subset of the squares forms a rectangle or square. See the solution here)

EVENTS
In 1472, the great daylight comet of 1472 passed within 10.5 million km of earth.*TIS (Johannes Müller von Königsberg (Regiomontanus) is said to have observed this comet)

1665 Samuel Pepys, having acquired a copy of Hooke’s Micrographia the day before, stays up to read it, “Before I went to bed I sat up till two o'clock in my chamber reading of Mr. Hooke's Microscopicall Observations, the most ingenious book that ever I read in my life.” *Pepy’s Diary

In 1807, the London Institution received a royal charter signed by King George III, to "promote the diffusion of Science, Literature, and the Arts, by means of Lectures and Experiments, and by easy access to an extensive collection of books, both ancient and modern, in all languages." The full name in the charter was the "London Institution for the Advancement of Literature and The Diffusion of Useful Knowledge." The first president was Sir Francis Baring. Its incorporation came after the Royal Society (1663) and Royal Institution (1800). The institution had an extensive lecture programme. Instruction in practical chemistry was given in its laboratory, and significant chemistry research was done there through the 19th century. *TIS

In 1840, Charles Wheatstone and William F. Cooke were granted the earliest English alphabetic telegraph patent. Wheatstone made contributions to a broad range of fields in the mid 19th century. The ABC telegraph was popular in England and Europe because it did not require a trained telegraphist to read or send the messages. The operator simply rotates a wheel to the desired letter. During rotation the instrument sends out the proper number of electric pulses to an electromagnetically controlled pointer on a remote synchronized slave receiver with a similarly lettered wheel which moves to the sender's letter. Electric telegraphs of the 1840-50's are of special historic importance as the earliest practical application of serial binary coded digital communication. *TIS

1888 Babbage's Analytical Engine Passes the First Test
The Analytical Engine of Charles Babbage was never completed in his lifetime, but his son Henry Provost Babbage built the mill portion of the machine from his father's drawings, and on January 21, 1888 computed multiples of pi to prove the adequacy of the design. Perhaps this represents the first successful test of a portion of a modern computer. Recently a portion of his earlier machine, the Difference Engine, was sold at auction by Christies of London to the Powerhouse Museum in Sydney, Australia.*CHM

1979 Pluto moves closer to the sun than Neptune. *VFR Pluto is usually farthest from the Sun. However, its orbit "crosses" inside of Neptune's orbit for 20 years out of every 248 years. Pluto last crossed inside Neptune's orbit on February 7, 1979, and temporarily became the 8th planet from the Sun. Pluto crossed back over Neptune's orbit again on February 11, 1999 to resume its place as the 9th planet from the Sun for the next 228 years (well, now it is now one of five known "dwarf planets").

BIRTHS

1793 Théodore Olivier (21 Jan 1793 in France - 5 Aug 1853 in France) From the 1840's Olivier wrote textbooks. His greatest fame, however, is as a result of the mathematical models which he created to assist in his teaching of geometry. Some of the models were of ruled surfaces, with moving parts to illustrate to students how the ruled surfaces were generated. Others were designed to illustrate the curves of intersection of certain surfaces. In fact Olivier earned quite a good income from selling these models, particularly in the United States.
The United States Military Academy at West Point had 23 mathematical models made for them by Olivier to use as teaching aids:=
These models are built on wooden boxes as bases, have metal supports, and consist of strings suspended from movable arms and arranged to form a variety of geometrical figures. The strings are held in place by lead weights that are concealed by the bases. The models illustrate such things as the intersection of two half cones, the intersection of a plane, hyperbolic paraboloid and a hyperboloid of one sheet, and the intersection of two half cylinders.
Other institutions in the United States such as the Columbia School of Mines also purchased models from Olivier while Princeton had copies of Olivier's models made for them. In 1849 Olivier presented a full set of the range of models he had created to the Conservatoire National des Arts et Métiers. The models had been manufactured by the firm of Pixii, Père et Fils, and later by the firm of Fabre de Lagrange which took over their manufacture. In 1857, four years after Olivier died, Harvard University purchased 24 of Olivier's models from Fabre de Lagrange and after the university received the order Benjamin Peirce gave a series of lectures on the mathematics which they illustrated. These models are still in Harvard's collection of scientific instruments.
Even after giving a complete set of his models to the Conservatoire National des Arts et Métiers, forty models were still in Olivier's possession at the time of his death. These were sold in 1869 to William Gillispie from Union College in Schenectady, east-central New York, United States. Gillispie exhibited the models at Union College which was appropriate since, twenty years earlier, Union College had became one of the first liberal arts colleges in the United States to give engineering courses. When Gillispie died Olivier's models were sold to the college. *SAU

1846 Pieter Hendrik Schoute (January 21, 1846, Wormerveer–April 18, 1923, Groningen) was a Dutch mathematician known for his work on regular polytopes and Euclidean geometry. *Wik Schoute was a typical geometer. In his early work he investigated quadrics, algebraic curves, complexes, and congruences in the spirit of nineteenth-century projective, metrical, and enumerative geometry. Schläfli's work of the 1850's was brought to the Netherlands by Schoute who, in three papers beginning in 1893 and in his elegant two-volume textbook on many-dimensional geometry 'Mehrdimensionale Geometrie' (2 volumes 1902, 1905), studied the sections and projections of regular polytopes and compound polyhedra. ... Alicia Boole Stott (1870-1940), George Boole's third daughter (of five), ... studied sections of four- and higher-dimensional polytopes after her husband showed her Schoute's 1893 paper, and Schoute later (in his last papers) gave an analytic treatment of her constructions. *SAU

1860 David Eugene Smith, Ph.D., LL.D. (January 21, 1860 in Cortland, New York – July 29, 1944 in New York) was an American mathematician, educator, and editor. David Eugene Smith attended Syracuse University, graduating in 1881 (Ph. D., 1887; LL.D., 1905). He studied to be a lawyer concentrating in arts and humanities, but accepted an instructorship in mathematics at the Cortland Normal School in 1884. He also knew Latin, Greek, and Hebrew. He became a professor at the Michigan State Normal College in 1891, the principal at the State Normal School in Brockport, New York (1898), and a professor of mathematics at Teachers College, Columbia University (1901).
Smith became president of the Mathematical Association of America in 1920.[3] He also wrote a large number of publications of various types. He was editor of the Bulletin of the American Mathematical Society; contributed to other mathematical journals; published a series of textbooks; translated Klein's Famous Problems of Geometry, Fink's History of Mathematics, and the Treviso Arithmetic. He edited Augustus De Morgan's Budget of Paradoxes (1915) and wrote many books on Mathematics and Mathematics History. *Wik

1874 René-Louis Baire (21 Jan 1874; 5 Jul 1932)
French mathematician whose study of irrational numbers and whose concept to divide the notion of continuity into upper and lower semi-continuity greatly influenced the French School of Mathematics. His doctoral thesis led to the solution of the problem of the characteristic property of limited functions of continuous functions and helped establish the theory of functions of real variables.*TIS

1897 Alexander Weinstein (21 Jan 1897 in Saratov, Russia - 6 Nov 1979 in Washington DC, USA) is famed for solving a variety of boundary value problems which have been used in a wide range of applications. Weinstein's method was developed to give accurate bounds for eigenvalues of plates and membranes. In examining singular partial differential equations he introduced a new branch of potential theory and applied the results to many different situations including flow about a wedge, flow around lenses and flow around spindles. *SAU

1908 Bengt Strömgren (21 Jan 1908; 4 Jul 1987) Bengt (Georg Daniel) Strömgren was a Danish astrophysicist who pioneered the present-day knowledge of the gas clouds in space. Researching for his theory of the ionized gas clouds around hot stars, he found relations between the gas density, the luminosity of the star, and the size of the "Strömgren sphere" of ionized hydrogen around it. He surveyed such H II regions in the Galaxy, and he also did important work on stellar atmospheres and ionization in stars. *TIS

1915 Yuri Vladimirovich Linnik (January 8, 1915 – June 30, 1972) was a Soviet mathematician active in number theory, probability theory and mathematical statistics.*Wik

DEATHS
1609 Joseph Justus Scaliger (5 Aug 1540, 21 Jan 1609) French scholar who was one of the founders of the science of chrolonology. Like Roger de Losinga, Bishop of Hereford, centuries before, Scaliger recognized that combining the three cycles of the 28-year solar cycle (S), the 19-year cycle of Golden Numbers (G) and the 15-year indiction cycle (I) produced one greater cycle of 7980 years (28×9×15). Scalinger applied this fact, called a Julian cycle, in his attempt to resolve a patchwork of historical eras and he used notation (S, G, I) to characterize years. The year of Christ's birth had been determined by Dionysius Exigus to be the number 9 on the solar cycle, by Golden Number 1, and by 3 of the indiction cycle, thus (9, 1, 3), which was 4713 of his chronological era. Hence, the year (1, 1, 1) was 4713 B.C. (later adopted as the initial epoch for the Julian day numbers).*TIS A formula for converting days to Julian day numbers is here.

1892 John Couch Adams (5 Jun 1819, 21 Jan 1892) In 1878 he published his calculation of Euler’s constant (Euler-Mascheronie constant) to 263 decimal places. (he also calculated the Bernoulli numbers up to the 62 nd) *VFR The Euler-Mascheronie constant is the limiting value of the difference between the sum of the first n values in the harmonic series and the natural log of n. (not 263 places, but the approximate value is 0.5772156649015328606065...)
He also predicted the location of the then unkown planet of Neptune, but it seems he failed to convince Airy to search for the planet. Independently, Urbanne LeVerrier predicted its locatin in Germany, and then assisted Galle in the Berlin Observatory in locating the planet on 23 September 1846. As a side note, when he was appointed to a Regius position at St. Andrews in Scotland, he was the last professor ever to have to swear and oath of “abjuration and allegience”, swearing fealty to Queen Victoria, and abjuring the Jacobite succession. The need for the oath was removed by the 1858 Universities Scotland Act. Adams made many other contributions to astronomy, notably his studies of the Leonid meteor shower (1866) where he showed that the orbit of the meteor shower was very similar to that of a comet. He was able to correctly conclude that the meteor shower was associated with the comet. *Wik & *TIS

1930 H(ugh) L(ongbourne) Callendar (18 Apr 1863, 21 Jan 1930) was an English physicist famous for work in calorimetry, thermometry and especially, the thermodynamic properties of steam. He published the first steam tables (1915). In 1886, he invented the platinum resistance thermometer using the electrical resistivity of platinum, enabling the precise measurement of temperatures. He also invented the electrical continuous-flow calorimeter, the compensated air thermometer (1891), a radio balance (1910) and a rolling-chart thermometer (1897) that enabled long-duration collection of climatic temperature data. His son, Guy S. Callendar linked climatic change with increases in carbon dioxide (CO2) resulting from mankind's burning of carbon fuels (1938), known as the Callendar effect, part of the greenhouse effect.*TIS

1931 Cesare Burali-Forti (13 August 1861 – 21 January 1931) was an Italian mathematician. He was born in Arezzo, and was an assistant of Giuseppe Peano in Turin from 1894 to 1896, during which time he discovered what came to be called the Burali-Forti paradox of Cantorian set theory.*Wik

1946 Harry Bateman FRS (29 May 1882 – 21 January 1946) was an English mathematician. He first grew to love mathematics at Manchester Grammar School, and in his final year, won a scholarship to Trinity College, Cambridge. There he distinguished himself in 1903 as Senior Wrangler (tied with P.E. Marrack) and by winning the Smith's Prize (1905). He studied in Göttingen and Paris, taught at the University of Liverpool and University of Manchester before moving to the US in 1910. First he taught at Bryn Mawr College and then Johns Hopkins University. There, working with Frank Morley in geometry, he achieved the Ph.D. In 1917 he took up his permanent position at California Institute of Technology, then still called Throop Polytechnic Institute.
Eric Temple Bell says, "Like his contemporaries and immediate predecessors among Cambridge mathematicians of the first decade of this century [1901–1910]... Bateman was thoroughly trained in both pure analysis and mathematical physics, and retained an equal interest in both throughout his scientific career."*Wik

1974 Arnaud Denjoy (5 January 1884 – 21 January 1974 in Paris) a French mathematician born in Auch, Gers. His contributions include work in harmonic analysis and differential equations. His integral was the first to be able to integrate all derivatives. Among his students is Gustave Choquet.*Wik

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 20

2012-01-20T00:10:00.001Z

If you are afraid of something, measure it, and you will realize it is a mere triple.

~Renato Caccioppoli

The 20th day of the year; 20 is the smallest number that cannot be either prefixed or followed by one digit to form a prime.

EVENTS

In 1633, Galileo, at age 68, left his home in Florence, Italy, to face the Inquisition in Rome. By 22 Jun 1633, he buckled under the threats and interrogation by the Inquisition, and renounced his belief that the Earth revolved around the Sun. *TIS

1748 In a surprising letter of January 20, 1748, D'Alembert wrote
to Euler [Euler 1980] to suggest a new theory: perhaps the moon (or at least its
distribution of mass) was not spherical. If, after all, we only see one side from the Earth, we can't know how far back it truly extends. And perhaps if it extends far enough back, the apsidal motion would indeed be 3 degrees, as observed. In an even more surprising response written less than four weeks later [Euler 1980], Euler says that he too had considered this idea, and had worked out the details! He found that moon would have to extend back about 2 1/2 Earth diameters in the direction away from us, which seemed untenable. *VFR

In 1969, astronomers at the University of Arizona established the first optical identification of a pulsar. *TIS

BIRTHS
1573 Simon Marius (20 Jan 1573, 26 Dec 1624) (Also known as Simon Mayr) German astronomer, pupil of Tycho Brahe, one of the earliest users of the telescope and the first in print to make mention the Andromeda nebula (1612). He studied and named the four largest moons of Jupiter as then known: Io, Europa, Ganymede and Callisto (1609) after mythological figures closely involved in love with Jupiter. Although he may have made his discovery independently of Galileo, when Marius claimed to have discovered these satellites of Jupiter (1609), in a dispute over priority, it was Galileo who was credited by other astronomers. However, Marius was the first to prepare tables of the mean periodic motions of these moons. He also observed sunspots in 1611 *TIS Galileo initially named his discovery the Cosmica Sidera ("Cosimo's stars"), but names that eventually prevailed were chosen by Simon Marius and were suggested by Johannes Kepler, in his Mundus Jovialis, published in 1614. *Wik You can find a nice blog about the conflict with Galileo by the Renaissance Mathematicus.

1775 André-Marie Ampère (20 January 1775 – 10 June 1836) was a French physicist and mathematician who is generally regarded as one of the main discoverers of electromagnetism. The SI unit of measurement of electric current, the ampere, is named after him.*Wik

1820 Alexandre-Emile Beguyer de Chancourtois (20 Jan 1820; 14 Nov 1886) French geologist who was the first to arrange the chemical elements in order of atomic weights (1862). De Chancourtois plotted the atomic weights on the surface of a cylinder with a circumference of 16 units, the approximate atomic weight of oxygen. The resulting helical curve which he called the telluric helix brought closely related elements onto corresponding points above or below one another on the cylinder. Thus, he suggested that "the properties of the elements are the properties of numbers." Although his publication was significant, it was ignored by chemists as it was written in the language of geology, and the editors omitted a crucial explanatory table. It was Dmitry Mendeleyev's table published in 1869 that became most recognized.*TIS

1831 Edward John Routh FRS (20 January 1831–7 June 1907), was an English mathematician, noted as the outstanding coach of students preparing for the Mathematical Tripos examination of the University of Cambridge in its heyday in the middle of the nineteenth century. He also did much to systematise the mathematical theory of mechanics and created several ideas critical to the development of modern control systems theory.*Wik

1834 William Watson born in Nantucket, MA. In 1862 he earned his Ph.D. at the University of Jena, being the ﬁrst American to receive a Ph.D. in mathematics at a foreign university. Later he taught at Harvard and MIT. In the same year Yale was the ﬁrst American school to grant a Ph.D. in mathematics (to J. H. Worall).*VFR

1895 Gabor Szego, Professor Emeritus at Stanford. He co-authored with George (originally Gy¨orogy) P´olya the renown book Problems and Theorems in Analysis. *VFR worked in the area of extremal problems and Toeplitz matrices.*SAU

1904 Renato Caccioppoli ( 20 January 1904 – 8 May 1959) was an Italian mathematician. His most important works, out of a total of around eighty publications, relate to functional analysis and the calculus of variations. Beginning in 1930 he dedicated himself to the study of differential equations, the first to use a topological-functional approach. Proceeding in this way, in 1931 he extended the Brouwer fixed point theorem, applying the results obtained both from ordinary differential equations and partial differential equations. *Wik

1931 David M. Lee (20 Jan 1931, ) American physicist who, with Robert C. Richardson and Douglas D. Osheroff, was awarded the Nobel Prize for Physics in 1996 for their joint discovery of superfluidity in the isotope helium-3.*TIS

DEATHS
1590 Giovanni Battista Benedetti died. In one of his books he forecast his death for 1592. Hence, on his deathbed, he recomputed his horoscope and declared that an error of four minutes must have been made in the original data, thus evincing his lifelong faith in the doctrines of judicial astrology.*VFR

1864 Giovanni Antonio Amedeo Plana (6 November 1781 – 20 January 1864) was an Italian astronomer and mathematician.
His contributions included work on the motions of the Moon, as well as integrals, elliptic functions, heat, electrostatics, and geodesy. In 1820 he was one of the winners of a prize awarded by the Académie des Sciences in Paris based on the construction of lunar tables using the law of gravity. In 1832 he published the Théorie du mouvement de la lune. In 1834 he was awarded with the Copley Medal by the Royal Society for his studies on lunar motion. He became astronomer royal, and then in 1844 a Baron. At the age of 80 he was granted membership in the prestigious Académie des Sciences. He died in Turin. He is considered one of the premiere Italian scientists of his age.
The crater Plana on the Moon is named in his honor.*Wik

1907 Agnes Mary Clerke (10 Feb 1842, 20 Jan 1907) Irish astronomical writer who was a diligent compiler of facts rather than a practicing scientist. Nevertheless, by 1885, her exhaustive treatise, A Popular History of Astronomy in the Nineteenth Century gained international recognition as an authoritative work. In 1903, with Lady Huggins, she was elected an honorary member of the Royal Astronomical Society, a rank previously held only by two other women, Caroline Herschel and Mary Somerville. Her publications included several books and 55 pieces in the Edinburgh Review. She contributed some astronomer biographies to the Dictionary of National Biography and some astronomical entries in the Encyclopaedia Britannica. *TIS

1921 Mary Watson Whitney (11 Sep 1847, 20 Jan 1921) American astronomer who trained with Maria Mitchell and succeeded her as professor and director of the Vassar College Observatory. As Mitchell had before her, Whitney championed science education the advancement of professional opportunities for women. She developed the astronomy department. Four years before her 1910 retirement, there were 160 students and eight different astronomy courses, including some of the first courses anywhere on astrophysics and on variable stars. During her tenure as director, the Observatory staff published 102 papers in major astronomical journals reporting their work on comets, asteroids, and variable stars. From 1896, photographic plates were used to study and measure star clusters.*TIS

1922 Camille Jordan (5 Jan 1838, 20 Jan 1922) French mathematician and engineer who prepared a foundation for group theory and built on the prior work of Évariste Galois. As a mathematician, Jordan's interests were diverse, covering topics throughout the aspects of mathematics being studied in his era. The topics in his published works include finite groups, linear and multilinear algebra, the theory of numbers, topology of polyhedra, differential equations, and mechanics.*TIS (His date of death is listed as 22 Jan by *SAU & *Wik)

1971 Jan Arnoldus Schouten (28 Aug 1883 in Nieuwer Amstel (now part of Amsterdam), Netherlands - 20 Jan 1971 in Epe, The Netherlands) worked on tensor analysis and its applications. He produced 180 papers and 6 books on tensor analysis, applying tensor analysis to Lie groups, general relativity, unified field theory, and differential equations. Influenced by Weyl and Eddington, Schouten investigated affine, projective and conformal mappings. Klein's Erlanger Programm of 1872 looked at geometry as properties invariant under the action of a group. This approach had a large influence on Schouten's approach to his topic. *SAU

2001 Crispin St. John Alvah Nash-Williams (December 19, 1932 – January 20, 2001) was a British and Canadian mathematician. His research interest was in the field of discrete mathematics, especially graph theory. *Wik

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 19

2012-01-19T00:10:00.003Z

Suppose a contradiction were to be found in the axioms of set theory.

Do you seriously believe that a bridge would fall down?

~Frank P Ramsey

The 19th day of the year; 19 is the smallest number n such that nⁿ contains all 10 digits *Number Gossip

EVENTS
1581 Andreas Dudith (1533–1589), mathematician and opponent of astrology, argued in a letter that observations of the comet of 1577 proved the Aristotelian explanation fallacious (for Aristotle, comets were accidental exhalations of hot air from the earth that rise in the sublunar sphere). Dudith’s use of mathematically precise observations to criticize a general physical theory of Aristotle betokens Galileo’s work ﬁfty years later. *VFR

1671 Wren and Hooke make a joint presentation on Hooke’s idea of arch design by using gravity and chain links to form an inverted dome. *Lisa Jardine, Ingenious Pursuits, pg 72

In 1894, Professor James Dewar exhibited several properties of liquid air, and produced solid air, at the Friday meeting of the Royal Institution. He had previously there exhibited, on 5 Jun 1885, liquid air obtained at the temperature of -192ºC. By Mar 1893 he had produced solid air in the form of ice. *TIS

2012 Mountain View, Ca—January 19, 2012—
The Computer History Museum (CHM), the world’s leading institution exploring the history of computing and its ongoing impact on society, today announced its 2012 Fellow Award honorees: Edward A. Feigenbaum, pioneer of artificial intelligence and expert systems; Steve Furber and Sophie Wilson, chief architects of the ARM processor architecture; and Fernando J. Corbató, pioneer of timesharing and the Multics operating system. The four Fellows will be inducted into the Museum’s Hall of Fellows on Saturday, April 28, 2012, at a formal ceremony where Silicon Valley insiders, technology leaders, and Museum supporters will gather to celebrate the accomplishments of the Fellows and their impact on society. This year’s celebration commemorates the 25th Anniversary of the Fellow Awards and will reunite pioneers from more than two decades.*CHM

BIRTHS
1736 James Watt (19 Jan 1736; 19 Aug 1819) Scottish instrument maker and inventor whose steam engine contributed substantially to the Industrial Revolution. In 1763 he repaired the model of Newcomen's steam engine belonging to Glasgow University, and began experiments on properties of steam. The Newcomen engine was simple in design: it acted as a pump and a jet of cold water was used to condense the steam. Watt improved on this design by adding a separate condenser and a system of valves to make the piston return to the top of the cylinder after descending. He took out a patent for the separate condenser in 1769. He later adapted the engine to rotary motion, making it suitable for a variety of industrial purposes, and invented the flywheel and the governor. *TIS

1747 Johann Elert Bode (19 Jan 1747; 23 Nov 1826) German astronomer best known for his popularization of Bode's law. In 1766, his compatriot Johann Titius had discovered a curious mathematical relationship in the distances of the planets from the sun. If 4 is added to each number in the series 0, 3, 6, 12, 24,... and the answers divided by 10, the resulting sequence gives the distances of the planets in astronomical units (earth = 1). Also known as the Titius-Bode law, the idea fell into disrepute after the discovery of Neptune, which does not conform with the 'law' - nor does Pluto. Bode was director at the Berlin Observatory, where he published Uranographia (1801), one of the first successful attempts at mapping all stars visible to the naked eye without any artistic interpretation of the stellar constellation figures.*TIS

1833 Rudolf Friedrich Alfred Clebsch (19 Jan 1833 in Königsberg, Germany (now Kaliningrad, Russia) - 7 Nov 1872 in Göttingen, Germany) Clebsch described the plane representations of various rational surfaces, especially that of the general cubic surface. Clebsch must also be credited with the first birational invariant of an algebraic surface, the geometric genus that he introduced as the maximal number of double integrals of the first kind existing on it.
Clebsch's brilliant career came to a sudden end in 1872 when he died of diphtheria. Max Noether and Brill, who were among his students at Giessen, continued his work on curves. Two volumes of his lectures on geometry were published after his death in 1876 and 1891. A second edition of part of one of these volumes, with Clebsch as joint author, was published in three parts in 1906, 1910 and 1932. *SAU

1851 Jacobus Cornelius Kapteyn (19 Jan 1851; 18 Jun 1922) Dutch astronomer who used photography and statistical methods in determining the motions and spatial distribution of stars. Such work was the first major step after the works of William and John Herschel. He tried to solve the questions of space density of stars as a function of distance from the sun, and the distribution of starts according to brightness per unit volume. Some of his results had lasting value, but some were superceded because he had failed to account for the interstellar absorption. In studies using proper motion to determine stellar distances, he discovered stellar motions are not random, as previously thought, but that stars move in two "star streams" (1904). He introduced absolute magnitude and colour index as standard concepts.*TIS

1879 Guido Fubini (19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini's theorem and the Fubini–Study metric.
Born in Venice, he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. He gained some early fame when his 1900 doctoral thesis, entitled Clifford's parallelism in elliptic spaces, was discussed in a widely-read work on differential geometry published by Bianchi in 1902.
During this time his research focused primarily on topics in mathematical analysis, especially differential equations, functional analysis, and complex analysis; but he also studied the calculus of variations, group theory, non-Euclidean geometry, and projective geometry, among other topics. With the outbreak of World War I, he shifted his work towards more applied topics, studying the accuracy of artillery fire; after the war, he continued in an applied direction, applying results from this work to problems in electrical circuits and acoustics. *Wik

1908 Aleksandr Gennadievich Kurosh (19 Jan 1908 in Yartsevo (near Smolensk), Russia - 18 May 1971 in Moscow) proved important results in Group Theory and is best-known as the author of one of the standard text-books in the subject.*SAU

1911 Garrett Birkhoff (January 19, 1911, Princeton, New Jersey, USA – November 22, 1996, Water Mill, New York, USA) was an American mathematician. He is best known for his work in lattice theory.During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra. During and after World War II, Birkhoff's interests gravitated towards what he called "engineering" mathematics. Birkhoff's research and consulting work (notably for General Motors) developed computational methods besides numerical linear algebra, notably the representation of smooth curves via cubic splines.
The mathematician George Birkhoff (1884–1944) was his father.*Wik

1912 Leonid Vitalyevich Kantorovich (19 Jan 1912; 7 Apr 1986) Soviet mathematician and economist who shared the 1975 Nobel Prize for Economics with Tjalling Koopmans for their work on the optimal allocation of scarce resources. Kantorovich's background was entirely in mathematics but he showed a considerable feel for the underlying economics to which he applied the mathematical techniques. He was one of the first to use linear programming as a tool in economics and this appeared in a publication Mathematical methods of organising and planning production which he published in 1939. The mathematical formulation of production problems of optimal planning was presented here for the first time and the effective methods of their solution and economic analysis were proposed. *TIS

1917 Graham Higman (19 Jan 1917 in Louth, Lincolnshire, England - 8 April 2008 in Oxford, England) is known for his outstanding work in all aspects of the theory of groups. He published on units in group rings, the subject of his doctoral thesis, in 1940 then there was a break in his publication record during the time he worked in the Meteorological Office. His 1948 papers are on somewhat different topics, being on topological spaces and linkages. They show the influences of Henry Whitehead and, to a lesser extent, Max Newman. *SAU

DEATHS
1878 Henri-Victor Regnault (21 Jul 1810, 19 Jan 1878) French chemist and physicist noted for his work on the properties of gases. His invaluable work was done as a skilful, thorough, patient experimenter in determining the specific heat of solids, liquids, gases, and the vapour-tensions of water and other volatile liquids, as well as their latent heat at different temperatures. He corrected Mariotte's law of gases concerning the variation of the density with the pressure, determined the coefficients of expansion of air and other gases, devised new methods of investigation and invented accurate instruments. Two laws governing the specific heat of gases are named after him. *TIS

1913 Robert Gauss of Denver and his brother Charles H. Gauss of Saint Louis both died on this date. They are grandsons of the mathematician Carl Friedrich Gauss *VFR (Robert died within a few hours of his brother, Charles Henry Gauss. Both died from heart disease.)The names of all the grandchildren of Gauss were listed in a letter from Robert to Felix Klein regarding the biography of Gauss which was being prepared:

P. S. The names and the present places of residence of the grandchildren of Carl Friedrich Gauss, who were born in the United States and are now living, are as follows:
The children of Eugene Gauss: Charles Henry Gauss, St. Charles, Missouri; Robert Gauss, Denver, Colorado; Albert F. Gauss, Los Angeles, California.
The children of William Gauss: Charles Friedrich Gauss, St. Louis, Missouri; Oscar W. Gauss, Greeley, Colorado; Mary Gauss, St. Louis, Missouri; William T. Gauss, Colorado Springs, Colorado; Joseph Gauss, St. Louis, Missouri.
The only one of the great-grandchildren of Carl Friedrich Gauss born in the United States, who has ever visited Germany is Helen W. Gauss, daughter of William T. Gauss of Colorado Springs, Colorado. while in Germany last year she was present at the dedication of the Gauss tower on the Hohenhagen.

1930 Frank Plumpton Ramsey (22 Feb 1903, 19 Jan 1930) English mathematician, logician and philosopher who died at age 26, but had already made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. He remains noted for his Ramsey Theory, a mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. This theory spans various fields of mathematics, including combinatorics, geometry, and number theory. His papers show he was also a remarkably creative and subtle philosopher. *TIS His father Arthur, also a mathematician, was President of Magdalene College. His brother, Michael Ramsey, later became Archbishop of Canterbury. Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy's Hospital in London at the age of 26. He is buried at the Parish of the Ascension Burial Ground in Cambridge, UK.*Wik

1954 Theodor Franz Eduard Kaluza (9 November 1885, Wilhelmsthal, today part of Opole – 19 January 1954, Göttingen) was a German mathematician and physicist known for the Kaluza-Klein theory involving field equations in five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in string theory. *Wik

2007 Asger Hartvig Aaboe (April 26, 1922 – January 19, 2007) was a historian of the exact sciences and mathematician who is known for his contributions to the history of ancient Babylonian astronomy. He studied mathematics and astronomy at the University of Copenhagen, and in 1957 obtained a PhD in the History of Science from Brown University, where he studied under Otto Neugebauer, writing a dissertation "On Babylonian Planetary Theories". In 1961 he joined the Department of the History of Science and Medicine at Yale University, serving as chair from 1968 to 1971, and continuing an active career there until retiring in 1992. In his studies of Babylonian astronomy, he went beyond analyses in terms of modern mathematics to seek to understand how the Babylonians conceived their computational schemes. *Wik

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 18

2012-01-18T00:10:00.000Z

Sooner or later every one of us breathes an atom that has been breathed before by anyone you can think of who has lived before us - Michelangelo or George Washington or Moses.
~Jacob Bronowski

The 18th day of the year; there is only one number (289=17²) for which the sum of its proper divisors is 18. (can you figure out which numbers can never appear as the sum of the proper divisors?)

EVENTS
1663/4 King Charles II’s letter which conﬁrmed the Lucasian statutes forbade the Professor to take any but a Fellow-commoner as his pupil, and Newton was never that. Thus Newton was NEVER Barrow’s pupil. This myth began after Newton’s death with Conduitt’s anecdote of Barrow examining Newton in Euclid as an undergraduate and ﬁnding him wanting. Newton did attend Barrow’s lectures in 1665 but would not allow that they were helpful to him; Newton was self-taught in mathematics. [Whiteside, Notes and Records of the Royal Society of London, 19(1964), p. 61; Westfall, p. 99] *VFR

1802 Gauss read in the newspaper that Olbers had rediscovered Ceres. Gauss wrote to get the observations and a long friendship ensued. Gauss was such an avid newspaper reader that students nicknamed him the “newspaper bear” because of his habits in the library reading room. If someone was reading the paper he wanted he would sit glumly nearby and stare at them until they gave up the paper. *VFR

In 1895, James Dewar demonstrated the intimate connection between phosphorescence and photographic action of the electric light on bodies cooled to the temperature of boiling liquid air. Presented at the Royal Institution, these experiments were reported as "very remarkable." *TIS

In 1896, The first x-ray machine is exhibited in the U.S. at Casino Chambers, New York City. For an admission charge of 25 cents, patrons could view the "Parisian sensation," *TIS

1938 J.W. Bryce writes a memorandum formalizing IBM's development of a computing machine for Harvard: the Harvard Mark I, completed in 1944. The Harvard Mark I was the first fully automatic machine to be completed and computed three additions or subtractions a second; its memory stored 72 numbers.(I can see my students trying to comprehend this. They laugh out loud when I tell them that my first computer had 4k of memory, embarrassment for me and sure that I MUST have meant 4 meg) Several of J.W. Bryce's major inventions—high-speed multiplying, dividing, cross adding, the read-out, and the emitter—were utilized in the Harvard Mark I. *CHM

In 1969, pulsars were first identified by University of Arizona astronomers. *TIS

1982 Guyana (on the Northeast coast of South America) issued a series of postage stamps celebrating their conversion to the metric system. Can you name two countries that have not yet adopted the metric system? *VFR (The usage of the metric system varies around the world. According to the American Central Intelligence Agency's Factbook, the International System of Units is the official system of measurement for all nations in the world except for Burma, Liberia and the United States... other sources say Liberia has adopted metric system. Russ Rowlett opines that "The U.S. adopted the metric system in 1866. What the U.S. has failed to do is to restrict or prohibit the use of traditional units in areas touching the ordinary citizen: construction, real estate transactions, retail trade, and education." )

BIRTHS
1825 Sir Edward Frankland (18 Jan 1825; 9 Aug 1899) English chemist who was one of the first investigators in the field of structural chemistry, invented the chemical bond, and became known as the father of valency. He studied organometallic compounds - hybrid molecules of the familiar organic non-metallic elements (such as carbon, hydrogen, nitrogen, sulphur, phosphorus) with true metals. By 1850, he had prepared small organic molecules containing such metals as zinc. Subsequently, he devised the theory of valence (announced 10 May 1852), that each type of atom has a fixed capacity for combination with other atoms. For his investigations on water purification and for his services to the government as water analyst, Frankland was knighted in 1897.
*TIS

1856 Luigi Bianchi (18 Jan 1856 in Parma, Italy - 6 June 1928 in Pisa, Italy) made important contributions to differential geometry.*SAU

1879 Peter Mark Roget (18 Jan 1779; 12 Sep 1869). In 1852, at age 73, he published his famous Thesaurus of English Words and Phrases. He was also one of the founders of the Medical and Chirurgical Society of London. Of more mathematical interest, Roget also invented the log-log scale on slide rules, making exponentiation & roots much easier to calculate. *Wik

1880 Paul Ehrenfest (January 18, 1880 – September 25, 1933) was an Austrian and Dutch physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem.*Wik

1901 Ivan Georgievich Petrovsky (18 Jan 1901 in Sevsk, Orlov guberniya, Russia - 15 Jan 1973 in Moscow, USSR) Petrovsky's main mathematical work was on the theory of partial differential equations, the topology of algebraic curves and surfaces, and probability. Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov.*SAU

1908 Jacob Bronowski (18 Jan 1908; 22 Aug 1974) Polish-British mathematician and science writer who eloquently presented the case for the humanistic aspects of science as the writer and presenter of the BBC television series, The Ascent of Man. Bronowski, who had a Ph.D. in algebraic geometry, spent WW II in Operations Research, and was an official observer of the after-effects of the Nagasaki and Hiroshima bombings. After this experience, he turned to biology, to better understand the nature of violence.*TIS

DEATHS
1873 Pierre Charles François Dupin (6 Oct 1784 in Varzy, France - 18 Jan 1873 in Paris, France) made contributions to differential geometry and in particular invented the 'Dupin indicatrix' which gives an indication of the local behavior of a surface up to the terms of degree two. His contributions to differential geometry include the introduction of conjugate and asymptotic lines on a surface. *SAU

1963 Edward Charles Titchmarsh (1 Jun 1899, 18 Jan 1963) English mathematician whose contributions to analysis placed him in the forefront of his profession. His contributions helped resolve the differences between the general theory of quantum mechanics and the methods used to solve particular problems in quantum theory. All Titchmarsh's work is in analysis. His early studies were on Fourier series, Fourier integrals, functions of a complex variable, integral equations and the Riemann zeta function. From 1939, Titchmarsh concentrated on the theory of series expansions of eigenfunctions of differential equations, work which helped to resolve problems in quantum mechanics. His work on this topic occupied him for the last 25 years of his life. *TIS

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 17

2012-01-17T00:10:00.003Z

*New Horizons. August 2001. Artwork commissioned for the New Horizons mission to Pluto. Pluto's horizon spans the foreground, looking past its moon, Charon, toward the distant, star-like Sun. Painting by Dan Durda...who learned some math, but not his art, from me.

Whenever you can, count.

~Sir Francis Galton

The 17th day of the year; there are 17 prime partitions of 17. No other number is equal to its number of prime partitions. (for example, 7 has 3 prime partitions, 7, 3+2+2, and 5+2)

EVENTS

In 1949, for the first time, full energy was released by the first synchrotron which was installed at the Radiation Laboratory, University of California, Berkeley. It was invented by Edwin Mattison of the same university, and would accelerate electrons by virtue of their negative charges, using a betatron-type magnet that weighed about 8 tons. The synchrotron was constructed at the General Electric Research Laboratory at Schnectady, N.Y. by Dr. Herbert C. Pollock and Willem F. Westendorp. *TIS

1974 HP introduces the ﬁrst programmable pocket calculator. The first desktop programmable calculators were produced in the mid-1960s by Mathatronics and Casio (AL-1000). These machines were, however, very heavy and expensive. The first programmable pocket calculator was the HP-65, in 1974; it had a capacity of 100 instructions, and could store and retrieve programs with a built-in magnetic card reader.Bill Hewlett's design requirement was that the calculator should fit in his shirt pocket. That is one reason for the tapered depth of the calculator. The magnetic program cards fed in at the thick end of the calculator under the LED display. The documentation for the programs in the calculator is very complete, including algorithms for hundreds of applications, including the solutions of differential equations, stock price estimation, statistics, and so forth.*Wik

1985 The last day for the card catalog at the New York Public Library. It contained 10 million dog-eared cards in 9,000 oak drawers. It was replaced by 800 bound volumes of photocopies of the cards and a computer catalog. *AP press release, 18 Jan 1985.

1996 Computer is Used in the Discovery of New Planets. Paul Butler and Geoffrey Marcy announced to the American Astronomical Society that they had discovered two new planets using an unconventional computer technique to analyze the movement of stars. Butler and Marcy let computers analyze spectrographic images of stars for eight years, looking for shifts in the light that would imply it is being pulled by the gravity of a planet. The first discovery, a planet orbiting the star 47 Ursae Majoris, was announced in December 1995 and, since then, this team found 12 planets outside of our solar system.*CHM

BIRTHS

1624 Guarino Guarini (17 Jan 1624; 6 Mar 1683) Italian architect and theologian whose study of mathematics led him to a career in architecture in which he created the most fantastic geometric elaboration of all baroque churches. In his Santissima Sindone, Guarini created a diaphanous dome - a geometrical optical illusion in the dome made through the use of the actual structure which creates the illusion that the dome recedes farther up into space than it really does. He wrote two architectural treatises and other works that concentrate on his mathematical knowledge. Therein, Guarini discusses Desargue's projective geometry, which reveal a scientific basis for his daring structures. He worked primarily in Turin and Sicily, with his influence stretching into Germany, Austria and Bohemia.*TIS

1647 Elisabeth Catherina Koopmann Hevelius (in Polish also called Elżbieta Heweliusz) (17 Jan 1647 in Danzig, now Gdańsk, Poland - Died: 22 Dec 1693 in Danzig, now Gdańsk, Poland) was the second wife of Johannes Hevelius. Like her husband, she was also an astronomer.
The marriage of the sixteen year old to fifty two year old Hevelius in 1663 allowed her also to pursue her own interest in astronomy by helping him manage his observatory. They had a son, who died soon, and three daughters who survived[2]. Following his death in 1687, she completed and published Prodromus astronomiae (1690), their jointly compiled catalogue of 1,564 stars and their positions.
She is considered one of the first female astronomers, and called "the mother of moon charts". Her life was recently novelized as The Star Huntress (2006).
The minor planet 12625 Koopman is named in her honour, as is the crater Corpman on Venus. *Wik

1706 Benjamin Franklin, (17 Jan 1706; 17 Apr 1790) American scientist. When he observed a balloon launch by the Montgolﬁer brothers he was asked of what use it was. He replied: Of what use is a new born baby? *VFR
While traveling on a ship, Franklin had observed that the wake of a ship was diminished when the cooks scuttled their greasy water. He studied the effects at Clapham common on a large pond there. "I fetched out a cruet of oil and dropt a little of it on the water...though not more than a teaspoon full, produced an instant calm over a space of several yards square." He later used the trick to "calm the waters" by carrying "a little oil in the hollow joint of my cane." *W. Gratzer, Eurekas and Euphorias, pgs 80,81
American printer and publisher, author, inventor and scientist, and diplomat. He become widely known in European scientific circles for his reports of electrical experiments and theories. He invented a type of stove, still being manufactured, to give more warmth than open fireplaces and the lightning rod, bifocal eyeglasses also were his ideas. Grasping the fact that by united effort a community may have amenities which only the wealthy few can get for themselves, he helped establish institutions people now take for granted: a fire company (1736), a library (1731), an insurance company (1752), an academy (1751), and a hospital (1751). In some cases these foundations were the first of their kind in North America. *TIS

1858 Gabriel Xavier Paul Koenigs (17 January 1858 Toulouse, France – 29 October 1931 Paris, France) was a French mathematician who worked on analysis and geometry. He was elected as Secretary General of the Executive Committee of the International Mathematical Union after the first world war, and used his position to exclude countries with whom France had been at war from the mathematical congresses.*Wik

1868 Louis Couturat (17 Jan 1868 in Ris-Orangis (near Paris), France - 3 Aug 1914 in Between Ris-Orangis and Melun, France), a logician whose historical researches led to the publication of Leibniz’s logical works in 1903.*VFR Couturat was killed in a car accident, his car being in hit by the car carrying the orders for mobilization of the French army the day World War I broke out. Ironically he was a noted pacifist. *SAU

1889 Sir Ralph Howard Fowler (17 Jan 1889; 28 Jul 1944) was an English physicist and astronomer whose university education in mathematics led him to working on thermodynamics and statistical mechanics with important applications in physical chemistry. Turning to astronomy, he collaborated with Arthur Milne on the spectra of stars, and their temperatures, and pressures. He also worked on the statistical mechanics of white dwarf stars (1926) with P.A.M. Dirac, whom he had introduced to quantum theory. Fowler proposed that white dwarf stars consist of a degenerate gas of extremely high density. *TIS

1905 Dattaraya Ramchandra Kaprekar (17 Jan 1905 in Dahanu, India - Died: 1986 in Devlali, India) was an Indian mathematician who discovered several results in number theory, including a class of numbers and a constant named after him. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well-known in recreational mathematics circles. A Kaprekar number is a positive integer with the property that if it is squared, then its representation can be partitioned into two positive integer parts whose sum is equal to the original number (e.g. 45, since 45²=2025, and 20+25=45, also 9, 55, 99 etc.) However, note the restriction that the two numbers are positive; for example, 100 is not a Kaprekar number even though 100²=10000, and 100+00 = 100. This operation, of taking the rightmost digits of a square, and adding it to the integer formed by the leftmost digits, is known as the Kaprekar operation.*Wik

1913 Shaun Wylie (17 January 1913 – 2 October 2009) was a British mathematician and World War II codebreaker. *Wik

DEATHS

1618 Luca Valerio (1552 in Naples, Italy - 17 Jan 1618 in Rome, Italy) was an Italian mathematician who applied methods of Archimedes to find volumes and centres of gravity of solid bodies. He corresponded with Galileo.*SAU

1675 Bernard Frénicle de Bessy (c. 1605 in Paris, France - 17 Jan 1675 in Paris, France), wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for Des quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all 880 essentially different normal magic squares of order 4. The Frénicle standard form, a standard representation of magic squares, is named after him. He solved many problems created by Fermat and also discovered the cube property of the number 1729, later referred to as a taxicab number.(see "Births" 22 Dec,1887 )
Like Fermat, Frénicle was an amateur mathematician, but he still corresponded with the likes of Descartes, Huygens, Mersenne and also Fermat, who was his personal friend. His major contributions were in number theory.
Frenicle's Methode, 1754 edition.
He challenged Christiaan Huygens to solve the following system of equations in integers,

x² + y² = z², x² = u² + v², x − y = u − v.

A solution was given by Théophile Pépin in 1880.
In 1973, he was posthumously recognized by the American Mathematical Society for his work in structural combinatorics *Wik

1775 Vincenzo Riccati (Castelfranco Veneto, 11 January 1707 – Treviso, 17 January 1775) was an Italian mathematician and physicist. He was the brother of Giordano Riccati, and the second son of Jacopo Riccati.
Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics. The Riccati equation is named after his father.*Wik

1910 Friedrich Wilhelm Georg Kohlrausch (14 Oct 1840, 17 Jan 1910)German physicist who investigated the properties of electrolytes (substances that conduct electricity in solutions by transfer of ions) and contributed to the understanding of their behaviour. Some of Kohlrausch's pioneering achievements include conductivity measurements on electrolytes, his work on the determination of basic magnetic and electrical quantities, and the enhancement of the associated measuring technologies. It was under his direction that the "Physikalisch-Technische Reichsanstalt" (the then Imperial Physical Technical Institute in Germany) created numerous standards and calibration standards which were also used internationally outside Germany.*TIS

1911 Sir Francis Galton (16 Feb 1822, 17 Jan 1911) English scientist, founder of eugenics, statistician and investigator of intellectual ability. He explored in south-western Africa. In meteorology, he was first to recognise and name the anticyclone. He interpreted the theory of evolution of (his cousin) Charles Darwin to imply inheritance of talent could be manipulated. Galton had a long-term interest in eugenics - a word he coined for scientifically selected parenthood to enable inheritance of beneficial characteristics. He coined the phrase "nature versus nurture." Galton experimentally verified the uniqueness of fingerprints, and suggested the first classification based on grouping the patterns into arches, loops, and whorls. On 1 Apr 1875, he published the first newspaper weather map - in The Times *TIS

1954 Leonard Eugene Dickson (22 Jan 1874,Independence, Iowa, 17 Jan 1954, Harlingen, Texas)American mathematician who made important contributions to the theory of numbers and the theory of groups. He published 18 books including Linear groups with an exposition of the Galois field theory. The 3-volume History of the Theory of Numbers (1919-23) is another famous work still much consulted today. *TIS

1997 Clyde William Tombaugh (4 Feb 1906 on Ranch near Streator, Illinois, 17 Jan 1997) was an American astronomer who discovered what was then recognized as the planet Pluto, which he photographed on 23 Jan 1930, the only planet discovered in the twentieth century, after a systematic search instigated by the predictions of other astronomers. Tombaugh was 24 years of age when he made this discovery at Lowell Observatory in Flagstaff, Ariz. He also discovered several clusters of stars and galaxies, studied the apparent distribution of extragalactic nebulae, and made observations of the surfaces of Mars, Venus, Jupiter, Saturn, and the Moon.Born of poor farmers, his first telescope was made of parts from worn-out farming equipment. *TIS
From my personal blog after a visit to Mars Hill, Flagstaff, Az. (much material from Wikipedia)
In the late 19th and early 20th century, observers of Mars drew long straight lines that appeared on the surface between 60 degrees north and south of the martian equator. Italian astronomer Giovanni Schiaparelli called these lines canali, which became canals in English. Lowell extended this observation to a theory that Mars had polar ice caps that would melt in the martian spring and fill the canals. He even extended the theory to include intelligent life on Mars that had designed the canals.
Eventually it became clear that there were no martian canals, but Mars hill went on to be the sight where a self educated Kansas schoolboy found his dream of working in astronomy in 1929, when the observatory director, V M Slipher, "handed the job of locating Planet X to Clyde Tombaugh, a 23-year-old Kansas man who had just arrived at the Lowell Observatory after Slipher had been impressed by a sample of his astronomical drawings."
On the nights of Jan 23 and 30th of January, 1830, he found a planet in the images that he thought was the Planet X. "The discovery made front page news around the world. The Lowell Observatory, who had the right to name the new object, received over 1000 suggestions, from "Atlas" to "Zymal". Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Name suggestions poured in from all over the world. Constance Lowell proposed Zeus, then Lowell, and finally her own first name. These suggestions were disregarded.
The name "Pluto" was proposed by Venetia Burney (later Venetia Phair), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, one of the alternate names of Hades, the Greek god of the Underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian of Oxford University's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in America. The object was officially named on March 24, 1930."
Among the many awards Tombaugh received was a scholarship to the Univ of Kansas, where he would eventually earn a Bachelors and Masters Degree. It is said that the Astronomy Dept head refused to allow him to take the introductory astronomy class because it would be undignified for the discoverer of a planet.

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 16

2012-01-16T00:10:00.000Z

*hastac.org

“It has nothing to do with defending our country, except to make it worth defending.”

~Robert R Wilson, 1969 (at Senate Hearing to justify Fermilab funding)

The 16th day of the year; 16 is the only number that can be written as a^b= b^a when a and b are not equal.

EVENTS
1777 Euler last attended a meeting of the St. Petersburg Academy on this date, after which he sent his papers in to the Academy with his assistants. *Ed Sandifer

1826 Neils Henrik Abel wrote his teacher and friend Holmboe: “The divergent series are the invention of the devil.” *VFR

1831 In an audience with the King of Sardinia, Cauchy answered ﬁve questions with “I expected Your Majesty would ask me this, so I have prepared to answer it.” Then he took a memoir from his pocket and read it. *VFR

1865 Founding of the London Mathematical Society. Despite its name, the London Mathematical Society (LMS) has, almost since its foundation, served as the national society for the British mathematical community. Its establishment in
1865 made Britain one of the first countries in the world to have such an organisation. What was to become the London Mathematical Society arose from a chance remark in a conversation between two former students of University College London in the summer of 1864. The two young men were Arthur Cowper Ranyard and George Campbell De Morgan, the son of one of the most influential British mathematicians of the day. Augustus De Morgan was the founding professor of mathematics at University College, which he had single-handedly established as the home of advanced mathematical education in London. Conscious of the key role the Professor's reputation could play in attracting members to the Society, it was agreed that George should ask his father to take the chair at the first meeting.
Agreeing to this, the senior De Morgan apparently insisted that their tentative title of The London University Mathematics Society, be changed, first to the University College Mathematical Society, and then, in order to widen the scope of the society's membership, to the London Mathematical Society. The newly-retitled society held its inaugural meeting at University College London on Monday, January 16th 1865, with De Morgan as its first president giving the opening address. Within months, it had attracted over 60 new members from around the country, including many of the leading British mathematicians of the 19th century, such as Arthur Cayley, James Joseph Sylvester, Henry John Stephen Smith, George Salmon, William Kingdon Clifford and James Clerk Maxwell. *A Brief History of the London Mathematical Society

1910 At six o’clock in the evening, Richard Courant was scheduled to be examined for his Ph.D. by Hilbert in mathematics, Voight in physics, and Husserl in philosophy. Hilbert arrived early and was anxious to get on with it so he could go home, but the others did not appear. Since Courant had written his dissertation under Hilbert, he had no need to probe Courant’s mathe¬matical knowledge, so they talked about non-mathematical things. After forty minutes, Husserl appeared. Hilbert excused himself and went home. After Husserl asked one question, Courant asked him to explain a delicate point in phenomenology. This took the remainder of the alloted time. Voight never appeared. Later several friends rented a horse-drawn carriage and hauled Courant around the quiet town of Gottingen while they blared over megaphones: “Dr. Richard Courant summa cum laude!” [Constance Reid, Courant in Gottingen and New York. The Story of an Improbable Mathematician (Springer 1976), pp. 33-34] *VFR

1913 Srinivasa Ramanujan, a 23 year old clerk in Madras, India, wrote G. H. Hardy, Professor at Cambridge, sending “a few examples of my theorems,” and asking for advice. Although he was inclined to dismiss it as a letter from a crank, Hardy and his colleague J. E. Littlewood puzzled out some of the 120 formulas in the letter after dinner and concluded that Ramanujan was a mathematical genius. Hardy immediately invited Ramanujan to England, where they collaborated on a number of important papers in number theory. *VFR ( Hardy figured that Ramanujan's theorems "must be true, because, if they were not true, no one would have the imagination to invent them".)

1956 The U.S. government's Semi-Automatic Ground Environment (SAGE) is disclosed to the public. SAGE, an air defense system, linked hundreds of radar stations in the United States and Canada in the first large-scale computer communications network. With the increasing possibility of a large-scale bomber attack on the United States in the mid-1950s, it became evident that further improvements in the nation's defense capability were needed. MIT's Lincoln Laboratory was commissioned to develop an automated nationwide computer-based air defense system. SAGE was completed in the early 1960s, revolutionizing air defense and civilian air traffic control. In 1979 SAGE was replaced by Regional Operations Control Centers (ROCC).*CHM

BIRTHS

1477 Johannes Schöner (16 Jan 1477; 16 Jan 1547) German geographer who is noted for making and printing geographical globes. A notable work from 1515 is one of the earliest surviving globes produced following the discovery of new lands by Christopher Columbus. It was the first to show the name America that had been suggested by Waldseemüller. Tantalizingly, it also depicts a passage around South America before it was recorded as having been discovered by Magellan. Schöner was a professor mathematics at the University of Nuremberg and was the author of numerous mathematical, astronomical and geographical works. In his first career, he was an ordained Roman Catholic priest, which he gave up on becoming a university professor and converted to a Lutheran. *TIS (image *cartographic-images.net)

1730 Jean-Baptiste-Gaspard Bochart de Saron (16 Jan 1730; 20 Apr 1794) French lawyer and natural scientist who pursued his interest in astronomy both as a productive amatuer and a patron. He assembled a significant collection of astronomical instruments made by renowned craftsmen. He both utilized then himself and gave access to his academic colleagues. In collaboration with Charles Messier, who provided the data, he calculated orbits of comets, helping his friend find them again after they had disappeared behind the sun. He funded the publication of Laplace's Theory of the Movement and Elliptic Figure of the Planets (1784). Bochart made calculations for what was at first called Herschel's comet, supposing a circular orbit at twelve time the Sun-Saturn distance. This was refined by Laplace, and contributed to the discovery of Uranus. Bochart died as a politician guillotined during the French Revolution.*TIS

1801 Thomas Clausen. (16 Jan 1801 in Snogbaek, Denmark - 23 May 1885 in Dorpat, Russia (now Tartu, Estonia)) In 1854 he factored the Fermat number F (6) = 2^2⁶ +1 as 274177 times 67280421310721, thus providing another counterexample to a conjecture of Fermat. (Euler factored F(5) in 1732.)*VFR Clausen wrote over 150 papers on pure mathematics, applied mathematics, astronomy and geophysics and worked with some of the best mathematicians of his day. *SAU

1807 Charles Henry Davis (16 Jan 1807; 18 Feb 1877) U.S. naval officer and scientist who published several hydrographic studies, was a superintendent of the Naval Observatory (1865–67, 1874–77) and worked to further scientific progress. Between his naval duties at sea, he studied mathematics at Harvard. He made the first comprehensive survey of the coasts of Massachusetts, Rhode Island, and Maine, including the intricate Nantucket shoals area. He helped establish and then supervised the preparation of the American Nautical Almanac (1849) for several years. Davis was a co-founder of the National Academy of Sciences (1863), and wrote several scientific books.*TIS

1906 Erich Kähler (16 January 1906, Leipzig – 31 May 2000, Wedel) was a German mathematician with wide-ranging geometrical interests.
As a mathematician he is known for a number of contributions: the Cartan–Kähler theorem on singular solutions of non-linear analytic differential systems; the idea of a Kähler metric on complex manifolds; and the Kähler differentials, which provide a purely algebraic theory and have generally been adopted in algebraic geometry. In all of these the theory of differential forms plays a part, and Kähler counts as a major developer of the theory from its formal genesis with Élie Cartan.
Kähler manifolds — complex manifolds endowed with a Riemannian metric and a symplectic form so that the three structures are mutually compatible — are named after him.
The K3 surface is named after Kummer, Kähler, and Kodaira.
His earlier work was on celestial mechanics; and he was one of the forerunners of scheme theory, though his ideas on that were never widely adopted.*Wik

1925 Germund Dahlquist (January 16, 1925 – February 8, 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations.*Wik

DEATHS
1547 Johannes Schöner (16 Jan 1477; 16 Jan 1547) German geographer who is noted for making and printing geographical globes. A notable work from 1515 is one of the earliest surviving globes produced following the discovery of new lands by Christopher Columbus. It was the first to show the name America that had been suggested by Waldseemüller. Tantalizingly, it also depicts a passage around South America before it was recorded as having been discovered by Magellan. Schöner was a professor mathematics at the University of Nuremberg and was the author of numerous mathematical, astronomical and geographical works. In his first career, he was an ordained Roman Catholic priest, which he gave up on becoming a university professor and converted to a Lutheran. *TIS

1834 Jean Nicolas Pierre Hachette was a French mathematician who worked on descriptive geometry. *SAU

1922 Pierre René Jean Baptiste Henri Brocard (12 May 1845 in Vignot (part of Commercy), France - 16 Jan 1922 in Bar-le-Duc, France) mathematician best known for his discovery of the so-called Brocard points of a triangle. His two major publications were the two volumes of Notes de bibliographie des corbes géométriques (1897, 1899) and the two volumes of Courbes géométriques remarkables the first of which was published in 1920, the second in 1967 long after his death. This last work was written in collaboration with T Lemoyne. The Notes may be regarded as a source book of geometric curves, with a painstakingly prepared index containing more than a thousand named curves. The text consists of brief descriptive paragraphs, with diagrams and equations of these curves. *SAU

1938 William Henry Pickering (15 Feb 1858, 16 Jan 1938) American astronomer who discovered Phoebe, the ninth moon of Saturn (1899). This was the first planetary satellite with retrograde motion to be detected, i.e., with orbital motion directed in an opposite sense to that of the planets. He set up a number of observing stations for Harvard. He made extensive observations of Mars and claimed, like Lowell, that he saw signs of life on the planet by observing what he took to be oases in 1892. He went further than Lowell however when in 1903 he claimed to observe signs of life on the Moon. By comparing descriptions of the Moon from Giovanni Riccioli's 1651 chart onward, he thought he had detected changes that could have been due to the growth and decay of vegetation.*TIS

1941 Charles Thurstan Holland (Mar 1863, 16 Jan 1941) English radiologist who pioneered the clinical use of X-rays in the UK, beginning shortly after Roentgen announced their discovery. He was present at the first clinical use of X-rays in England, (7 Feb 1896) in the laboratory of Oliver Lodge, head of the physics department at Liverpool University. The wrist of a 12-year-old boy who had shot himself the previous month was examined. The boy had been brought there by surgeon Sir Robert Jones who with Lodge reported the case in the 22 Feb 1896 of The Lancet. Jones subsequently financed an X-ray apparatus for Holland to pioneer radiology at Royal Southern Hospital, Liverpool. During WWI, he perfected methods of detecting bullets and shell fragments in patients' bodies. *TIS

1967 Robert Jemison Van de Graaff (20 Dec 1901; 16 Jan 1967) American physicist and inventor of the Van de Graaff generator, a type of high-voltage electrostatic generator that can be used as a particle accelerator in atomic research. The potential differences achieved in modern Van de Graaff generators can be up to 5 MV. It is a principle of electric fields that charges on a surface can leap off at points where the curvature is great, that is, where the radius is small. Thus, a dome of great radius will inhibit the electric discharge and added charge can reach a high voltage. This generator has been used in medical (such as high-energy X-ray production) and industrial applications (sterilization of food). In the 1950s, Van de Graaff invented the insulating core transformer able to produce high voltage direct current.*TIS

2000 Robert Rathbun Wilson (4 Mar 1914, 16 Jan 2000) was an American physicist who was the first director of Fermilab. From 1967, he led the design and construction of Fermilab (the Fermi National Accelerator Laboratory) near Chicago, Illinois. He also improved the environment by restoring prairie at the site. It began operating in 1972 with the world's most powerful particle accelerator. With later improvements, it retained that status for well over three decades until it was superceded by the LHC (Large Hadron Collider) at the CERN laboratory in Geneva, Switzerland. Wilson is remembered for his justification of the needed financing at a Senate hearing in 1969, where he said “It has nothing to do with defending our country, except to make it worth defending.” He resigned in 1978 because he did not believe the government was giving it sufficient funding for its research mission.*TIS

2002 Robert Hanbury Brown (31 Aug 1916, 16 Jan 2002) English astronomer who was a pioneer in radar and observational astronomy. During and after WW II he worked with R.A. Watson-Watt and then E.G. Bowen to develop radar for uses in aerial combat. In the 1950s he applied this experience to radio astronomy, developing radio-telescope technology at Jodrell Bank Observatory and mapping stellar radio sources. He designed a radio interferometer capable of resolving radio stars while eliminating atmospheric distortion from the image (1952). With R.Q. Twiss, Brown applied this method to measuring the angular size of bright visible stars, thus developing the technique of intensity interferometry. They set up an intensity interferometer at Narrabri in New South Wales, Australia, for measurements of hot stars.*TIS

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 15

2012-01-15T00:10:00.001Z

Today's science is tomorrow's technology.

~Edward Teller

The 15th day of the year; 15 is the maximum number of pieces that can be produced from a cylindrical cake with four planar slices. These are called "cake numbers" and the first four are 2, 4, 8, and 15. What comes next?

EVENTS
In 1759, the British Museum, in Bloomsbury, London, the world's oldest public national museum, opened to the public who were admitted in small groups, by ticket obtained in advance, for a conducted tour. It was established on 7 Jun 1753 when King George II gave his royal assent to an Act of Parliament on 5 Apr 1753 to acquire the collection of Sir Hans Sloane. (Sloan had only died a few months before, Jan 11, 1753.. and we must also thank Sloan for the invention of Hot Chocolate). In his will, he had offered the nation his lifetime collection of 71,000 objects, mostly plant and animal specimens. In return, he requested £20,000 for his heirs (which today would be over £2,000,000). The present museum buildings date from the mid-19th century. Its natural history collection moved to its own museum in 1881. The British Museum set up a laboratory in 1920 for its scientific studies. *TIS

1827 Only once, in a book review of 1816, did Gauss hint publically at his ideas on non-Euclidean Geometry. On this date Gauss wrote his friend Schumacher that their published ideas were “besmirched with mud” by critics. *VFR

In 1907, the three-element vacuum tube was issued a U.S. patent to its inventor, Dr Lee de Forest as a "device for amplifying feeble electric currents - such, for example, as telephone currents" (No. 841,387). The tube was evacuated, with some remaining conducting gas molecules, and it was suggested using for the heated electrode such material as platinum, tantalum or carbon. He had made a public annoucement of his device a few months earlier, on 20 Oct 1906 at a meeting of the American Institute of Electrical Engineers held in New York City. On 18 Feb 1908, he received another patent for the grid electrode tube (No. 879,532).*TIS

1934 Artiﬁcial radioactive substances are ﬁrst produced by husband and wife Pierre and Marie Joliet-Curie. *VFR

1941 The Des Moines Tribune pictured Cliﬀord Berry holding part of a machine that he and John V. Atanasoﬀ were building to solve systems of simultaneous linear equations. They expected it to contain 300 vacuum tubes when completed. [Goldstein, The Computer from Pascal to von Neumann, p. 124] *VFR (Image *Wik)

1943 The ﬁve-story, ﬁve-sided Pentagon, the world’s largest oﬃce building with 3.7 million square feet of oﬃce space, was completed after 16 months of round-the-clock labor. *VFR

1969 John Cocke, Michael Disney and Bob McCallister discover the ﬁrst optical pulsar. Inadvertently they tape recorded their own voices so this is perhaps the only recording of a scientific discovery as it was taking place. The whole story is available as an audio-visual package “An optical pulsar discovery.” [Center for the History of Physics Newsletter, vol. 16, no. 1, May 1984.] *VFR

1986 The National Science Foundation opens the National Center for Supercomputer Applications (NCSA) at the University of Illinois, a national “Center of excellence” for research into high-performance computing. Its most famous alumnus, Marc Andreesen, invented his Mosaic browser for the network known as the “World Wide Web” while a student there, an effort he later transformed into the Netscape browser company. *CHM

2006 The NASA spacecraft, Stardust, used an ultralight absorbent substance called aerogel to capture more than a million particles from a comet. The materials were returned to earth in a robotic capsule that descended in a parachute in Utah, in the USA on this date. The first images of the particles were released on the 20th of January. *NASA,

BIRTHS
1648 Henry Aldrich (15 Jan 1648 in Westminster, London, England - 14 Dec 1710 in London, England) was an English theologian and philosopher.He had wide interests including mathematics, music, and architecture. He was well known as a humorist and Suttle describes him as".. a punner of the first value. "
In 1674 he published Elementa geometricae which led to him being described by his Christ Church colleagues as ".. a great mathematician of our house."
In 1691 he published Artis logicae compendium a treatise on logic which was to be the main text on the topic for 150 years in England. Even when Richard Whately published Elements of logic in 1826 it still took Aldrich's work as his starting point. *SAU

1704 Johann Castillon (born Giovanni Francesco Melchiore Salvemini) (January 15 1704 in Castiglione , Tuscany , October 11 1791 in Berlin ) His ﬁrst two papers dealt with the cardiod, a curve which he named in 1741. *VFR He also dealt with conic sections and quadratic equations .
Castillon published exchange of letters between Gottfried Wilhelm Leibniz and Johann Bernoulli , edited works of Leonhard Euler and published a review of Newton's Arithmetica Universalis. He also translated Locke's basic concepts of physics into French. In 1753 he became a member of the Royal Society of London. *Wik He is also known for 'Castillon's problem' which is, "To inscribe in a given circle a triangle the sides of which pass through three given points."
This problem was posed by Gabriel Cramer and solved by Castillon in 1776. *SAU

1717 Matthew Stewart (15 Jan 1717 in Rothesay, Isle of Bute, Scotland - 23 Jan 1785 in Catrine, Ayrshire, Scotland)was a Scottish geometer who wrote on geometry and planetary motion. Stewart's fame is based on General theorems of considerable use in the higher parts of mathematics (1746), described by Playfair as, "... among the most beautiful, as well as most general, propositions known in the whole compass of geometry." *SAU

1814 Ludwig Schläfli (15 Jan 1814 in Grasswil, Bern, Switzerland - 20 March 1895 in Berne, Switzerland) Schläfli is best known for the so-called Schläfli symbols which are used to classify polyhedra. In this work, Theorie der vielfachen Kontinuität (Theory of continuous manifolds), Schläfli introduced polytopes (although he uses the word polyschemes) which he defines to be higher dimensional analogues of polygons and polyhedra. Schläfli introduced what is today aclled the Schläfli symbol. It is defined inductively. {n} is a regular n-gon, so {4} is a square. There {4, 3} is the cube, since it is a regular polyhedron with 3 squares {4} meeting at each vertex. Then the 4 dimensional hypercube is denoted as {4, 3, 3}, having three cubes {4, 3} meeting at each vertex. Euclid, in the Elements, proves that there are exactly five regular solids in three dimensions. Schläfli proves that there are exactly six regular solids in four dimensions {3, 3, 3}, {4, 3, 3}, {3, 3, 4}, {3, 4, 3}, {5, 3, 3}, and {3, 3, 5}, but only three in dimension n where n ≥ 5, namely {3, 3, ..., 3}, {4, 3, 3, ....,3}, and {3, 3, ...,3, 4}.
Most of Schläfli's work was in geometry, arithmetic and function theory. He gave the integral representation of the Bessel function and of the gamma function. His eight papers on Bessel functions played an important role in the preparation of G N Watson's major text Treatise on the theory of Bessel functions (1944). *SAU

1815 Warren De la Rue (15 Jan 1815; 19 Apr 1889) English astronomer who pioneered in astronomical photography, the method by which nearly all modern astronomical observations are made. *TIS In 1851 his attention was drawn to a daguerreotype of the Moon by G. P. Bond,(see births, 1825) shown at the great exhibition of that year. Excited to emulation and employing the more rapid wet-collodion process, he succeeded before long in obtaining exquisitely defined lunar pictures, which remained unsurpassed until the appearance of the Lewis Morris Rutherfurd photographs in 1865.
In 1854 he turned his attention to solar physics, and for the purpose of obtaining a daily photographic representation of the state of the solar surface he devised the photoheliograph, described in his report to the British Association, On Celestial Photography in England (1859), and in his Bakerian Lecture (Phil. Trans. vol. clii. pp. 333–416). Regular work with this instrument, inaugurated at Kew by De la Rue in 1858, was carried on there for fourteen years; and was continued at the Royal Observatory, Greenwich, from 1873 to 1882. *Wik

1850 Sonya Kovalevsky (Sofya Vasilyevna Kovalevskaya) (15 Jan 1850; 10 Feb 1891). Her bedroom was wallpapered with the pages of a text from her father’s schooldays, namely, Ostrogradsky’s lithographed lecture notes on the calculus. Study of the novel wallpaper introduced her to the calculus at age 11. She became the greatest woman mathematician prior to the twentieth century. *VFR a Russian mathematician and novelist who made valuable contributions to the theory of differential equations.*TIS

1877 Lewis M(adison) Terman (15 Jan 1877; 21 Dec 1956) was a U.S. psychologist who pioneered individual intelligence tests. During WW I, he was involved in mass testing of intelligence for the U.S. army. He expanded an English version of the French Binet-Simon intelligence test with which he introduced the IQ (Intelligence Quotient), being a ratio of chronological age to mental age times 100. (Thus an average child has an IQ of 100). He wrote about this metric in The Measurement of Intelligence (1916). He made a long-term study of gifted children (with IQ above 140) examining mental and physical aspect of their lives reported in the multi-volume Genetic Studies of Genius (1926-59).*TIS

1883 James Mercer FRS (15 January 1883 – 21 February 1932) was a mathematician, born in Bootle, close to Liverpool, England. He was educated at University of Manchester, and then University of Cambridge. He became a Fellow, saw active service at the Battle of Jutland in World War I, and after decades of suffering ill health died in London, England.
He proved Mercer's theorem, which states that positive definite kernels can be expressed as a dot product in a high-dimensional space. This theorem is the basis of the kernel trick (applied by Aizerman), which allows linear algorithms to be easily converted into non-linear algorithms. *Wik

1900 Richard Bevan Braithwaite (15 Jan 1900; 21 Apr 1990) was an English philosopher who trained in physics and mathematics, but turned to the philosophy of science. He examined the logical features common to all the sciences. Each science proceeds by inventing general principles from which are deduced the consequences to be tested by observation and experiment. Braithwaite was concerned with the impact of science on our beliefs about the world and the responses appropriate to that. He wrote on the statistical sciences, theories of belief and of probability, decision theory and games theory. He was interested in particular with the laws of probability as they apply to the physical and biological sciences.*TIS

1908 Edward Teller (15 Jan 1908; 9 Sep 2003) Hungarian-American nuclear physicist who participated in the production of the first atomic bomb (1945) and who led the development of the world's first thermonuclear weapon, the hydrogen bomb. After studying in Germany he left in 1933, going first to London and then to Washington, DC. He worked on the first atomic reactor, and later working on the first fission bombs during WW II at Los Alamos. Subsequently, he made a significant contribution to the development of the fusion bomb. His work led to the detonation of the first hydrogen bomb (1952). He is sometimes known as “the father of the H-bomb.” Teller's unfavourable evidence in the Robert Oppenheimer security-clearance hearing lost him some respect amongst scientists. *TIS

1918 David George Kendall (15 Jan 1918 in Ripon, Yorkshire, England - 23 Oct 2007 in Cambridge, England) was a leading world authority on applied probability and data analysis. *SAU

DEATHS
1790 John Landen (23 Jan 1719, 15 Jan 1790) British mathematician who made important contributions on elliptic integrals. As a trained surveyor and land agent (1762-88), Landen's interest in mathematics was for leisure. He sent his results on making the differential calculus into a purely algebraic theory to the Royal Society, and also wrote on dynamics, and summation of series. Landen devised an important transformation, known by his name, giving a relation between elliptic functions which expresses a hyperbolic arc in terms of two elliptic ones. He also solved the problem of the spinning top and explained Newton's error in calculating the precession. Landen was elected a Fellow of the Royal Society in 1766. He corrected Stewart's result on the Sun-Earth distance (1771).*TIS

1945 Wilhelm Wirtinger (15 July 1865 – 15 January 1945) was an Austrian mathematician, working in complex analysis, geometry, algebra, number theory, Lie groups and knot theory. He worked in many areas of mathematics: according to Hornich (1948) he authored 71 works. His first significant work, published in 1896, was on theta functions. He proposed a generalization of eigenvalues, the spectrum of an operator, in an 1897 paper; the concept was extended by David Hilbert into spectral theory. Wirtinger also contributed papers on complex analysis, geometry, algebra, number theory, and Lie groups. He collaborated with Kurt Reidemeister on knot theory, showing in 1905 how to compute the knot group (fundamental group of a knot complement). Also, he was one of the editors of the Analysis section of Klein's encyclopedia.
Among his students were Wilhelm Blaschke, Leopold Vietoris, Erwin Schrödinger, Olga Taussky-Todd, and Kurt Gödel.*Wik

1948 Henri-Alexandre Deslandres (24 Jul 1853, 15 Jan 1948)French astrophysicist who invented a spectroheliograph (1894) to photograph the Sun in monochromatic light (about a year after George E. Hale in the U.S.) and made extensive studies of the solar chromosphere and solar activity. He worked at the Paris and Meudon Observatories. His investigation of molecular spectra produced empirical laws presaging those of quantum mechanics. He observed spectra of planets and stars and measured their radial velocities of, and he determined the rotation rates of Uranus, Jupiter and Saturn (shortly after James E. Keeler).*TIS

1958 Aurel Friedrich Wintner (8 April 1903 in Budapest, Hungary - 15 Jan 1958 in Baltimore, Maryland, USA) studied at Budapest and Leipzig. He spent most of his career in Johns Hopkins University in Baltimore, USA. He published on Number Theory, Differential Equations, Probability and Celestial Mechanics. Along with Poincaré and George Birkhoff, he placed celestial mechanics on a more sound mathematical basis.*SAU

1968 Leopold Infeld (20 Aug 1898 in Kraków, Poland - 15 Jan 1968 in Warsaw, Poland) was a Polish theoretical physicist In 1948 he published Whom the Gods Love, a biographical novel about Evariste Galois. *VFR Leopold Infeld went to England as a Fellow of the Rockefeller Foundation. In Cambridge he met Rutherford and Dirac and entered into the collaboration with Max Born, who had just arrived in England. The result of this collaboration was the Born-Infeld electrodynamics. In Princeton, Infeld collaborated with Einstein writing a popular text Evolution of Physics (1938).*SAU

1973 Ivan Georgievich Petrovsky (18 Jan 1901 in Sevsk, Orlov guberniya, Russia - 15 Jan 1973 in Moscow, USSR) Petrovsky's main mathematical work was on the theory of partial differential equations, the topology of algebraic curves and surfaces, and probability. Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov.*SAU

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 14

2012-01-14T00:10:00.004Z

*Wik

The invention of logarithms, by shortening the labors, double the life of the astronomer.

~Laplace

The 14th day of the year; there are exactly the same number of composite and prime numbers less than fourteen. There is no larger number for which that is true.

EVENTS
1667/8 In his diary Samuel Pepys mentions a “very pretty, but not very useful” arithmetical machine devised by Sir. Samuel Morland (1625–1695 or 6). After a successful diplomatic career under Cromwell, Morland was appointed salaried “Master of Mechanics” to the King and devoted the rest of his life to instrument making. *Oldenburg Correspondence, 9, 432,

1980 Robert J. Griess, Jr. announced that he had constructed the conjectured sporadic simple group F1 known as the “monster.” This group consists 808,017,424,794,512,875,886,459,904, 961,710,757,005,754,368,000,000 square matrices each of size 196,883 by 196,883. This led to the completion of the classiﬁcation of the ﬁnite simple groups. [Mathematics Magazine 53(1980),
p. 253 and 54(1981), p. 41]. *VFR

BIRTHS
1806 Matthew Fontaine Maury (14 Jan 1806; 1 Feb 1873) As a U.S. naval officer, Maury was a pioneer hydrographer. He was the first person to undertake a systematic and comprehensive study of the ocean. His work on oceanography and navigation led to an international conference (Brussels, 1853) the first ever of its kind in the world. In 1855, during the Western gold rush, Maury’s updated information helped sea captains cut a ship’s average travel time from New York to San Francisco from 180 to 133 days. That same year, Maury prepared a report that proved the practicality — and assured the success — of the first trans-Atlantic cable between the United States and Europe. Maury was director of the U.S. Naval Observatory from 1844 to 1861. *TIS

1819 James Cockle (14 Jan 1819 in Great Oakley, Essex, England - 27 Jan 1895 in Bayswater, London, England) Cockle was remarkably productive as a mathematician publishing over 100 papers. He wrote papers on both pure and applied mathematics, as well as on the history of science. On the former topic he wrote on fluid dynamics and magnetism. Most of his work, however, was in pure mathematics where he studied algebra, the theory of equations, and differential equations. He had a collaborator on mathematical work, a Congregationalist minister named Robert Harley. *SAU

1887 Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach-Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.
Author of around 170 scientific articles and books, Steinhaus has left its legacy and contribution on many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early founders of the game theory and the probability theory preceding in his studies, later, more comprehensive approaches, by other scholars. *Wik
His Mathematical Snapshots is a delight to read, but get the ﬁrst English edition if you can—there are lots of surprises there. *VFR

1902 Alfred Tarski, (14 Jan 1902; 26 Oct 1983) Polish-born American mathematician and logician who made important studies of general algebra, measure theory, mathematical logic, set theory, and metamathematics. Formal scientific languages can be subjected to more thorough study by the semantic method that he developed. He worked on model theory, mathematical decision problems and with universal algebra. He produced axioms for "logical consequence", worked on deductive systems, the algebra of logic and the theory of definability. Group theorists study 'Tarski monsters', infinite groups whose existence seems intuitively impossible. *TIS

1919 Nathaniel Rochester, The chief architect of IBM's first scientific computer, the 701, is born. Rochester also developed the prototype for the IBM 702, the growing company's first commercial computer. Both machines signaled IBM’s slow transition from its lucrative punch card accounting business to markets based on developments in electronics resulting from WW II research and development. *CHM

1924 Linards Eduardovich Reizins (14 Jan 1924 in Riga, Latvia - 1991 in Latvia) Of the many other important contributions made by Reizins we should mention in particular his work on Pfaff's equations and his contributions to the history of mathematics. In particular he edited the Complete Works of Piers Bohl which was published in 1974. Other important historical papers include Mathematics in University of Latvia 1919-1969 (1975, joint with E Riekstins) and From the History of the General Theory of Ordinary Differential Equations (1977). *SAU

DEATHS
1679 Jacques de Billy (18 March 1602 in Compiègne, France - 14 Jan 1679 in Dijon, France) was a French Jesuit. Billy corresponded with Fermat and produced a number of results in number theory which have been named after him. Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum (New discovery in the art of analysis) as an annex to his edition of the Arithmetica of Diophantus (1670). *SAU

1687Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his Germanic name Kauffmann, was a 17th-century mathematician. He lived in the Netherlands from 1642 to 1648. He lectured at the University of Copenhagen during 1648–1654 and lived in Paris from 1655 to 1657. He was mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth, Sussex (1657). He taught mathematics in London (1658–1682). In 1666 he became a member of the Royal Society. He designed a marine chronometer for Charles II, and designed and constructed the fountains at the Palace of Versailles (1682–1687).
Mathematically, he is most well known for his treatise Logarithmo-technica on logarithms, published in 1668. In this treatise he described the Mercator series, also independently discovered by Gregory Saint-Vincent:

It was also in this treatise that the first known use of the term natural logarithm appears, in the Latin form log naturalis. His use of this term is somewhat surprising, since it predates the development of infinitesimal calculus, in which the most natural properties of this logarithm appear.
To the field of music he contributed the first precise account of 53 equal temperament, which was of theoretical importance, but not widely practiced. *Wik
In 1683 he accepted Colbert’s commission to plan the waterworks at Versailles. Payment was contingent upon turning Catholic. This he refused to do and soon died of frustration and poverty. * VFR He gave the first accepted derivation of Kepler's 2nd Law. *@Rmathematicus, Twitter

1742 Edmund Halley (8 Nov 1656, 14 Jan 1742) He is best known for his accurate prediction that the comet of 1682 would return in 1758. The BAYEUX TAPESTRY (Tapisserie de la Reine Mathilde) includes a clear picture of Halley's Comet.*VFR
He became professor of geometry at Oxford and was later appointed the second Astronomer Royal. After originating the question that prodded Newton to write the Principia, Halley edited and arranged the publication of this seminal work. Halley identified the proper motion of stars, studied the moon's motion and tides, realized that nebulae were clouds of luminous gas among the stars, and that the aurora was associated with the earth's magnetism. His prediction of the transit of Venus led to Cook's voyage to Tahiti.*TIS
Halley was buried in the graveyard of the old church of St. Margaret, Lee (in London). In the same vault is Astronomer Royal John Pond; the unmarked grave of Astronomer Royal Nathaniel Bliss is nearby. *Wik

1753 Bishop George Berkeley (12 March 1685 in Kilkenny, County Kilkenny, Ireland
- 14 Jan 1753 in Oxford, England). In 1734 he published The Analyst, Or a Discourse Addressed to an Inﬁdel Mathematician (namely, Edmund Halley). This work was a strong and reasonably justiﬁed attack on the foundation of the diﬀerential calculus. He called diﬀerentials “the ghosts of departed quantities.” *VFR

1814 Charles Bossut (11 Aug 1730 in Tartaras (near Rive de Gier), Rhône-et-Loire, France - 14 Jan 1814 in Paris, France) Bossut is famed for his textbooks which were widely used throughout France. He wrote his first textbook Traité élémentaire de méchanique et de dinamique appliqué principalement aux mouvements des machines (1763) while at the École du Génie. He also published the more famous Cours complet de mathematiques in 1765. The economist Turgot, Baron De L'Aulne, was appointed 'comptroller general' of France by Louis XVI on 24 August 1774. Among his first actions was the creation of a chair of hydrodynamics at the Louvre, where he himself had studied. Turgot's friend the Marquis de Condorcet, who he had appointed as Inspector General of the Mint, may well have influenced him to create the chair. Since Condorcet and Bossut were close collaborators it may have essentially been created for Bossut who certainly was appointed and filled it until 1780. In 1775 Bossut participated with d'Alembert and Condorcet in experiments on fluid resistance. Also during this period he was editing an edition of the works of Pascal which was published in five volumes in 1779.
He was later to collaborate with d'Alembert on the mathematical part of Diderot's Encyclopédie méthodique. Also later in his career he wrote Méchanique en général (1792) and his treatise on the history of mathematics in two volumes Essai sur l'histoire générale des mathématique (1802). *SAU

1898 Charles Lutwidge Dodgson, pen-name Lewis Carroll (27 Jan 1832, 14 Jan 1898), was an English logician, mathematician, photographer, and novelist, remembered for Alice's Adventures in Wonderland (1865) and its sequel. After graduating from Christ Church College, Oxford in 1854, Dodgson remained there, lecturing on mathematics and writing treatises until 1881. As a mathematician, Dodgson was conservative. He was the author of a fair number of mathematics books, for instance A syllabus of plane algebraical geometry (1860). His mathematics books have not proved of enduring importance except Euclid and his modern rivals (1879) which is of historical interest. As a logician, he was more interested in logic as a game than as an instrument for testing reason.*TIS (I once read that if Dodgson had not written "Alice", he would be remembered today for his photography, and if he had not done either of those, then, if he was remembered at all, it would be for his logic book. One of my favorite Lewis Carroll stories is about his gift of a book to Queen Victoria. Here is the version as it is told on the Mathworld page):

Several accounts state that Lewis Carroll (Charles Dodgson ) sent Queen Victoria a copy of one of his mathematical works, in one account, An Elementary Treatise on Determinants. Heath (1974) states, "A well-known story tells how Queen Victoria, charmed by Alice in Wonderland, expressed a desire to receive the author's next work, and was presented, in due course, with a loyally inscribed copy of An Elementary Treatise on Determinants," while Gattegno (1974) asserts "Queen Victoria, having enjoyed Alice so much, made known her wish to receive the author's other books, and was sent one of Dodgson's mathematical works." However, in Symbolic Logic (1896), Carroll stated, "I take this opportunity of giving what publicity I can to my contradiction of a silly story, which has been going the round of the papers, about my having presented certain books to Her Majesty the Queen. It is so constantly repeated, and is such absolute fiction, that I think it worth while to state, once for all, that it is utterly false in every particular: nothing even resembling it has occurred" (Mikkelson and Mikkelson)

1901 Charles Hermite (24 Dec 1822, 14 Jan 1901) French mathematician whose work in the theory of functions includes the application of elliptic functions to provide the first solution to the general equation of the fifth degree, the quintic equation. In 1873 he published the first proof that e is a transcendental number. Hermite is known also for a number of mathematical entities that bear his name, Hermite polynomials, Hermite's differential equation, Hermite's formula of interpolation and Hermitian matrices. Poincaré is the best known of Hermite's students.*TIS

1905 Ernst Abbe (23 Jan 1840, 14 Jan 1905) German physicist who made theoretical and technical innovations in optical theory. He improved microscope design, such as the use of a condenser lens to provide strong, even illumination (1870). His optical formula, now called the Abbe sine condition, applies to a lens to form a sharp, distortion-free image He invented the Abbe refractometer for determining the refractive index of substances. In 1866, he joined Carl Zeiss' optical works, later became his partner in the company, and in 1888 became the owner of the company upon Zeiss' death. Concurrently, he was appointed professor at the Univ. of Jena in 1870 and director of its astronomical and meteorological observatories in 1878.*TIS His monument at Jenna has the formula for the diffraction limit which he found. (image http://www.w-volk.de/museum)

1912 Arnold Droz-Farny (12 Feb 1856 in La Chaux-de-Fonds, Switzerland - 14 Jan 1912 in Porrentruy, Switzerland) Droz-Farny is best known for results published in the publications of 1899 and 1901 mentioned in this quote. The first of these was Question 14111 in The Educational Times 71 (1899), 89-90. In this he stated the following remarkable theorem without giving a proof:
If two perpendicular straight lines are drawn through the orthocentre of a triangle, they intercept a segment on each of the sidelines. The midpoints of these three segments are collinear.
This is known as the Droz-Farny line theorem, but it is not known whether Droz-Farny had a proof of the theorem. Looking at other work by Droz-Farny, one is led to conjecture that indeed he would have constructed a proof of the theorem. The 1901 paper we mentioned above is, for example, one in which he gives a proof of a theorem stated by Steiner without proof. Droz-Farny's proof appears in the paper Notes sur un théorème de Steiner in Mathesis 21 (1901), 268-271. The theorem is as follows:
If equal circles are drawn on the vertices of a triangle they cut the lines joining the midpoints of the triangle in six points. These six points lie on a circle whose centre is the orthocentre of the triangle.
Droz-Farny died "a long and painful disease".
See this page at Cut-The-Knot for more detail *SAU

1914 Benjamin Osgood Peirce (11 February 1854 Beverly, Massachusetts, USA — 14 January 1914 Cambridge, Massachusetts, USA) was an American mathematician and a holder of the Hollis Chair of Mathematics and Natural Philosophy at Harvard from 1888 until his death in 1914.*Wik

1931 William Ernest Johnson (June 23, 1858 – January 14, 1931) was a British logician mainly remembered for his Logic (1921–1924), in 3 volumes.
He taught at King's College, Cambridge for nearly thirty years. He wrote a bit on economics, and John Maynard Keynes was one of his students. Johnson was a colleague of Keynes's father, John Neville Keynes.
Logic was dated at the time of its publication, and Johnson can be seen as a member of the British logic "old guard" pushed aside by the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. But an article entitled "The Logical Calculus" (Johnson 1892) reveals that he had nontrivial technical capabilities in his youth, and that he was significantly influenced by the formal logical work of Charles Sanders Peirce. *Wik

1970 William (Vilim) Feller born Vilibald Srećko Feller (July 7, 1906 – January 14, 1970), was a Croatian-American mathematician specializing in probability theory. Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators". *Wik

1978 Kurt Gödel (28 Apr 1906, 14 Jan 1978)Austrian-born U.S. mathematician, logician, and author of Gödel's proof. He is best known for his proof of Gödel's Incompleteness Theorems (1931) He proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved. This ended a hundred years of attempts to establish axioms to put the whole of mathematics on an axiomatic basis. *TIS
In later life, Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he would only eat food his wife, Adele, prepared for him. Late in 1977, Adele was hospitalized for six months and could no longer prepare Gödel's food. In her absence, he refused to eat, eventually starving to death. He weighed 65 pounds (approximately 30 kg) when he died. His death certificate reported that he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978 *Wik

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 13

2012-01-13T00:10:00.005Z

On two occasions I have been asked [by members of Parliament], 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.
~ Charles Babbage

The 13th day of the year; there are 13 Archimedian Solids. (different from the Platonic solids, which are have only one type of polygon meeting in identical vertices)

EVENTS
In 1404, English alchemists were forbidden to use their knowledge to create precious metals. Since the time of Roger Bacon, it had fascinated the imagination of many ardent men in England. During the reign of Henry IV, the Act of Multipliers was passed by the Parliament, declaring the use of transmutation to "multiply" gold and silver to be felony. Great alarm was felt at that time lest any alchymist should succeed in his projects, and perhaps bring ruin upon the state, by furnishing boundless wealth to some designing tyrant, who would make use of it to enslave his country. In 1689, Robert Boyle lobbied for repeal of the Act.*TIS

1610 Galileo discovers a fourth moon (Callisto) of Jupiter. Galileo initially named his discovery the Cosmica Sidera ("Cosimo's stars"), but names that eventually prevailed were chosen by Simon Marius. Marius discovered the moons independently at the same time as Galileo, and gave them their present names, which were suggested by Johannes Kepler, in his Mundus Jovialis, published in 1614.*Wik

1659 Hendrik van Heuraet sends van Schooten his rectiﬁcation of the semi-cubical parabola. This was published—his only publication—in the second Latin edition of Descartes’s Geometrie. This result broke the spell of Aristotle’s dictum that curved lines could not in principle be compared with straight lines. *VFR

1874 The U.S. Patent Office issues a patent for the Spalding Adding Machine. The precursor of calculators and computers, mechanical adding machines could do simple arithmetic and were popular in businesses until supplanted by computers in the 1960s. *CHM

1911 A. V. Vasil’ev gave a lecture entitled, “Non-Euclidean Geometry and the Non-Aristotelian Logic.” This is his claim to the discovery of three-valued logics. He did not work out the system in detail, so credit usually goes to LLukasiewicz. *VFR

In 1958, Linus Pauling (1901-1994) presented the petition of 9,000 scientists to the U.N., asking to halt the testing of nuclear bombs. Pauling, together with his wife, was instrumental in collecting thousands of signatures from scientists all over the world for the petition to end nuclear bomb testing, which was presented to Dag Hammarskjöld, secretary general of the United Nations. A few months later the Soviet Union called for an immediate halt to nuclear testing, and in October, after more tests by both sides that added markedly to world concern about fallout, talks began in Geneva to discuss details of a possible test ban. *TIS

2012 Friday the Thirteenth will occur three times this year, today, in April, and again in July. At least one Friday the 13th will occur each year, and never more than three. This year the three Fridays occur as densely packed as they can possibly be. The last year with three Friday the 13ths was 2009, and the next will be 2015. There seems to be no written evidence of the superstition in English until 1869. Interestingly, the Spanish and Greek Cultures have a similar tradition about Tuesday the 13th. *Wik

2012 Not Unlucky for some... Friday, January 13, 2012 the Institute for Advanced Studies Princeton, New Jersey announced:

The 2012 Wolf Prize in Physics has been awarded to Jacob D. Bekenstein, former Member (2009–10) in the School of Natural Sciences, for his work on black holes. Bekenstein is Polak Professor of Theoretical Physics at the Racah Institute of Physics, Hebrew University of Jerusalem. The 2012 Wolf Prize in Mathematics has been awarded to Michael Aschbacher, former Member (1978–79) in the School of Mathematics, for his work on the theory of finite groups, and Luis Caffarelli, former Professor (1986–96) and Member (2009) in the School of Mathematics, for his work on partial differential equations. Aschbacher is the Shaler Arthur Hanisch Professor of Mathematics at the California Institute of Technology. Caffarelli is Professor of Mathematics at the University of Texas, Austin. The awards will be presented in May at the Knesset in Jerusalem.

BIRTHS
1845 François-Félix Tisserand (13 Jan 1845; 20 Oct 1896) was a French astronomer whose 4-volume textbook Traité de mécanique céleste (1889-96; "Treatise on Celestial Mechanics") updated Pierre-Simon Laplace's work. At age 28, he was named Director at Toulouse Observatory (1873-78). He went to Japan to observe the 1874 transit of Venus. The 83-cm telescope he installed at the Toulouse Observatory in 1875 had a wooden base insufficiently stable for photographic work, but he was able to use it for observation of the satellites of Jupiter and of Saturn. From 1892 until his death he was director of the Paris Observatory, where he completed the major work, Catalogue photographique de la carte du ciel, and arranged for its publication. *TIS

1864 Wilhelm Wien (13 Jan 1864; 30 Aug 1928) German physicist who received the Nobel Prize for Physics in 1911 for his displacement law concerning the radiation emitted by the perfectly efficient blackbody (a surface that absorbs all radiant energy falling on it). While studying streams of ionized gas Wien, in 1898, identified a positive particle equal in mass to the hydrogen atom. Wien, with this work, laid the foundation of mass spectroscopy. J. J. Thomson refined Wien's apparatus and conducted further experiments in 1913 then, after work by Ernest Rutherford in 1919, Wien's particle was accepted and named the proton. Wien also made important contributions to the study of cathode rays, X-rays and canal rays.*TIS

1876 Erhard Schmidt (13 January 1876 – 6 December 1959) was a German mathematician whose work significantly influenced the direction of mathematics in the twentieth century. He was born in Tartu, Governorate of Livonia (now Estonia). His advisor was David Hilbert and he was awarded his doctorate from Georg-August University of Göttingen in 1905. His doctoral dissertation was entitled Entwickelung willkürlicher Funktionen nach Systemen vorgeschriebener and was a work on integral equations.
Together with David Hilbert he made important contributions to functional analysis. He is best known for the Gram-Schmidt orthogonalisation process, which constructs an orthogonal base from any vector space. *Wik

1876 Luther Pfahler Eisenhart (13 January 1876 – 28 October 1965) was an American mathematician, best known today for his contributions to semi-Riemannian geometry.
Eisenhart played a central role in American mathematics in the early twentieth century. He served as chairman of the mathematics department at Princeton University and later as Dean of the Graduate School there. He is widely credited with guiding the development in America of the mathematical background needed for the further development of general relativity, through his influential textbooks and his personal interaction with Albert Einstein, Oswald Veblen, and John von Neumann at the nearby Institute for Advanced Study, as well as with gifted students such as Abraham Haskel Taub. *Wik

1900 Gertrude Mary Cox (January 13, 1900 – October 17, 1978) was an influential American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of the Consolidated University of North Carolina and the Statistics Research Division of North Carolina State University. Her most important and influential research dealt with experimental design; she wrote an important book on the subject with W. G. Cochran. In 1949 Cox became the first female elected into the International Statistical Institute and in 1956 she was president of the American Statistical Association.*Wik The choice of a woman to hold such a post was unusual at that time and came about in a curious way. G W Forster of North Carolina State College contacted Professor Snedecor for names of individuals who would be viable candidates for the position. Professor Snedecor prepared a list of persons (all males) and before mailing it to Dr Forster showed the list to Miss Cox. Her immediate reaction was, "Why didn't you put my name on the list?" Her name was then added in a footnote to the letter, "Of course if you would consider a woman for this position I would recommend Gertrude Cox of my staff." The choice of a woman on the basis of a footnote was an administrative decision which had far-reaching effects. *SAU

1902 Karl Menger (Vienna, Austria, January 13, 1902 – Highland Park, Illinois, U.S.A., October 5, 1985) was a mathematician. He was the son of the famous economist Carl Menger. He is credited with Menger's theorem. He worked on mathematics of algebras, algebra of geometries, curve and dimension theory, etc. Moreover, he contributed to game theory and social sciences. He is remembered for the creation of the Menger Sponge*Wik

DEATHS
1614 Jeremiah Horrocks (1618, 13 Jan 1641) (some sources give 3 Jan as date of death, England had not converted to Gregorian Calendar) English astronomer and clergyman who applied Johannes Kepler's laws of planetary motion to observations of the Moon and Venus. Once Horrocks managed to obtain a small telescope, his observations convinced him that Lansberg's tables were incorrect. He accepted Kepler's elliptical orbits, and in working on the moon he applied an elliptical orbit to it and established that the line of apsides precessed, an effect which he ascribed to the influence of the sun. Horrocks predicted and observed a transit of Venus on 24 Nov 1639, the first one ever observed, and from the observation he corrected the solar parallax, indicating a much greater distance of the sun than anyone before him had admitted. He died at age only 22.*TIS The only person to predict, and one of only two people to observe and record, the transit of Venus of 1639, which was the first transit of Venus to be convincingly predicted and observed. *Wik
Thony Christie has stated that the "clergyman" notation is incorrect. *@rmathematicus, Twitter

1934 Paul Urich Villard (28 Sep 1860, 13 Jan 1934) was a French physicist and chemist who in 1900 identified a third kind of natural radiation, later called gamma rays. He was studying the radiations from uranium salts discovered by Henri Becquerel four years before. Charged particles whose paths were bent in a magnetic field were known, but Villard found a form of penetrating radiation that was not deviated, but it drew little attention from contemporary scientists. A year before, in 1899, Ernest Rutherford named the first two kinds of natural radiation—positive alpha particles and negative beta rays. The third kind became known as gamma rays—with energy higher than X-rays, weak power of ionization, and which Rutherd characterized (1914) as a form of electromagnetic radiation, like light. Villard invented several radiological instruments, including the osmoregulator and Villard's valve. He researched hydrates, and discovered silver hydrate. He wrote Les Rayons Cathodiques (1900). *TIS

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

2012-01-12T18:27:00.000Z

Just came across a James Tanton blog that has some nice extensions of the old joke about bad cancellations in fractions. I used to show my students that you could simplify 16/64 by just crossing out the sixes to get 1/4. Among the similar type examples that he gives in the blog is the rather clever:

Cancel all the common numerals top and bottom and get...

See it all here, and enjoy

2012-01-12T00:28:00.000Z

I came across an account of this interview in "Eurekas and Euphorias" by Walter Gratzer, but found this copy on a web page from Rutgers which has not been updated since 2004.... Dirac was famous as a man of extremely few words:

ROUNDY INTERVIEWS PROFESSOR DIRAC

An Enjoyable Time Is Had By All

By Roundy I been hearing about a fellow they have up at the U. this spring --- a mathematical physicist, or something, they call him --- who is pushing Sir Isaac Newton, Einstein and all the others off the front page. So I thought I better go up and interview him for the benefit of State Journal readers, same as I do all other top notchers. His name is Dirac and he is an Englishman. He has been giving lectures for the intelligentsia of math and physics departments --- and a few other guys who got in by mistake.
So the other afternoon I knocks at the door of Dr. Dirac's office in Sterling Hall and a pleasant voice says "Come in." And I want to say here and now that this sentence "come in" was about the longest one emitted by the doctor during our interview. He sure is all for efficiency in conversation. It suits me. I hate a talkative guy. I found the doctor a tall youngish-looking man, and the minute I seen the twinkle in his eye I knew I was going to like him. His friends at the U. say he is a real fellow too and a good company on a hike --- if you can keep him in sight, that is.
The thing that hit me in the eye about him was that he did not seem to be at all busy. Why if I went to interview an American scientist of his class --- supposing I could find one --- I would have to stick around an hour first. Then he would blow in carrying a big briefcase, and while he talked he would be pulling lecture notes, proof, reprints, books, manuscript, or what have you out of his bag. But Dirac is different. He seems to have all the time there is in the world and his heaviest work is looking out the window. If he is a typical Englishman it's me for England on my next vacation!
Then we sat down and the interview began.
"Professor," says I, "I notice you have quite a few letters in front of your last name. Do they stand for anything in particular?"
"No," says he.
"You mean I can write my own ticket?"
"Yes," says he.
"Will it be all right if I say that P.A.M. stands for Poincare' Aloysius Mussolini?"
"Yes," says he.
"Fine," says I, "We are getting along great! Now doctor will you give me in a few words the low-down on all your investigations?"
"No," says he.
"Good," says I. "Will it be all right if I put it this way --- `Professor Dirac solves all the problems of mathematical physics, but is unable to find a better way of figuring out Babe Ruth's batting average'?"
"Yes," says he.
"What do you like best in America?", says I.
"Potatoes," says he.
"Same here," says I. "What is your favorite sport?"
"Chinese chess," says he.
That knocked me cold! It was sure a new one on me! Then I went on: "Do you go to the movies?"
"Yes," says he.
"When?", says I.
"In 1920 --- perhaps also in 1930," says he.
"Do you like to read the Sunday comics?"
"Yes," says he, warming up a bit more than usual.
"This is the most important thing yet, doctor," says I. "It shows that me and you are more alike than I thought. And now I want to ask you something more: They tell me that you and Einstein are the only two real sure-enough high-brows and the only ones who can really understand each other. I wont ask you if this is straight stuff for I know you are too modest to admit it. But I want to know this --- Do you ever run across a fellow that even you can't understand?"
"Yes," says he.
"This well make a great reading for the boys down at the office," says I. "Do you mind releasing to me who he is?"
"Weyl," says he.
The interview came to a sudden end just then, for the doctor pulled out his watch and I dodged and jumped for the door. But he let loose a smile as we parted and I knew that all the time he had been talking to me he was solving some problem that no one else could touch.
But if that fellow Professor Weyl ever lectures in this town again I sure am going to take a try at understanding him! A fellow ought to test his intelligence once in a while.

On This Day in Math - Jan 12

2012-01-12T00:10:00.000Z

Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.
~Hermann Minkowski

The 12th day of the year; 12 is the smallest abundant number (number whose proper factors add up to more than the number itself). It is also the largest number of spheres that may be in contact with a given sphere in 3-D (This is not trivial, Newton couldn't prove it). See Kissing Number.

EVENTS
1721 John Hadley showed up at a meeting of the Royal Society with a reﬂecting telescope six feet long which magniﬁed 200 times and was made according to Newton’s plan. *VFR

1820 Founding of the Royal Astronomical Society of England. Charles Babbage was one of the founding members. *Goldstine, The Computer from Pascal to von Neumann, p. 10 *VFR

In 1896, the first x-ray photograph in the U.S. was taken by Dr. Henry Louis Smith, a professor of physics and astronomy at Davidson College, Davidson, NC. It showed the location of a bullet in the hand of a corpse, using a 15 minute exposure. Immediately after he first heard of Roentgen's discovery in Germany, Smith obtained the hand of the corpse, and fired a bullet into it, for this experiment. In Feb 1896, he published this X-Ray photograph in the Charlotte Observer. He was subsequently elected president of Davidson College in 1901. In 1905, Smith established the first electric light plant in the town of Davidson.*TIS

1898 Charlotte Agnes Scott wrote to to M. Carey Thomas: “I am most disturbed and disappointed at present to ﬁnd you taking the position that intellectual pursuits must be ‘watered down’ to make them suitable for women and that a lower standard must be adopted in a woman’s college than in a man’s.” At the time Scott, who received a “First Class” D.Sc. from the University of London in 1885, was a faculty member at Bryn Mawr. Thomas was president of Bryn Mawr and the ﬁrst American woman to earn a doctorate in any ﬁeld (linguistics from Zurich in 1882). *Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell, 196-197 *VFR

1924 The ﬁrst U.S. History of Science Society was organized in Boston “to encourage and maintain active interest in the history of science and the various sciences in particular.” The movement to form the society was begun by David Eugene Smith and today is the most important historical society in the world. *VFR
1997 The fictional HAL 9000 computer becomes operational, according to Arthur C. Clarke's 2001: A Space Odyssey. In the 1968 movie adaptation, the computer's statement -- I am a HAL 9000 computer, Production Number 3. I became operational at the HAL Plant in Urbana, Illinois, on January 12, 1997 -- put his birthdate in 1992. Both dates have now passed with no super-intelligent, human-like HAL computer in sight. *CHM

BIRTHS
1716 Antonio de Ulloa (12 Jan 1716; 5 Jul 1795) Spanish scientist and naval officer who discovered the element platinum (atomic number 78). In 1735, the French and Spanish governments sent an scientific expedition to Peru and Equador to measure a degree of meridian at Quinto, close to the equator. Ulloa was one of the officers appointed to take charge of the expedition. In 1744, the ship on which he returned was captured by the British, and he was taken prisoner, though treated respectfully by the English naval officers for they "were not at war with the arts and sciences." The log of his voyage to Peru published in 1748 contains a description of platinum. He established the first museum of natural history and the first metallurgical laboratory in Spain, as well as the Cadiz observatory.*TIS

1853 Gregorio Ricci-Curbastro (12 Jan 1853; 6 Aug 1925) Italian mathematician instrumental in the development of the absolute differential calculus (also called the Ricci calculus), now known as tensor analysis. Ricci-Curbastro's early work was in mathematical physics, particularly on the laws of electric circuits and differential equations. He changed area somewhat to undertake research in differential geometry and was the inventor of the absolute differential calculus between 1884 and 1894. Ricci-Curbastro's absolute differential calculus became the foundation of tensor analysis and was used by Einstein in his theory of general relativity. As a councillor for his home town of Lugo, he was involved in many projects relating to the supply of water and to swamp drainage.*TIS

1857 Knut Johan Angstrom (12 Jan 1857; 4 Mar 1910) Swedish physicist, son of Anders Angstrom, who invented an electric compensation pyrheliometer and other devices for infra-red photography. With these, he studied the sun's heat radiation*TIS

1896 David Wechsler (12 Jan 1896; 2 May 1981) U.S. psychologist and inventor of several widely used intelligence tests for adults and children. During WW I, while assisting Edwin Garrigues Boring (1886-1968) in testing army recruits, Wechsler realized the inadequacies of the Army Alpha Tests (designed to measure abilities of conscripts and match them to suitable military jobs). He concluded that academically defined "intelligence" did not apply to "real life" situations. After leaving the military and more years of research, he developed the Wechsler Adult Intelligence Scale, and introduced deviation scores in intelligence tests. He developed the Wechsler Memory Scale in 1945, Wechsler Intelligence Scale for Children (1949), and Wechsler Preschool and Primary Scale of Intelligence (1967).*TIS

1903 Igor Vasilyevich Kurchatov (12 Jan 1903; 7 Feb 1960) Soviet nuclear physicist who from 1932 conducted nuclear science research in the Soviet Union, during which time his team built a cyclotron, a proton accelerator and studied artificial radioactivity and neutron-proton interactions. During WW II, he was chosen as director for the development of his country's first atomic bomb, detonated 29 Aug 1949. Meanwhile, in Dec 1946, Kurchatov demonstrated a working prototype reactor, though limited to producing only a few watts and by Jun 1948, a plutonium production reactor. He subsequently produced the world's first practical thermonuclear bomb (1952). Before 1978, the Soviet name for element-104 was kurchatovium (Ku), though subsquently rutherfordium (Rf) became the accepted name. *TIS

1906 Kurt Hirsch (12 Jan 1906 in Berlin, Germany - 4 Nov 1986 in London, England) worked in various areas of Group Theory.*SAU

1915 Herbert Ellis Robbins (January 12, 1915 – February 12, 2001) was an American mathematician and statistician who did research in topology, measure theory, statistics, and a variety of other fields. He was the co-author, with Richard Courant, of What is Mathematics?, a popularization that is still (as of 2007) in print. The Robbins lemma, used in empirical Bayes methods, is named after him. Robbins algebras are named after him because of a conjecture (since proved) that he posed concerning Boolean algebras. The Robbins theorem, in graph theory, is also named after him, as is the Whitney–Robbins synthesis, a tool he introduced to prove this theorem. The well-known unsolved problem of minimizing in sequential selection the expected rank of the selected item under full information, sometimes referred to as the fourth secretary problem, also bears his name: Robbins' problem (of optimal stopping).*WIK

DEATHS
1665 Pierre de Fermat, age 65, died without publishing a single mathematical work. However, because of his correspondence he was known as one of he best mathematicians in Europe. *VFR
(17 Aug 1601, 12 Jan 1665)French mathematician, often called the founder of the modern theory of numbers. Together with Rene Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. He anticipated differential calculus with his method of finding the greatest and least ordinates of curved lines. He proposed the famous Fermat's Last Theorem while studying the work of the ancient Greek mathematician Diophantus. He wrote in pencil in the margin, "I have discovered a truly remarkable proof which this margin is too small to contain," that when the Pythagorean theorem is altered to read aⁿ + bⁿ = cⁿ, the new equation cannot be solved in integers for any value of n greater than 2. *TIS The quote in the margin is given this way by *SAU : "To divide a cube into two other cubes, a fourth power or in general any power whatever into two powers of the same denomination above the second is impossible, and I have assuredly found an admirable proof of this, but the margin is too narrow to contain it."

1849 James Thomson (13 Nov 1786 in Annaghmore, near Ballynahinch, Co. Down, Ireland - 12 Jan 1849 in Glasgow, Scotland) campaigned to reform Glasgow University. He wrote many textbooks. He was the father of Lord Kelvin.*SAU

1909 Hermann Minkowski (22 Jun 1864, 12 Jan 1909) German mathematician who developed the geometrical theory of numbers and who used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity. By 1907, Minkowski realised that the work of Lorentz and Einstein could be best understood in a non-euclidean space. He considered space and time, which were formerly thought to be independent, to be coupled together in a four-dimensional "space-time continuum". Minkowski worked out a four-dimensional treatment of electrodynamics. His idea of a four-dimensional space (since known as "Minkowski space"), combining the three dimensions of physical space with that of time, laid the mathematical foundation of Albert Einstein's general theory of relativity.*TIS

1996 Bartel Leendert van der Waerden (February 2, 1903, Amsterdam, Netherlands – January 12, 1996, Zürich, Switzerland) was a Dutch mathematician and historian of mathematics. Van der Waerden is mainly remembered for his work on abstract algebra. He also wrote on algebraic geometry, topology, number theory, geometry, combinatorics, analysis, probability and statistics, and quantum mechanics (he and Heisenberg had been colleagues at Leipzig). In his later years, he turned to the history of mathematics and science. His historical writings include Ontwakende wetenschap (1950), which was translated into English as Science Awakening (1954), Geometry and Algebra in Ancient Civilizations (1983), and A History of Algebra (1985).*Wik

2001 William (Redington) Hewlett (20 May 1913, 12 Jan 2001) was an American electrical engineer who co-founded the Hewlett-Packard Company, a leading manufacturer computers, computer printers, and analytic and measuring equipment. In 1939, he formed a partnership known as Hewlett-Packard Company with David Packard, a friend and Stanford classmate. (The order of their names was determined by a coin toss.) HP's first product was an audio oscillator based on a design developed by Hewlett when he was in graduate school. Eight were sold to Walt Disney for Fantasia. Lesser-known early products were: bowling alley foul-line indicator, automatic urinal flusher, weight-loss shock machine. The company's first "plant" was a small garage in Palo Alto, with $538 initial capital.*TIS

2004 Olga Aleksandrovna Ladyzhenskaya (March 7, 1922, Kologriv – January 12, 2004, St. Petersburg) was a Soviet and Russian mathematician. She was known for her work on partial differential equations (especially Hilbert's 19th problem) and fluid dynamics. She provided the first rigorous proofs of the convergence of a finite difference method for the Navier-Stokes equations. She was a student of Ivan Petrovsky. She was awarded the Lomonosov Gold Medal in 2002.*Wik

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 11

2012-01-11T00:10:00.002Z

As yet, if a man has no feeling for art he is considered narrow-minded, but if he has no feeling for science this is considered quite normal. This is a fundamental weakness.
~Isidor Isaac Rabi, 1958

The 11th day of the year; 11 is the only prime comprising an even number of identical digits. (Can you find a prime which is comprised of an odd number of identical digits?)

EVENTS
1672 Newton presents his telescope to the Royal Society of London. At the same meeting he was elected FRS. *VFR

1753 Sir Hans Sloan died today. He was an avid collector of natural history curiosities, of coins, medals, stuffed animals and historical objects. He had thousands of trays full of exhibits from around the world and bought entire collections from others, to the extent that he could virtually single-handedly fill the British Museum, which opened shortly after he died. He is here because he invented hot chocolate. I need no other reason. *R. Hall, The Georgian Gentleman Blog

1775 Gaspard Monge (1746–1818) presents a memoir before the Academie des Sciences in which he made use of two planes of projection in his descriptive geometry. Descriptive geometry, which deals with the accurate two dimensional rendering of three dimensional solids, had been suggested by Frezier in 1738, but it is mainly to Monge that the mathematical theory owes its development. [Smith, Source Book, p. 426] *VFR

In 1787, William Herschel, a German astronomer, discovered the first two moons of Uranus, six years after he had discovered the planet, on 13 Mar 1781. Titania's diameter is 998.2 miles (1610 km) and its distance from Uranus is 271,104 miles (436,300 km). Oberon, the outermost of the major moons of Uranus, has a mean diameter of 1523 km and a mean distance from Uranus of 583,500 km. These names were suggested by Herschel's son John Herschel in 1852 at the request of William Lassell, who had discovered two more moons of Uranus the year before which became known as Ariel and Umbriel. *TIS In his later career, Herschel discovered two moons of Saturn, Mimas and Enceladus; as well as two moons of Uranus, Titania and Oberon. He did not give these moons their names; they were named by his son John in 1847 and 1852, respectively, well after his death.
Recently, some evidence has been cited by Dr. Stuart Eves that Herschel might have discovered rings around Uranus.*Wik

In 1911, the "Kaiser Wilhelm Society for the Advancement of Science" was founded in Berlin. This became the present Max Planck Society.**TIS

1960 ACM/GAMM committee, a team of computer industry luminaries, convenes to develop Algol 60, the first block-structured language and one that eventually led to the more widely used Pascal. Algol (Algorithmic Language) and Algol 60 were designed to solve scientific computations and were meant to be more portable than most languages in existence at the time. Alan Perlis described Algol as the lingua franca of computer science. *CHM

1989 “We should dispel, once and for all, the nonsensical notion that mathematics is a man’s game. The appearance of more women in mathematics in recent years is encouraging, but we need to do better in publicizing their successes.” So wrote Edward A. Connors, chairman of the AMS Committee on Employment and Educational Policy, in an Opinion article in The Chronicle of Higher Education entitled “America’s scientiﬁc future threatened by the decline in mathematical education.” [AWM Newsletter, vol. 19, no. 2, p. 2] *VFR

BIRTHS
1545 Guidobaldo Marchese del Monte (11 Jan 1545 in Pesaro, Italy - 6 Jan 1607 in Montebaroccio, Italy) was an Italian mathematician who wrote on statics and also on perspective and astronomy. *SAU

1707 Vincenzo Riccati (Castelfranco Veneto, 11 January 1707 – Treviso, 17 January 1775) was an Italian mathematician and physicist. He was the brother of Giordano Riccati, and the second son of Jacopo Riccati.
Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics. The Riccati equation is named after his father.*Wik

1734 Achille-Pierre Dionis du Séjour (January 11, 1734 – August 22, 1794) was a French mathematician, astronomer and politician.*SAU

1825 William Spottiswoode FRS (11 January 1825, London – 27 June 1883, London)[1] was an English mathematician and physicist. He was President of the Royal Society from 1878 to 1883. *Wik

1826 Giuseppe Battaglini ( Naples , 11 January 1826 - Naples , April 29 1894 ) was an Italian Mathematician. His most important contribution was the development of knowledge of non-Euclidean geometry in Italy, who developed both with their studies through an intense relationship with Italian and foreign mathematicians. His activities as an innovator in the field of mathematics was opposed by the more traditional classical schools. Moreover, his figure stands out as a man committed to keeping the Risorgimento in the field of science and civil life. *Wik

1889 Calvin Blackman Bridges (11 Jan 1889; died 27 Dec 1938) American geneticist who advanced understanding of the role of chromosomes in heredity using the fruit fly, Drosophila melanogaster. He began, in 1910, as a laboratory assistant for Thomas Hunt Morgan tracking how observable changes in its chromosomes led to inherited variations. Bridges used natural "mistakes" in sex chromosome segregation to show that an improper number of chromosomes produced abnormal fruit flies. Such "mistakes," called nondisjunction because chromosomes are not properly disjoined, result in gametes with either an extra copy of a sex chromosome or none at all. He created a nomenclature system for naming fly mutants. He correlated Drosophila genes with banding patterns in salivary chromosomes.*TIS

1934 Charles Antony Richard (Tony) Hoare is born., the Developer of the Axiomatic Approach. He received an MA from University of Oxford in 1959. During 1960 - 1968 he had worked at Elliot Bros. (London) Ltd. During 1968 - 1977 Hoare taught at the University of Belfast. Since 1977 he has become James Martin Professor of Computing at Oxford. He was a major contributor to the understanding of the logic of programs, and in particular was the developer of the Axiomatic Approach to program description. He received the 1980 ACM Turing Award and the 1990 Computer Society Pioneer Award. *CHM

1938 Fischer Sheffey Black (January 11, 1938 – August 30, 1995) was an American economist, best known as one of the authors of the famous Black–Scholes equation.
The Nobel Prize is not given posthumously, so it was not awarded to Black in 1997 when his co-author Myron Scholes received the honor for their landmark work on option pricing along with Robert C. Merton, another pioneer in the development of valuation of stock options. In the announcement of the award that year, the Nobel committee prominently mentioned Black's key role.
Black has also received recognition as the co-author of the Black–Derman–Toy interest rate derivatives model, which was developed for in-house use by Goldman Sachs in the 1980s but eventually published. *Wik

DEATHS
1757 Louis Bertrand Castel (15 Nov 1688 in Montpellier, France - 11 Jan 1757 in Paris, France) was a French mathematician who was a strong opponent of Newton's philosophy.Castel's physics was based on reason, not observation. He also opposed Newton on religious grounds, believing Newtonian theory to be materialistic. He made this clear in an early article written in the Journal de Trévoux in 1721 in which he stated that Newton had been influenced by Democritus in substituting the void for divine intelligence.Castel's system to replace the theories of Newton did not bring him fame. However he did achieve this from a rather unusual source. In the November 1725 issue of Mercure de France he set out his ideas for an instrument, the clavecin oculair, which made colours and musical tones correspond. Two articles in the Journal de Trévoux in 1735, namely Nouvelles expériences d'optique et d'acoustique and L'optique des couleurs fondée sur les simples observations, took the idea further describing an instrument to accomplish the colour-tone correspondence, namely the ocular harpsichord. *SAU

. 1763 Francis Hauksbee, the Younger (1687, 11 Jan 1763) English instrument maker, scientist, and lecturer who was the nephew and assistant experimenter to Francis Hauksbee the Elder. He contributed to early studies of electricity with his own independent research. From c. 1714, he gave lectures and demonstrations. He manufactured scientific instruments, including air pumps, hydrostatic balances, and reflecting telescopes. Hauksbee published an Essay for Introducing a Portable Laboratory, 1731), and other works on chemistry, astronomical instruments, electricity, and pneumatics. In 1723, he became clerk and housekeeper to the Royal Society. In 1728, (with Benjamin Robinson) he obtained a patent "for preserving the Planks and Sheathing of Ships sailing to the East and West Indies. *TIS

1903 Henry William Watson (25 Feb 1827 in Marylebone, London, England - 11 Jan 1903 in Berkswell (near Coventry), England) was an English mathematician who wrote some influential text-books on electricity and magnetism. *SAU

1988 Isidor Isaac Rabi (29 Jul 1898, 11 Jan 1988) was American physicist who was awarded the Nobel Prize for Physics in 1944 for his invention (in 1937) of the atomic and molecular beam magnetic resonance method of measuring magnetic properties of atoms, molecules, and atomic nuclei. He spent most of his life at Columbia University (1929-67), where he performed most of his pioneering research in radar and the magnetic moment associated with electron spin in the 1930s and 1940s. His Nobel-winning work led to the invention of the laser, the atomic clock, and diagnostic uses of nuclear magnetic resonance. He originated the idea for the CERN nuclear research center in Geneva (founded 1954). *TIS

1941 Emanuel Lasker (24 Dec 1868 in Berlinchen, Prussia (now Barlinek, Poland) - 11 Jan 1941 in New York, USA) Lasker became World Chess Champion in 1894 and held the championship until 1921. In mathematics he introduced the notion of a primary ideal. *SAU

1949 Torsten Carleman (8 July 1892, Visseltofta, Osby Municipality – 11 January 1949, Stockholm), born Tage Gills Torsten Carleman, was a Swedish mathematician, known for his results in classical analysis and its applications. As the director of the Mittag-Leffler Institute for more than two decades, Carleman was the most influential mathematician in Sweden. *Wik

1991 Carl David Anderson (3 Sep 1905, 11 Jan 1991) American physicist who, with Victor Francis Hess of Austria, won the Nobel Prize for Physics in 1936 for his discovery of the positron, or positive electron, the first known particle of antimatter. He examined the photographs of cosmic rays taken as they passed through a Wilson cloud chamber in a strong magnetic field. Besides the curved paths of negative electrons, he found also paths deviating in the opposite direction, corresponding to positively charged particles - yet having the the same mass as an electron! Previously, Dirac had predicted such particles by theoretical solution to electromagnetic field equations. Anderson has now found the existance of positron.*TIS

2007 Donald Edward Osterbrock (13 July 1924, 11 Jan 2007) was an American astronomer who was a leading authority on the history of astronomy, and director of the University of California's Lick Observatory. He applied physics to produce accurate models of stars. For example, treating the outer part of the sun as turbulent and convective, he explained the seemingly anomalous fact that the sun's corona is hotter than its surface. He investigated the nature of ionized gas around hot stars, and was a pioneer in the use of spectroscopic methods for the study of gaseous nebulae. He discovered new types of active galactic nuclei, which are powered by black holes in the centers of galaxies. He fostered the construction of the 10-meter Keck Telescopes in Hawaii.*TIS

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 10

2012-01-10T00:10:00.001Z

The sun comes up just about as often as it goes down, in the long run, but this doesn't make its motion random.
~Donald Knuth

The 10th day of the year; 10 balls can be arranged in the plane as a triangle, and in space as a tetrahedron.

EVENTS
1765 When Frederick the Great saw Lambert for the ﬁrst time he exclaimed that the greatest blockhead had been suggested for his Academy. He based this opinion on Lambert’s strange dress and behavior, but later he saw the “immesurableness of insight" that Lambert possessed and so appointed him to the Academy on this date. *VFR

1844 George Boole submitted his ﬁrst paper to the Philosophical Transactions of the Royal Society. The council of the Royal Society almost rejected it without looking at it because the author was unknown. After considerable argument it was sent to two referees—thereby setting a precedent of refereeing papers. One referee rejected it, the other recommended a special prize. In 1844 this paper was the ﬁrst mathematics paper to receive a gold medal from the Royal Society. *MacHale, George Boole, His Life and Work, p 61. (This seems to only be partly true. I find the following in the Stanford Encyclopedia of Philosophy: "In 1841 Boole also published his first paper on invariants, a paper that would strongly influence Eisenstein, Cayley, and Sylvester to develop the subject. Arthur Cayley (1821–1895), the future Sadlerian Professor in Cambridge and one of the most prolific mathematicians in history, wrote his first letter to Boole in 1844, complimenting him on his excellent work on invariants. He became a close personal friend, one who would go to Lincoln to visit and stay with Boole in the years before Boole moved to Cork, Ireland. In 1842 Boole started a correspondence with Augustus De Morgan (1806–1871) that initiated another lifetime friendship. In 1843 the schoolmaster Boole finished a lengthy paper on differential equations, combining an exponential substitution and variation of parameters with the separation of symbols method. The paper was too long for the CMJ—Gregory, and later De Morgan, encouraged him to submit it to the Royal Society. The first referee rejected Boole's paper, but the second recommended it for the Gold Medal for the best mathematical paper written in the years 1841–1844, and this recommendation was accepted." )

1854 Riemann presents a paper to the philosophical faculty at G¨ottingen in which he challenged the mathematical world to redeﬁne the concept of inﬁnity to be either endless or unbounded. [George Martin, Foundation of Geometry and the Non-Euclidean Plane, Intext, 1975, p. 311] *VFR

1942 Peter Hilton arrived at Bletchley Park where he was greeted by the question “Do you play chess?” The “somewhat strange individual” who asked the question was the logician Alan Turing. Thus much of Hilton’s ﬁrst day of war service was spent solving a chess problem. The group of pure mathematicians at Bletchley Park was involved in breaking German codes during WW II. (Peter Hilton, “Reminiscences of Bletchley Park, 1942–1945,” pp. 291–301 in A Century of Mathematics in America, Part I, especially p. 292.) *VFR

In 1946, the U.S. Army Project Diana team detected radar signals reflected off the moon's surface. A 180 cycle wave pulse with a 1/4 sec duration was beamed by the Army Signal Corps from the Evans Signal Laboratories, Belmar, N.J. The echo was received 2.4 sec. later, proving that radio waves could penetrate Earth's atmosphere. The experiment was supervised by Lt. Col. John H. De Witt, the broadcasting pioneer and amateur astronomer who first came up with the idea in 1940. His early amateur attempts were unsuccessful, but his chance came a few years later, after WW II, courtesy of the U.S. Army, at the Signal Corps Laboratories. During the war, he had developed radar for locating mortars and directing counterfire.*TIS

1991 Here is one for those of you who have always distrusted statistics: “... according to a study conducted by Caroline Nielsen of the University of Connecticut. She followed 10 women who joined an expensive health club and another 10 who joined a ‘simple’ club; after three months, 63 percent of those who joined the no-frills club improved in ﬁtness, compared with 25 percent for those at the luxury club.” “It must be a joke, but I just don’t get it.” writes (on the computer net) Richard Griﬃth of Carleton University in Ottawa, Canada, who found it in the Globe and Mail, page A18, Social Studies, Gyms: Less is More. *VFR

BIRTHS
1573 Simon Marius (10 Jan 1573; 26 Dec 1624) (Also known as Simon Mayr) German astronomer, pupil of Tycho Brahe, one of the earliest users of the telescope and the first in print to make mention the Andromeda nebula (1612). He studied and named the four largest moons of Jupiter as then known: Io, Europa, Ganymede and Callisto (1609) after mythological figures closely involved in love with Jupiter. Although he may have made his discovery independently of Galileo, when Marius claimed to have discovered these satellites of Jupiter (1609), in a dispute over priority, it was Galileo who was credited by other astronomers. However, Marius was the first to prepare tables of the mean periodic motions of these moons. He also observed sunspots in 1611. *TIS

1875 Issai Schur (10 Jan 1875 in Mogilev, Russian Empire (now Belarus) - 10 Jan 1941 in Tel Aviv, Palestine (now Israel)) is mainly known for his fundamental work on the representation theory of groups but he also worked in number theory and analysis.*SAU

1905 Ruth Moufang (10 Jan 1905 in Darmstadt, Germany - 26 Nov 1977 in Frankfurt, Germany) Moufang studied projective planes, introducing Moufang planes and non-associative systems called Moufang loops. *SAU

1906 Grigore Constantin Moisil (10 January 1906 in Tulcea, Romania – 21 May 1973 in Ottawa, Canada) was a Romanian mathematician, computer pioneer, and member of the Romanian Academy. His research was mainly in the fields of mathematical logic, (Łukasiewicz-Moisil algebra), Algebraic logic, MV-algebra, algebra and differential equations. He is viewed as the father of computer science in Romania.*wik

1936 Robert Woodrow Wilson (10 Jan 1936, ) American radio astronomer who shared, with his coworker Arno Penzias, the 1978 Nobel Prize for Physics for their discovery of cosmic microwave background radiation using a microwave horn antenna at Bell Laboratories, Holmdel, New Jersey. Their discovery in 1964 is now widely interpreted as being the remnant radiation from the "big bang" model for the creation of the universe several billion years ago. Wilson is continuing his astrophysics work with Penzias, looking for interstellar molecules and determining the relative abundances of interstellar isotopes. (Soviet physicist Pyotr Leonidovich Kapitsa also shared the Nobel award, for unrelated research.)*TIS

1938 Donald Ervin Knuth, born, best known for his ongoing multi-volume book series The Art of Computer Programming. Knuth's books provide surveys of the software field, comparing algorithms for performing some of the most fundamental computer science procedures. The book project, which is expected to last his entire lifetime, was born out of a desire to eliminate duplication of effort by programmers. Knuth also took a decade-long diversion from the book series to create the language TeX, when he received galley-proofs of one of his books and noticed how poor the state of technical typesetting was. Knuth has based much of his writing on his theory that programming a computer is an art form, like the creation of poetry or music. He received the 1980 Computer Society Pioneer Award.*CHM

1949 Ann Watkins born in Los Angeles. Today she is professor at Los Angeles Pierce College and editor of The College Mathematics Journal. Of her ﬁrst love, teaching, she says: “It’s often said that the best way to learn something is to teach it. That’s certainly true about mathematics. If you can get the math clear enough in your heat to explain it to someone else, either orally or in writing, then you’ve really ‘got it’.” [Quoted from Karl J. Smith, The Nature of Mathematics, sixth edition, 1991, p. 646.] *VFR

DEATHS
1833 Adrien-Marie Legendre (18 Sep 1752, 10 Jan 1833) French mathematician who contributed to number theory, celestial mechanics and elliptic functions. In 1794, he was put in charge of the French government's department that was standardizing French weights and measures. In 1813, he took over as head of the Bureau des Longitudes upon the death of Lagrange, its former chief. It was in a paper on celestial mechanics concerning the motion of planets (1784) that he first introduced the Legendre Polynomials. His provided outstanding work on elliptic functions (1786), and his classic treatise on the theory of numbers (1798) and also worked on the method of least squares.*TIS

1864 Nicholas Joseph Callan (22 Dec 1799, 10 Jan 1864) Irish pioneering scientist in electrical science, who invented the induction coil (1836) before that of better-known Heinrich Ruhmkorff. Callan's coil was built using a horseshoe shaped iron bar wound with a secondary coil of thin insulated wire under a separate winding of thick insulated wire as the "primary" coil. Each time a battery's current through the "primary" coil was interrupted, a high voltage current was produced in the electrically separate "secondary" coil. By 1837, Callan used a clock mechanism to rock a wire in and out of a small cup of mercury to interrupt the circuit 20 times/sec on a giant induction machine, producing 15-inch sparks (estimated at 600,000 volts).*TIS

1919 Wallace Clement Ware Sabine (13 Jun 1868, 10 Jan 1919) was a U.S. physicist who founded the science of architectural acoustics. After experimenting in the Fogg lecture room at Harvard, to investigate the effect of absorption on the reverberation time, on 29 of October 1898 he discovered the type of relation between these quantities. The duration T of the residual sound to decay below the audible intensity, starting from a 1,000,000 times higher initial intensity is given by: T = 0.161 V/A (V=room volume in m3, A=total absorption in m2). The first auditorium Sabine designed applying his new insight in acoustics, was the new Boston Music Hall, formally opened on 15 Oct 1900. Now known as the Symphony Hall, and still considered one of the world's three finest concert halls.*TIS

1929 Karl Heun (3 April 1859 in Wiesbaden, Germany - 10 Jan 1929 in Karlsruhe, Germany) was a German mathematician best known for the Heun differential equation which generalises the hypergeometric differential equation. *SAU

1941 Issai Schur (10 Jan 1875 in Mogilev, Russian Empire (now Belarus) - 10 Jan 1941 in Tel Aviv, Palestine (now Israel))is mainly known for his fundamental work on the representation theory of groups but he also worked in number theory and analysis.*SAU

1944 Thomas Scott Fiske (12 May 1865 in New York - 10 Jan 1944 in Poughkeepsie, New York) was an American mathematician. He was born in New York City and graduated in 1885 (Ph.D., 1888) from Columbia University, where he was a fellow, assistant, tutor, instructor, and adjunct professor until 1897, when he became professor of mathematics. In 1899 he was acting dean of Barnard College. He was president in 1902–04 of the American Mathematical Society, and he also edited the Bulletin (1891–99) and Transactions (1899-1905) of this society. In 1902 he became secretary of the College Entrance Examination Board. In 1905–06 he also served as president of the Association of Teachers of Mathematics of the Middle States and Maryland. Besides his mathematical papers, he was author of Theory of Functions of a Complex Variable (1906; fourth edition, 1907)*Wik

1984 Lancelot Stephen Bosanquet (26 Dec 1903 in St. Stephen's-by-Saltash, Cornwall, England - 10 Jan 1984 in Cambridge, Cambridgeshire, England) Bosanquet wrote many papers on the convergence and summability of Fourier series. He also wrote on the convergence and summability of Dirichlet series and studied specific kinds of summability such as summability factors for Cesàro means. His later work on integrals include two major papers on the Laplace-Stieltjes integral published in 1953 and 1961. Other topics he studied included inequalities, mean-value theorems, Tauberian theorems, and convexity theorems. *SAU

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum

On This Day in Math - Jan 9

2012-01-09T00:10:00.003Z

An animation showing the construction of the Witch of Agnesi, *Wik

Nature is never so admired as when she is understood.

~Bernard le Bovier de Fontenelle

The 9th day of the year; of all the odd numbers in the Fibonacci sequence, none has a factor of nine. (students might search for the smallest odd prime number that is not a factor of any of the Fibonacci numbers)

EVENTS
1621 J. WELLES (author of Sciographia, or the Art of Shadows,) writes to HENRY BRIGGS at MERTON COLLEGE IN OXFORD to offer help in the construction of logarithms for base ten. It appears that he assisted in the calculations for the Arithmetica Logarithmica. * Augustus De Morgan, Correspondence of scientific men of the seventeenth century ..., Volume 1

In 1643, Giovanni Riccioli first reported the phenomenon known as the Ashen Light of Venus. It is said to be a faint luminescence on the night side of the planet, similar in appearance to "earthshine" on the Moon, although not so bright. Ashen Light has been most often sighted when Venus was in the evening sky, when the evening terminator of the planet is toward the Earth. Studies have been attempted by several space missions, including Pioneer and the Russian Venera 11 and 12 landers. Still, the phenomenon remains sporadic and the explanation elusive. *TIS

In 1816, Sir Humphry Davy's safety lamp was first used in a coal mine. Deadly explosions had been a continual hazard caused by the flammable gas, methane, leaking out of the coal seams ignited by the flame of a miner's lamp. There had been previous attempts by others to make a safety lantern. Davy applied a scientific approach to determine the suitable fineness of wire gauze placed around the flame which would avoid ignition of flammable gas outside. He determined that the holes in the gauze should be less than 1/22 inch in diameter, and that the wire itself should be between 1/40 to 1/60 inch thick. Since the flame changed colour in the presence of methane, it also served as a warning to the miner to take protective action.*TIS

1839 Henderson announces ﬁrst stellar parallax. *VFR The Scottish Astronomer Royal, Thomas Henderson, published the results of his measurement, the first made of a stellar parallax. He observed the star Alpha Centauri from the Cape of Good Hope, South America. (It is not visible from Britain.) His measurements were made in 1831-33. After that time, but before Henderson completed his calculations and published his results, both Friedrich Bessel and Friedrich Struve had been recognized as the first to make measurements of stellar parallax.*TIS

In 1901, the first application for a patent for Meccano was submitted, as "Improvements in toy or educational devices for children and young people. Known at first as "Mechanics Made Easy," this invention of Frank Hornby became a worldwide success. The British patent (No. 587) showed the familiar perforated strips, pulleys, axles, brackets and clips assembled as a model railway crane with tracks that had operating points. The patent was published on 30 Nov 1901.*TIS (In the U S these are called "Erector Sets")

1956 The Soviet Union issued a stamp commemorating the tenth anniversary of the death of Alexei N. Krylov (1863–1945), mathematician and naval architect. [Scott #1792] *VFR

1972 Mariner 9 transmitted black and white pictures of Mars back to Earth using the ﬁrst order (32, 6, 16) Reed-Muller code. See Chester J. Salwach, “Codes that detect and correct errors,” The College Mathematics Journal, 19(1988), 402–416. *VFR

In 1998, two teams of international collaborations of scientists announced the discovery that galaxies are accelerating, flying apart at ever faster speeds, by observing distant, ancient exploding stars. This observation - named as Science magazine's "Breakthrough of the Year for 1998" - implies the existence of a mysterious, self-repelling property of space first proposed by Albert Einstein, which he called the cosmological constant. Researchers in England, France, Germany, and Sweden are among the members of the Supernova Cosmology Project based at Berkeley National Laboratory (headed by Saul Perlmutter) and the High-z Supernova Search Team based in Australia (led by Brian Schmidt)*TIS

BIRTHS
1864 Vladimir Andreevich Steklov (9 January 1864 – 30 May 1926) was a Soviet/Russian mathematician, mechanician and physicist. Steklov's primary scientific contribution is in the area of orthogonal functional sets. He introduced a class of closed orthogonal sets, developed asymptotic Liouville–Steklov method for orthogonal polynomials, proved theorems on generalized Fourier series, and developed an approximation technique later named Steklov function. He also worked on hydrodynamics and the theory of elasticity. Steklov also wrote a number of works on the history of science. Wik

1869 Richard Wilhelm Heinrich Abegg (9 Jan 1869; 3 Apr 1910) German physical chemist who, with Boländer proposed a theory of valency (1899) to explain the capacity of an atom to combine with another atom in light of the newly discovered presence of electrons within the atom. He saw that the configurations of electrons in the noble gas elements are particularly stable. Thus, a halide element, such as chlorine, with one electron less than a noble gas element, would easily tend to accept one electron. An alkali metal element, such as sodium, having one electron more than a noble gas element, would tend to give it up. Thus a sodium atom could transfer an electron to a chlorine atom, forming a positively charged sodium ion bound electrostatically to a negatively charged chloride ion. He died in a balloon crash. *TIS

1873 Birthdate of Hans Blichfeldt (9 Jan 1873 in Illar, Denmark - 16 Nov 1945 in Palo Alto, California, USA). When he graduated from Stanford in 1896 he didn’t have enough money to go to Europe for a doctorate, as was then the custom, so he borrowed the money from a Stanford professor (Rufus L Green). In one year he received his doctorate, summa cum laude, from Leipzig. *VFR
His lifework was devoted to group theory and number theory. Some of the many topics that he covered were diophantine approximations, orders of linear homogeneous groups, theory of geometry of numbers, approximate solutions of the integers of a set of linear equations, low-velocity fire angle, finite collineation groups, and characteristic roots.*SAU

1915 Mollie Orshansky, (January 9, 1915 – December 18, 2006), was an American economist and statistician who, in 1963–65, developed the Orshansky Poverty Thresholds, which are used in the United States as a measure of the income that a household must not exceed to be counted as poor.*Wik

1930 Jacob Theodore "Jack" Schwartz (January 9, 1930 – March 2, 2009) was an American mathematician, computer scientist, and professor of computer science at the New York University Courant Institute of Mathematical Sciences. He was the designer of the SETL programming language and the NYU Ultracomputer. He founded the New York University Department of Computer Science, chairing it from 1964 to 1980.
His research interests included: the theory of linear operators, von Neumann algebras, quantum field theory, time-sharing, parallel computing, programming language design and implementation, robotics, set-theoretic approaches in computational logic, proof and program verification systems; multimedia authoring tools; experimental studies of visual perception; multimedia and other high-level software techniques for analysis and visualization of bioinformatic data.
He authored 18 books and more than 100 papers and technical reports.*Wik

1950 Sir Alec Jefferys (9 Jan 1950, ) English geneticist who discovered the technique of DNA fingerprinting, used for unique identification of humans, animals and other organisms from their DNA material on 10 Sep 1984. This came about unexpectedly while Jeffreys was working on another project concerning genes for another purpose - to trace genetic markers through families to understand inheritance patterns of illness. DNA fingerprinting has become important for forensic science investigations, paternity issues, and detection of hereditary disease. He was knighted in 1994 for his research in genetics. *TIS

DEATHS
1587 Paul Wittich died. (c.1546 – 9 January 1586) In 1580, with the help of Tycho Brahe, he rediscovered the method of prostaphaeresis. *VFR German mathematician and astronomer whose Capellan geoheliocentric model, in which the inner planets Mercury and Venus orbit the sun but the outer planets Mars, Jupiter and Saturn orbit the Earth, may have directly inspired Tycho Brahe's more radically heliocentric geoheliocentric model in which all the 5 known primary planets orbited the Sun, which in turn orbited the stationary Earth.*Wik
Others think Wittich did not have, or need Brahe's help.

It is considered unlikely that Tycho was actually involved in the re-invention/re-discovery of prosthaphaeresis although he himself claimed that he was. The first person to publish an account of prosthaphaeresis was Nicolaus Reimers Baer who attributed his knowledge of it to Jost Bürgi who he said had learnt it from Paul Wittich. It was at this point that Tycho claimed that he had discovered the technique together with Wittich, as part of his dispute with Baer on the origins of the so-called Tychonic astronomical system. Tycho accused Baer of having stolen the system. However Tycho’s claim is highly dubious, although Bürgi and Baer both obviously fully understood the prosthaphaerasis method and could utilise it perfectly, Tycho just as obviously didn’t understand it properly and made serious errors when using it. Not the achievements of somebody who supposedly invented the method. Given these facts it is now accepted that Wittich either re-invented the method or had access to a manuscript containing Johannes Werner’s original discovery and taught the method to both Bürgi who understood it and Tycho who didn’t really.

*Thony Christie
(I will leave it to Thony to someday explain to me why he credits Werner with the original discovery, rather than Christopher Clavius.... for students, Prosthaphaeresis is a combination of the Greek words for addition, prosth and subtraction aphaeresis. Prior to the discovery of logarithms it was very difficult to solve spherical triangle equations because it required several multiplications of sines and/or cosines to solve for a single unknown. Since in many tables sines and cosines were represented as chords of a radius of 10^7, it involved the equivalent of multiplying two seven digit numbers together by hand for each multiplication. In 1582, a Jesuit Priest named Christopher Clavius (or perhaps Johannes Werner) found a better way. He showed how to employ the trigonometric identity, Cos(A) Cos(B) = [Cos(a + b) + Cos(a - b)]/2 to make faster work of such problems.)

1757 Bernard Le Bovier, sieur de Fontenelle (11 Feb 1657, 9 Jan 1757) French scientist and author, whose Conversations on the Plurality of Worlds (1686), was one of the first works to present science for the lay reader. He popularized the astronomical theories of Descartes. Many of the characteristic ideas of the Enlightenment are found in embryonic form in his works. From 1697 he became permanent secretary to the Académie des Sciences. He held the office for 42 years, and in this official capacity, he wrote the Histoire du renouvellement del Académie des Sciences (Paris, 3 vols., 1708, 1717, 1722) containing extracts and analyses of the proceedings, written with great simplicity and delicacy. Fontenelle presented many obituary notices to the Académie, including those of Newton and Leibniz. *TIS

1799 Maria Gaetana Agnesi (16 May 1718, 9 Jan 1799) Italian mathematician and philosopher who was the first woman in the Western world considered to be a mathematician. In Propositiones Philosophicae (1738) she presented a series of essays on philosophy and natural science that she had defended in discourses with invited intellectuals who were invited her father's home. In 1748, her two volumes of Analytical Institutions, were acclaimed by the academic world as one of the first and complete publications that brought together the works of various mathematicians on finite and infinitesimal analysis. After the death of her father in 1752, Agnesi entirely devoted herself and spent her money to do charitable work. She died in total poverty in the poorhouse of which she had been the director. *TIS

1848 Caroline Lucretia Herschel (16 Mar 1750, 9 Jan 1848) German-born British astronomer, sister of Sir William Herschel, who assisted in his astronomical researches making calculations associated with his studies. In her own telescope observations, she found three nebulae (1783) and eight comets (1786-97). In 1787, King George III gave Caroline a salary of 50 pounds per year as assistant to William. She published the Index to Flamsteed's Observations of the Fixed Stars and a list of his mistakes in 1797. At the age of 10 she had been struck with typhus, which subsequently stunted her growth. She never grew taller than 4' 3" and remained frail throughout her life. *TIS

1973 Harry Schultz Vandiver (21 Oct 1882 in Philadelphia, Pennsylvania, USA - 9 Jan 1973 in Austin, Texas, USA) Harry developed an antagonism towards public education and left Central High School at an early age to work as a customshouse broker for his father's firm. D H Lehmer writes, "He was self-taught in his youth and must have had little patience with secondary education since he never graduated from high school. This impatience, especially with mathematical education, was to last the rest of his life."
When he was eighteen years old he began to solve many of the number theory problems which were posed in the American Mathematical Monthly, regularly submitting solutions. In addition to solving problems, he began to pose problems himself. By 1902 he was contributing papers to the Monthly. For example he published two short papers in 1902 A Problem Connected with Mersenne's Numbers and Applications of a Theorem Regarding Circulants.
In 1904 he collaborated with Birkhoff on a paper on the prime factors of a^n - b^n published in the Annals of Mathematics. In fact the result they proved was not new, although they were not aware of the earlier work which had been published by A S Bang in 1886. Also in the year 1904, Vandiver published On Some Special Arithmetic Congruences in the American Mathematical Monthly and, although still working as an agent for his father's firm, he did attend some graduate lectures at the University of Pennsylvania. He also began reading papers on algebraic number theory and embarked on a study of the work of Kummer, in particular his contributions to solving Fermat's Last Theorem. Over the next few years he published papers such as Theory of finite algebras (1912), Note on Fermat's last theorem (1914), and Symmetric functions formed by systems of elements of a finite algebra and their connection with Fermat's quotient and Bernoulli's numbers (1917).
The outbreak of World War I in 1914 did not directly affect the United States since the Democratic president Woodrow Wilson made a declaration of neutrality. This policy was controversial but popular enough to see him re-elected in 1916. However US shipping was being disrupted (and sunk) by German submarines and, under pressure from Republicans, Wilson declared war on Germany on 6 April 1917. Vandiver joined the United States Naval Reserve and continued to serve until 1919 when the war had ended. After leaving the Naval Reserve, Birkhoff persuaded Vandiver to become a professional mathematician and to accept a post at Cornell University in 1919. Despite having no formal qualifications, his excellent publication record clearly showed his high quality and he was appointed as an instructor. He also worked during the summer with Dickson at Chicago on his classic treatise History of the Theory of Numbers. In 1924 he moved to the University of Texas where he was appointed as an Associate Professor. He spent the rest of his career at the University of Texas, being promoted to full professor in 1925, then named as distinguished professor of applied mathematics and astronomy in 1947. He continued in this role until he retired in 1966 at the age of 84. *SAU

1975 Petr Sergeevich Novikov, (Aug. 15 (28), 1901, )Novikov’s main works deal with set theory, mathematical logic, the theory of algorithms, and group theory. He devised a powerful method called the index comparison principle for investigating problems of descriptive set theory. He proved that in the second class of projective sets there hold laws of separability inverse to those in the first projective class. He also developed a method, based on the concept of regular formula, of proving the consistency of formal systems. Novikov demonstrated the unsolvability of the problems of identity, conjugacy, and isomorphism in group theory. With his student S. I. Adian, he obtained a solution of Burnside’s problem of periodic groups. Founder of the school of mathematical logic in the USSR, Novikov received the Lenin Prize in 1957 and has been awarded two Orders of Lenin, the Order of the Red Banner of Labor, and various medals. *The Free Encyclopedia

1976 Rupert Wildt (25 Jun 1905, 9 Jan 1976) German-American astronomer who studied atmospheres of planets. He identified (1932) certain absorption bands (observed by Slipher) in the spectra of Jupiter and the outer planets as indicative of ammonia and methane as minor components of these planets which are primarily composed of hydrogen and helium. He speculated (1937) that droplets of formaldehyde formed the clouds of Venus, since water was not detected. (In fact, surface water is absent on Venus, but the clouds do contain water with sulphur and sulphuric acid.) In 1939, he realized the importance of the negative hydrogen ion for stellar opacity. By the 1940s, he proposed the greenhouse theory to explain how atmospheric gases produced unexpectedly high temperatures of Venus.*TIS

1979 Pier Luigi Nervi (21 Jun 1891, 9 Jan 1979) Italian engineer and architect who gained international recognition for his dramatic designs for large-span structures made possible with the use of reinforced concrete. In the 1940s he developed ideas for a reinforced concrete which allowed him to create structures of "strength, simplicity and grace". His services as an engineering consultant were highly sought as a result of his experimentation with structural concrete. His important works include a prefabricated 309-foot-span arch for the Turin Exhibition Building consisting of a single undulating large-span roof, the UNESCO building in Paris, the cathedral at New Norcia, near Perth, Australia, and as structural engineer for the first skyscraper in Italy, the Pirelli Building in Milan. *TIS

1989 Marshall Harvey Stone (8 April 1903 in New York, USA - 9 Jan 1989 in Madras, India) Stone is best known for the Stone-Weierstrass theorem on uniform approximation of continuous functions by polynomials.*SAU

1992 Hans Jenny (7 Feb 1899, 9 Jan 1992) Swiss agricultural chemist and pedologist (soil scientist) who developed numerical functions to describe soil in terms of five interacting factors in his classic book Factors of Soil Formation (1941). These related Climate (temperature and moisture); Organisms (those living on the soil and in the soil, vegetation and animals, fungi algae and bacteria, decay of organic matter, humus); Relief (topography, and geomorphic landscape); Parent Material (bedrock or sediment type); and Time (ranging from 100's to 1000's of years while maturity or equilibrium of soil development is attained). He moved to the U.S. in 1926. After retirement, he studied the soil relationships in the unusual ecological community of the Pygmy Forest in California, known for its stunted and twisted confers. *TIS

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 8

2012-01-08T00:10:00.002Z

But I do not feel obliged to believe that that same God who has endowed us with senses, reason, and intellect has intended to forgo their use and by some other means to give us knowledge which we can attain by them.
~Galileo Galilei

The 8th day of the year; the well known Fibonacci sequence has only two cubes, one and eight.
EVENTS
1610 It is highly probable that Simon Marius (1573 – 1624) court astronomer in Ansbach Franconia used a telescope as an astronomical instrument before Galileo but it is not possible to determine when. On 7th January 1610: Galileo discovers the first three moons of Jupiter. On 8th January 1610: Marius discovers the first three moons of Jupiter independently of Galileo. *Renaissance Mathematicus

1816 The public was disappointed that Sophie Germain did not appear at the awards ceremony for a prixe oﬀered by the Institut de France on the mathematical theory of elastic surfaces. Ger¬main received an honorable mention. [Women of Mathematics. A Biobibliographic Sourcebook (1987), edited by Louise S. Grinstein and Paul J. Campbell, p. 49] *VFR

1838. William Rowan Hamilton assumes the chair as President of the Royal Irish Academy. “SIR Wm. R. HAMILTON, A. M., President, in the Chair. The President, on taking the Chair, delivered an Address to the Academy. *Proceedings of the Royal Irish Academy (1836-1869), Vol. 1, (1836 - 1840), pp. 106-126

1889 Dr. Herman Hollerith of New York City received patent #395,782 for the ﬁrst tabulating machine. It used punched cards and electrical counters operated by electromagnets. Its ﬁrst extensive use was in the compilation of the population statistics for the eleventh U.S. census in 1890. See 1 June 1890. *FFF
His system was designed to record separate statistical items by means of combinations of holes in a punched card to carry information about an individual. The information contained on numerous cards could then be tallied by passing the cards through electrical counters operated by electromagnets. The patent described its application in compilation of the statistics of the population for the U.S. Census. The first extensive application of this system was for the 1890 census counting data items such as age, sex, occupation, etc., of which tallies could be made in combinations such as how many males of certain ages.*TIS (These punched cards were once a principle element of writing computer programs)

1901, Another apportionment paradox brings angry letters about political mathematics.. John C Bell of Colorado, and Math vrs the State of Maine ..

*MAA article

In 1935, the first U.S. patent for a spectrophotometer was issued to Professor Arthur Cobb Hardy of Wellesley, Mass. (No. 1,987,441) which he called a "photometric apparatus." It could detect two million different shades of colour and make a permanent record chart of the results. The patent was assigned to the General Electric Company of Schenectady, N.Y. which sold the first machine on 24 May 1935. It used a photo-electric device to receive light alternately from a sample and from a standard for comparison. It eliminated any need for the two beams (from sample and from standard) to travel different optical paths which in previous designs could introduce inaccuracies if one path varied from the other*TIS

1947 Norbert Wiener refuses to address a Harvard symposium on computers because they are used “for war work” and announces he will not publish work “which may do damage in the hands of irresponsible militarists.” *VFR

1970 The Bangor Daily News contained this item with the headline “Had to Happen”: “Hell, Norway (UPI)–The water froze in Hell Wednesday when the temperature dropped to 6 degrees below zero.” *VFR

BIRTHS
1587 Johannes Fabricius (8 Jan 1587; c. 1615) Dutch astronomer who was perhaps the first to observe sunspots. On 9 Mar 1611, at dawn, Johannes directed his telescope at the rising sun and saw several dark spots on it. He called his father to investigate this new phenomenon with him. The brightness of the Sun's center was very painful, and the two quickly switched to a projection method by means of a camera obscura. Johannes was the first to publish information on such observations. He did so in his Narratio de maculis in sole observatis et apparente earum cum sole conversione. ("Narration on Spots Observed on the Sun and their Apparent Rotation with the Sun"), the dedication of which was dated 13 Jun 1611. He died aged 29. *TIS

1829 Heinrich Eduard Schroeter (January 8th 1829 in Königsberg , January 3 1892 in Breslau ) was a German mathematician , who worked in synthetic geometry in the tradition of Jacob Steiner. *Wik

1852 Giovanni Frattini (January 8, 1852 Rome – July 21, 1925, Rome) was an Italian mathematician, noted for his contributions to group theory.
He entered the University of Rome in 1869, where he studied mathematics with Giuseppe Battaglini, Eugenio Beltrami, and Luigi Cremona, obtaining his PhD. in 1875.*Wik

1868 Sir Frank (Watson) Dyson (8 Jan 1868; 25 May 1939) was a Cambridge-educated, British astronomer, who spent his entire career (except for 5 years in Edinburgh) at the Royal Greenwich Observatory, where he was Astronomer Royal from 1910-33. He directed measurements of terrestrial magnetism, latitude, and time, and he initiated the radio broadcast of time. He determined proper motions of northern stars and completed his portion of the international Carte du Ciel project of photographing the entire sky. Dyson is best known for directing (with Eddington) the 1919 eclipse expedition which confirmed the bending of starlight by the sun's gravitational field. This bending of light, predicted by Einstein, was evidence supporting his general theory of relativity. *TIS

1888 Richard Courant (8 Jan 1888; 27 Jan 1972) German-born American mathematician, who upon joining the faculty of New York University in 1934, began to build the nucleus of a small research group based on the Göttingen model he had experienced as a student of David Hilbert in Germany. Courant's published papers were in variational problems, finite difference methods, minimal surfaces, and partial differential equations. He encouraged the publication of mathematical texts and high quality monographs, such as Methods of Mathematical Physics by Courant and Hilbert. His leadership was commemorated in 1964 when the institute he founded was named the Courant Institute of Mathematical Sciences at New York University.*TIS

1889 Percy John Daniell (9 January 1889 – 25 May 1946) was a pure and applied mathematician. In a series of papers published between 1918 and 1928, he developed and expanded a generalized theory of integration and differentiation, which is today known as the Daniell integral. In mathematics, the Daniell integral is a type of integration that generalizes the concept of more elementary versions such as the Riemann integral to which students are typically first introduced. One of the main difficulties with the traditional formulation of the Lebesgue integral is that it requires the initial development of a workable measure theory before any useful results for the integral can be obtained. However, an alternative approach is available, developed by Percy J. Daniell (1918) that does not suffer from this deficiency, and has a few significant advantages over the traditional formulation, especially as the integral is generalized into higher dimensional spaces and further generalizations such as the Stieltjes integral. The basic idea involves the axiomatization of the integral. *Wik

1891 Walther Wilhelm Georg Bothe (8 Jan 1891; 8 Feb 1957) was a German physicist who developed the coincidence method of detecting the emission of electrons by x-rays in which electrons passing through two adjacent Geiger tubes at almost the same time are registered as a coincidental event. He used it to show that momentum and energy are conserved at the atomic level. In 1929 he applied the method to the study of cosmic rays and was able to show that they consisted of massive particles rather than photons. This research brought him a share (with Max Born) in the Nobel Prize for 1954. In 1930, he observed a strange radiation emitted from beryllium when it was exposed to alpha particles, later identified by Chadwick as consisting of neutrons. He built Germany's first cyclotron (1943).*TIS

1924 Paul Moritz Cohn FRS (8 January 1924, Hamburg, Germany – 20 April 2006, London, England)[1] was Astor Professor of Mathematics at University College London, 1986-9, and author of many textbooks on algebra. His work was mostly in the area of algebra, especially non-commutative rings.*Wik

1942 Stephen W. Hawking (8 Jan 1942, )English theoretical physicist who is one of the world's leaders in his field. His principal areas of research are theoretical cosmology and quantum gravity. Hawking is the Lucasian Professor of Mathematics at Cambridge University (formerly held by Sir Isaac Newton). Afflicted with Lou Gehrig's disease (amyotrophic lateral sclerosis; ALS), Hawking is confined to a wheelchair and is unable to speak without the aid of a computer voice synthesizer. However, despite his challenges, he has utilized his intelligence, knowledge and abilities to make remarkable contributions to the field of cosmology (the study of the universe as a whole). *TIS

DEATHS
1642 Galileo Galilei (15 Feb 1564, 8 Jan 1642) Italian natural philosopher, astronomer, and mathematician who applied the new techniques of the scientific method to make significant discoveries in physics and astronomy. His great accomplishments include perfecting (though not inventing) the telescope and consequent contributions to astronomy. He studied the science of motion, inertia, the law of falling bodies, and parabolic trajectories. His formulation of the scientific method parallel the writings of Francis Bacon. His progress came at a price, when his ideas were in conflict with religious dogma. *TIS

1956 Greenleaf Whittier Pickard (14 Feb 1877, 8 Jan 1956) U.S. electrical engineer whose invention of the crystal detector was one of the first devices widely used for receiving radio broadcasts until superseded by the triode vacuum tube. His patent of 20 Nov 1906 described it as "a means for receiving intelligence communicated by electric waves." He was also one of the first scientists to demonstrate the wireless electromagnetic transmission of speech. Pickard conducted numerous experiments to determine the effect of the sun and sunspots on radio. In his study of the polarisation of radio waves, he contributed to development of the direction finder, and noted as early as 1908 that errors in reading radio compasses might be caused by buildings, trees and other objects.*TIS

1968 Charles Loewner (29 May 1893 Lány, Bohemia – 8 January 1968, Stanford, California) was an American mathematician. His name was Karel Löwner in Czech and Karl Löwner in German.
Loewner received his Ph.D. from the University of Prague in 1917 under supervision of Georg Pick. One of his central mathematical contributions is the proof of the Bieberbach conjecture in the first highly nontrivial case of the third coefficient. The technique he introduced, the Loewner differential equation, has had far-reaching implications in geometric function theory; it was used in the final solution of the Bieberbach conjecture by Louis de Branges in 1985.*Wik

1980 John W. Mauchly (30 Aug 1907, 8 Jan 1980) American physicist and engineer, who with John P. Eckert invented (1946) the Electronic Numerical Integrator and Computer (ENIAC), the first general-purpose electronic computer. Mauchly initially conceived of the computer's architecture, and Eckert possessed the engineering skills to bring the idea to life. ENIAC was developed (1946) for the US Army Ordnance Department as what was probably the first general-purpose electronic computer. It was a vast machine, consuming 100 kW of electric power and containing 18,000 electronic valves. Their successful UNIVAC computer (1951) was the first commercial computer, and introduced magnetic tape for programming.*TIS

2002 Aleksandr Mikhaylovich Prokhorov (11 Jul 1916, 8 Jan 2002) is the Soviet physicist who received, (with Nikolay G. Basov, USSR and Charles H. Townes, US), the Nobel Prize for Physics in 1964 "for fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based on the maser-laser principle." "Maser" stands for "microwave amplification by stimulated emission of radiation." An amplification can occur only if the stimulated emission is larger than the absorption, requiring that there should be more atoms in a high energy state than in a lower one. This state is called an inverted population. Prokhorov had researched the maser independently but simultaneously with the other prize recipients. *TIS

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

On This Day in Math - Jan 7

2012-01-07T00:10:00.004Z

From Galileo's Sidereus Nuncius (p 44)

The purpose of computation is insight, not numbers.

~Richard Hamming

The 7th day of the year; the smallest regular polygon that can not be constructed by straight-edge and compass has seven sides (heptagon).

EVENTS
1610 Galileo discovered the ﬁrst three moons of Jupiter , or the Medicean Stars, as he named them after his patron. *VFR Actually Galileo must have discovered the moons sometime in late December or early January. On January 7, 1610, Galileo wrote a letter containing the first mention of Jupiter’s moons. At the time, he saw only three of them, and he believed them to be fixed stars near Jupiter. He continued to observe these celestial orbs from January 8 to March 2, 1610. In these observations, he discovered a fourth body, and also observed that the four were not fixed stars, but rather were orbiting Jupiter. He discovered the fourth on 13 January. *Wik
and also from the same letter:
In 1610, Galileo dated his first letter describing telescopic observations in which he saw the moon's cratered surface using his twenty-powered spyglass. He wrote, “... it is seen that the Moon is most evidently not at all of an even, smooth, and regular surface, as a great many people believe of it and of the other heavenly bodies, but on the contrary it is rough and unequal. In short it is shown to be such that sane reasoning cannot conclude otherwise than that it is full of prominences and cavities similar, but much larger, to the mountains and valleys spread over the Earth's surface.” Galileo went on to describe the phenomena in considerable detail, rehearsing, as it were, the observations and conclusions he was to publish more elaborately a few months later in Sidereus Nuncius. *TIS

In 1785, Frenchman Jean Pierre Blanchard and American physician and scientist John Jeffries made the first air crossing of the English Channel from England to France in a hot-air balloon - the first international flight. This was the second of two balloon flights Jeffries financed. To accompany him, Jeffries chose Blanchard for his prior experience in balloon flight. The voyage across the Channel was successful, though not without difficulty, because to maintain height they were forced to jettison everything in the basket, including rope and most of their clothes. Their previous flight took place on 30 Nov 1784, in London, for the purpose of taking scientific and meteorological measurements.*TIS

1791 Benjaman Bannaker arrived in Washington D.C. to begin laying out the boundaries of the District of Columbia. He did his ﬁrst observations on Friday the 11th. The ﬁrst two lines were completed on Saturday. *VFR

1810 Gauss wrote his astronomer friend Bessel: “This winter I am teaching two courses for three listeners, of whom one is only modestly prepared, one scarcely modestly prepared, and the third lacks preparation as well as ability. These are the onera of a mathematical professor.”*VFR

1947 President Henry Wriston of Brown University announced the establishment of a new department: History of Mathematics. It was then, and remains today, the only such department in the U.S. Otto Neugebauer (1899–1990) was named the ﬁrst head of the department. Today the department is world famous for its work in ancient mathematics and astronomy. *VFR (Is this still the only History of Mathematics Dept in the U.S.?)

1963 Ivan Sutherland introduces the Sketchpad submitting his Ph.D. thesis to MIT. The Sketchpad, one of the earliest programs for the TX-0, allowed direct manipulation of objects on a computer screen. Using the Sketchpad, a user could create and manipulate graphical figures with a light pen. This thesis provided the basis for later graphical user interfaces and is considered one of the seminal papers in computer science. *CHM

1981 Cathleen S. Morawetz, of the Courant Institute, delivered the 54th Gibbs Lecture entitled “The mathematical approach to the sound barrier.” She was the ﬁrst woman to be invited to give this prestigious address to the AMS. *VFR

BIRTHS
1755 Stephen Groombridge (7 Jan 1755; 30 Mar 1832) English astronomer and merchant, who compiled the Catalogue of Circumpolar Stars (corrected edition published 1838), often known as the Groombridge Catalog. For ten years, from 1806, he made observations using a transit circle, followed by another 10 years adjusting the data to correct for refraction, instrument error and clock error. He retired from the West Indian trade in 1815 to devote full time to the project. He was a founder of the Astronomical Society (1820). His work was continued by others when he was struck (1827) with a "severe attack of paralysis" from which he never fully recovered. The catalog eventually listed 4,243 stars situated within 50° of the North Pole and having apparent magnitudes greater than 9. Editions of the catalog were published posthumously. The 1833 edition was withdrawn due to errors, and corrected in 1838 by A Catalog of Circumpolar Stars, Reduced to January 1, 1810, edited by G. Biddell Airy. *TIS

1827 Sir Sandford Fleming (7 Jan 1827; 22 Jul 1915) Scottish surveyor and leading railway engineer who divided the world into time zones. He emigrated at age 17 years to Quebec, Canada, on 24 Apr 1845, as a surveyor. Later he became one of the foremost railway engineers of his time. While in charge of the initial survey for the Canadian Pacific Railway, the first Canadian railway to span the continent, he realized the problems of coordinating such a long railway. This lead him to the idea of time zones, which contribution to the adoption of the present system of time zones earned him the title of "Father of Standard Time." Fleming also designed the first Canadian postage stamp. Issued in 1851, it cost three pennies and depicted the beaver, now the national animal of Canada.*TIS

1834 Johann Philipp Reis (7 Jan 1834; 14 Jan 1874) German physicist whose invention of an early telephone preceded Bell's work. After years of experimentation, by the age of 27, he constructed a rudimentary transmitter by placing an animal ear membrane in front of an electrical contact. A galvanic inductor oscillated in the receiver in the same manner as the transmitted signal. Reis's instrument conveyed certain sounds, poorly, but no more than that; intelligible speech could not be reproduced. Reis was ready to present his device to Frankfurt's Physics Association (Der Physikalische Verein) on 26 Oct 1861. He gave a lecture titled "Telephony Using Galvanic Current" ("Das Telefonieren durch galvanischen Strom"). During this, the first public demonstration of the successful conversion of electrical into auditory waves, verses of a song were transmitted from the lecture room to a hospital room over a 300-ft away. Reis coined the word "telephone" for his device. The professors to whom this invention was presented were not very impressed and this version of the "telephone" never received any financial support and no patent ensued. Reis' devices were fragile and clumsy laboratory models, never put to public use.*TIS

1859 Marie Georges Humbert (7 Jan 1859 in Paris, France - 22 Jan 1921 in Paris, France) His doctorate extended Clebsch's work on curves. He then studied Abel's work which he developed and put into a geometric setting. It was as a direct consequence of his work on using abelian functions in geometry which won for him the 1892 Académie des Sciences prize for work on Kummer surfaces. As Costabel writes, "He thus enriched analysis and gave the complete solution of the two great questions of the transformation of hyperelliptic functions and of their complex multiplication. "
He also extended work of Hermite considering applications to number theory throughout his life.
Humbert would be better known today if the area of mathematics in which he worked had remained in favor. Since it has now become merely something of an historical curiosity rather than mainstream mathematics, his contribution is less well known. It does, however, indicate the quality of his mathematics that, despite this, his name and results are known today. To some extent this is a consequence of the fact that although he worked in a specialized area he had a remarkably broad knowledge of mathematics and his results form links between areas. *SAU

1871 Birthdate of (Félix-Édouard-Justin-) Émile Borel. “In Paris as a scholarship student preparing for the university, he entered the family circle of G. Darboux through friendship with his son, saw the “good life” of a leading mathematician, and set his heart on it.” *VFR (7 Jan 1871; 3 Feb 1956) was a French mathematician who (with René Baire and Henri Lebesgue), was among the pioneers of measure theory and its application to probability theory. In one of his books on probability, he proposed the thought experiment that a monkey hitting keys at random on a typewriter keyboard will - with absolute certainty - eventually type every book in France's Bibliothèque nationale de France (National Library). This is now popularly known as the infinite monkey theorem. He was first to develop (1899) a systematic theory for a divergent series. He also published (1921-27) a number of research papers on game theory and became the first to define games of strategy. *TIS

1904 Gordon Thomas Whyburn (January 7 1904 , September 8 1969) American mathematician who worked on the topology of point sets. *Wik

1907 Raymond Edward Alan Christopher Paley (7 January 1907 – 7 April 1933) was an English mathematician. Paley was born in Bournemouth, England. He was educated at Eton. From there he entered Trinity College, Cambridge where he showed himself the most brilliant student among a remarkable collection of fellow undergraduates. He won a Smith's Prize in 1930 and was elected a fellow of Trinity College.
His contributions include the Paley construction for Hadamard matrices (closely related to the Paley graphs in graph theory) and his collaboration with Norbert Wiener in the Paley–Wiener theorem (harmonic analysis). He collaborated with A. Zygmund on Fourier series (see also Paley–Zygmund inequality) and worked with J. E. Littlewood on what became known as Littlewood–Paley theory, an application of real-variable techniques in complex analysis.
On 7 April 1933, Paley died in a skiing accident when skiing alone at an altitude of 9,600 ft in Banff, Alberta. He was killed by an avalanche at Deception Pass, Fossil Mountain, in the Canadian Rockies. His death was witnessed by companions lower down the mountainside. Park wardens and a member of the Royal Canadian Mounted Police recovered the body. He is buried in the Banff town cemetery.*Wik

DEATHS
1893 Josef Stefan (24 Mar 1835, 7 Jan 1893) Austrian physicist who proposed a law of radiation (1879) stating that the amount of energy radiated per second from a black body is proportional to the fourth power of its absolute temperature. (A black body is a theoretical object that absorbs all radiation that falls on it.) This law is known as Stefan's law or the Stefan-Bolzmann law. He also studied electricity, the kinetic theory of gases and hydrodynamics.*TIS

1935 Ivan Vsevolodovich Meshchersky (10 Aug 1859 in Arkhangelsk, Russia - 7 Jan 1935 in Leningrad, USSR (now St Petersburg, Russia)) mathematician who gained fame for his work on mechanics, notably the motion of bodies of variable mass. *Wik

1935 Sir Alfred Ewing (27 Mar 1855, 7 Jan 1935) was a Scottish physicist who discovered and named hysteresis (1881), the resistance of magnetic materials to change in magnetic force. Ewing was born and educated in Dundee and studied engineering on a scholarship at Edinburgh University. He helped Sir William Thomson, later Lord Kelvin in a cable laying project. In 1878 he became professor of Mechanical Engineering and Physics at Tokyo University, where he devised instruments for measuring earthquakes. In 1903 he moved to the Admiralty as head of education and training, where during WW I, he and his staff took on the task of deciphering coded messages. *TIS

1943 Nikola Tesla (10 Jul 1856, 7 Jan 1943)Serbian-American inventor and researcher who designed and built the first alternating current induction motor in 1883. He emigrated to the United States in 1884. Having discovered the benefits of a rotating magnetic field, the basis of most alternating-current machinery, he expanded its use in dynamos, transformers, and motors. Because alternating current could be transmitted over much greater distances than direct current, George Westinghouse bought patents from Tesla the system when he built the power station at Niagara Falls to provide electricity power the city of Buffalo, NY.*TIS

1984 Alfred Kastler (3 May 1902, 7 Jan 1984) French physicist who won the Nobel Prize for Physics in 1966 for his discovery and development of methods for observing Hertzian resonances within atoms. This research facilitated the greater understanding of the structure of the atom by studying the radiations that atoms emit when excited by light and radio waves. He developed a method called "optical pumping" which caused atoms in a sample substance to enter higher energy states. This idea was an important predecessor to the development of masers and the lasers which utilized the light energy that was re-emitted when excited atoms released the extra energy obtained from optical pumping.*TIS

1989 John Frank Adams (5 Nov 1930 in Woolwich, London, England -7 Jan 1989 Near Brampton, Huntingdonshire, England) was an English algebraic topologist who pioneered methods for calculating the homotopy of spheres. *Wik

1998 Richard Wesley Hamming (11 Feb 1915, 7 Jan 1998) was an American mathematician who devised computer Hamming codes - error-detecting and correcting codes (1947). These add one or more bits to the transmission of blocks of data, used for a parity check, so that errors can be corrected automatically. By making a resend of bad data unnecessary, efficiency improved for modems, compact disks and satellite communications. He also worked on programming languages, numerical analysis and the Hamming spectral window (used to smooth data before Fourier analysis is carried out). He taught at University of Louisville, then during WW II worked (1945) on computers with the Manhattan Project creating the atomic bomb. From 1946, he spent 30 years with Bell Telephone Labs, eventually becoming head of computing science research.*TIS

2004 Oswald Garrison Villard (17 Sep 1916, 7 Jan 2004) American electronics engineer who developed over-the-horizon radar (a way to detect objects out of direct sight by bouncing radar off the ionosphere, an electrically charged layer in the upper atmosphere) so radar could peer around the Earth's curvature to detect aircraft and missiles thousands of miles away. His interest in electricity began with a copy of Harper's Electricity Book for Boys. At age 12, he put together a radio from a kit. During WW II, he researched countermeasures to protect Allied forces against enemy radio and radar devices. He made pioneering studies of radar jamming. In 1947, he designed a simplified voice transmitter permitting two-way communication on a single radio channel, such as a telephone conversation.*TIS

2012 Herbert Saul Wilf (1931-2012) was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylvania. He wrote numerous books and research papers. Together with Neil Calkin he founded The Electronic Journal of Combinatorics in 1994 and was its editor-in-chief until 2001.
In number theory, the Calkin–Wilf tree is a tree in which the vertices correspond 1-for-1 to the positive rational numbers. The tree is rooted at the number 1, and any rational number expressed in simplest terms as the fraction a/b has as its two children the numbers a/(a + b) and (a + b)/b. Every positive rational number appears exactly once in the tree.
The sequence of rational numbers in a breadth-first traversal of the Calkin–Wilf tree is known as the Calkin–Wilf sequence.*Wik

Credits
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts