Sunday, 13 June 2021

On This Day in Math - June 13

Mathematics is not a careful march
down a well-cleared highway,
but a journey into a strange wilderness,
where the explorers often get lost.
Rigour should be a signal to the historian
that the maps have been made,
and the real explorers have gone elsewhere.
~W.S. Anglin

The 164th day of the year; With the ordered digits of 164 we can form 3 2-digits numbers. Those 3 numbers ± 3 are all prime (16 + 3 = 19, 16 - 3 = 13, 14 + 3 = 17, 14 - 3 = 11, 64 + 3 = 67, 64 - 3 = 61). *Prime Curios

In base 10, 164 is the smallest number that can be expressed as a concatenation of two squares in two different ways: as 1 + 64 or 16 + 4

There are 164 ways to place 5 nonattacking queens on a 5 by 8 board. */

164 is a palindrome in base 3 (20002) or 2*3^4 + 2


1611 a publication on the newly discovered phenomenon of sunspots was dedicated. 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"). This first publication on such observations, was the work of Johannes Fabricius, a Dutch  astronomer who was among the first ever to observe sunspots through a telescope. On 9 Mar 1611, at dawn, Johannes had used his telescope to view the rising sun and had seen 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.

1676 Newton sent Oldenburg the “Epistola prior” for transmission to Leibniz. Among other things it contained the first statement of the binomial theorem for negative and fractional exponents. *VFR This may be the first use of fractional and negative exponents in the modern sense (cajori, 308 pgs 370-371)
The idea and limited use had been mentioned by Viete, but in a rhetorical manner. Wallis, twenty years earlier, had mentioned both negative and fractional "indices" and gives an example using 1/sqrt(2) has index (-1/2). On October 24 of the same year, Newton would use irrational exponents in a letter to Oldenburg. 

1699 John Wallis writes a letter to the Archbishop of Canterbury suggesting that switching from the Julian to Gregorian calendar might be a mistake and expressing his fear that, "..if we go to alter that, it will be attended with a greater mischief than the present inconvenience. "
In a postscript he comments that Lock's suggestion of omitting the Feb 29 from eleven consecutive leap years would lead to ".. a confusion for four and forty years together, wherein we should agree neither with the old nor with the new account." *Philosophical Transactions, 1699 21, 343-354
In accordance with a 1750 act of Parliament, England and its colonies changed calendars in 1752. *Wik

1771 Lagrange presented, to the Berlin Academy, the first proof of Wilson’s theorem (n is prime iff n divides (n − 1)! + 1). Edward Waring published the theorem in 1770, but Leibniz knew it previously . *VFR

1865 Only three months before his death, Sir William Rowan Hamilton received a letter from the American astronomer, Benjamin Gould, informing him that the newly created U.S. National Academy of Sciences had elected him first on its list of Foreign Associates, thereby signifying that the academy considered him the greatest living scientist. [T. L. Hawkins, Hamilton, p. xv] *VFR

1878 Arthur Cayley addresses the London Mathematical Society brings the four color theorem to a wider audience when printed in the Society’s proceedings (Dave Richeson, Euler’s Gem, pg 132) 
The conjecture was first proposed in 1852 when Francis Guthrie, while trying to color the map of counties of England, noticed that only four different colors were needed. At the time, Guthrie's brother, Fredrick, was a student of Augustus De Morgan at University College. Francis inquired with Fredrick regarding it, who then took it to De Morgan (Francis Guthrie graduated later in 1852, and later became a professor of mathematics in South Africa). According to De Morgan:
"A student of mine [Guthrie] asked me to day to give him a reason for a fact which I did not know was a fact — and do not yet. He says that if a figure be any how divided and the compartments differently coloured so that figures with any portion of common boundary line are differently coloured — four colours may be wanted but not more — the following is his case in which four colours are wanted. Query cannot a necessity for five or more be invented…   *Wik
Others have suggested that Mobius presented the challenge of drawing a map requiring five colors as early as 1840.

1878 Thomas Craig received his Ph.D. at The Johns Hopkins University under the direction of J. J. Sylvester for a dissertation on “The representation of one surface upon another; and on some points in the theory of the curvature of surfaces.” He was one of the four to receive his degree there (the philosopher Josiah Royce was another). These were the first Ph.D.s offered by Johns Hopkins, a university founded in 1876 to advance graduate education. *VFR

1893, Bertha (Lamme) Feicht earned a degree in mechanical engineering with a specialty in electrical engineering from Ohio State University. Many refer to her as the first Woman Engineering graduate outside of civil engineering in the US.
During her 12 years at Westinghouse, she worked with the company’s best and brightest, including her pioneering brother, Benjamin, and eventual husband, Russell Feicht.
Benjamin put himself on the map by helping to design the electrical system for the 1893 Chicago World’s Fair. He later worked on the hydroelectric dam on the Niagara River, helping to solve the practical problems of using electric power to light the city of Buffalo.
A highlight for Russell Feicht was designing the then huge 2,000-horsepower motor Westinghouse displayed at the 1904 St. Louis World’s Fair. Both men both served as the company’s chief engineer.
But little record survives about Bertha’s own work, which “Women in Science” says is normal, if not good. *Springfield News-Sun

1959 France issued a stamp picturing Jean Le Rond d’Alembert.
D'ALEMBERT (1717 1783) was abandoned by his parents on the steps of Saint Jean le Rond, which was the baptistery of Notre-Dame. Foster parents were found and he was christened with the name of the saint of the church. When he became famous, his mother attempted to reclaim him, but he rejected her.

1983 Pioneer 10, launched 3 March 1972, leaves the solar system, being the first man-made object to do so. It has traveled over three billion miles.

1994 Lynchburg College Professor Thomas Nicely, discovers a flaw in the Pentium chip from Intel while trying to calculate Brun's constant,(The sum of the reciprocals of all the twin primes, 1/3+1/5+1/5+1/7+1/11+1/13.... which converges to about 1.902.)
The Pentium chip occasionally gave wrong answers to a floating-point (decimal) division calculations due to errors in five entries in a lookup table on the chip. Intel spent millions of dollars replacing the faulty chips.
Nicely first noticed some inconsistencies in the calculations on June 13, 1994 shortly after adding a Pentium system to his group of computers, but was unable to eliminate other factors until October 19, 1994. On October 24, 1994 he reported the issue to Intel. According to Nicely, his contact person at Intel later admitted that Intel had been aware of the problem since May 1994, when the flaw was discovered during testing of the FPU for its new P6 core, first used in the Pentium Pro. *Wik


1555 Giovanni Antonio Magini (in Latin, Maginus) (June 13, 1555; Padua, Italy – February 11, 1617; Bologna, Italy) was an Italian astronomer, astrologer, cartographer, and mathematician.
Dedicating himself to astronomy, in 1582 he wrote Ephemerides coelestium motuum, translated into Italian the following year.
In 1588 he was chosen over Galileo Galilei to occupy the chair of mathematics at the University of Bologna after the death of Egnatio Danti. He died in .
Magini supported a geocentric system of the world, in preference to Copernicus's heliocentric system. Magini devised his own planetary theory, in preference to other existing ones. The Maginian System consisted of eleven rotating spheres, which he described in his Novæ cœlestium orbium theoricæ congruentes cum observationibus N. Copernici (Venice, 1589).
In his De Planis Triangulis (1592), he described the use of quadrants in surveying and astronomy. In 1592 Magini published Tabula tetragonica, and in 1606 devised extremely accurate trigonometric tables. He also worked on the geometry of the sphere and applications of trigonometry, for which he invented calculating devices. He also worked on the problem of mirrors and published on the theory of concave spherical mirrors.
He also published a commentary on Ptolemy’s Geographia (Cologne, 1596).
As a cartographer, his life's work was the preparation of Italia or the Atlante geografico d'Italia (Geographic Atlas of Italy), printed posthumously by Magini's son in 1620. This was intended to include maps of every Italian region with exact nomenclature and historical notes. A major project, its production (begun in 1594) proved expensive and Magini assumed various additional posts in order to fund it, including becoming tutor in mathematics to the sons of Vincenzo I of Gonzaga, Duke of Mantua, a major patron of the arts and sciences. He also served as court astrologer. The Duke of Mantua, to whom the atlas is dedicated, assisted him with this project and allowed for maps of the various states of Italy to be brought to Magini. The governments of Messina and Genoa also assisted Magini financially in this project. Magini did not do any of the mapping himself.
He was also interested in pursuits which today would be considered pseudoscientific. A strong supporter of astrology, he defended its use in medicine in his De astrologica ratione (Venice, 1607). Magini collaborated closely with Valentine Naibod, and in this book he published De annui temporis mensura in Directionibus and De Directionibus from Naibod's unfinished manuscript Claudii Ptolemaei Quadripartitae Constructionis Apotelesmata Commentarius novus et Eiusdem Conversio nova. He was also interested in metoposcopy.
He corresponded with Tycho Brahe, Clavius, Abraham Ortelius, and Johann Kepler.

1580 Willebrord Snellius (Willebrord Snel van Royen) (13 June 1580; Leiden, Netherlands – 30 October 1626, Leiden) was a Dutch astronomer and mathematician, known in the English-speaking world as Snell. In the west, especially the English speaking countries, his name has been attached to the law of refraction of light for several centuries, but it is now known that this law was first discovered by Ibn Sahl in 984. The same law was also investigated by Ptolemy and in the Middle Ages by Witelo, but due to lack of adequate mathematical instruments (trigonometric functions) their results were saved as tables, not functions.
Snell also improved the classical method of calculating approximate values of π by polygons which he published in Cyclometricus (1621). Using his method 96 sided polygons gives π correct to 7 places while the classical method yields only 2 places. Van Ceulen's 35 places could be found with polygons of 230 sides rather than 262. In fact Van Ceulen's 35 places of π appear in print for the first time in this book by Snell.
*Wik *SAU

1773 Thomas Young (13 June 1773 – 10 May 1829) was an English polymath. He is famous for having partly deciphered Egyptian hieroglyphs (specifically the Rosetta Stone) before Jean-François Champollion eventually expanded on his work. He was admired by, among others, Herschel and Einstein.
Young made notable scientific contributions to the fields of vision, light, solid mechanics, energy, physiology, language, musical harmony and Egyptology.*Wik .. For someone as talented as Young, he received relatively few honours. The one which pleased him most was election as a foreign member of the Institute in Paris in 1827. When Young died two years later, Arago gave the eulogy at the Institute saying:-
The death of Young in his own country attracted but little regard. *SAU

I recently learned that Young was also the first Secretary of the Board of Longitude, and also served as Superintendent of the Nautical Almanac" thanks to * Sophie Waring @atinybitwaring

1806 George Parker Bidder (13 June 1806 – 20 September 1878) was an English engineer and calculating prodigy. Born in the town of Moretonhampstead, Devon, England, he displayed a natural skill at calculation from an early age. In childhood, his father, William Bidder, a stonemason, exhibited him as a "calculating boy", first in local fairs up to the age of six, and later around the country. In this way his talent was turned to profitable account, but his general education was in danger of being completely neglected.
Still many of those who saw him developed an interest in his education, a notable example being Sir John Herschel. His interest led him to arrange it so George could be sent to school in Camberwell. There he did not remain long, being removed by his father, who wished to exhibit him again, but he was saved from this misfortune and enabled to attend classes at the University of Edinburgh, largely through the kindness of Sir Henry Jardine,
On leaving college in 1824 he received a post in the ordnance survey, but gradually drifted into engineering work.
Bidder died at Dartmouth, Devon and was buried at Stoke Fleming.
His son, George Parker Bidder, Jr. (1836–1896), who inherited much of his father's calculating power, was a successful parliamentary counsel and an authority on cryptography. His grandson, also named George Parker Bidder, became a marine biologist and president of the Marine Biological Association of the United Kingdom from 1939 to 1945. *Wik

1831 James Clerk Maxwell (13 June 1831 – 5 November 1879)  Scottish physicist and mathematician. Maxwell's researches united electricity and magnetism into the concept of the electro-magnetic field. In London, around 1862, Maxwell calculated that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He proposed that the phenomenon of light is therefore an electromagnetic phenomenon. The four partial differential equations, now known as Maxwell's equations, first appeared in fully developed form in Electricity and Magnetism (1873). He died relatively young; some of the theories he advanced in physics were only conclusively proved long after his death. Maxwell's ideas also paved the way for Einstein's special theory of relativity and the quantum theory. *TIS  My favorite anecdote about Maxwell:  It is said that on his arrival at Cambridge University he was informed that there would be a compulsory 6 a.m. church service.  After a moment of thought he replie, "Aye, I suppose I could stay up that late. "

1871 Ernst Steinitz (13 June 1871 – 29 September 1928) In 1910 he gave a general abstract definition of a field. He is responsible for introducing a number of concepts into the Theory of Fields, including prime subfields, separable elements, and perfect fields. *VFR

1868  Wallace Clement Ware Sabine (June 13, 1868, Richwood, Ohio, U.S.—died Jan 10, 1919, Cambridge, Mass.) 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

1872 Jessie Chrystal MacMillan (13 June 1872 in Edinburgh, Scotland - 21 September 1937 in Edinburgh, Scotland) was the first female science graduate at Edinburgh University and the first female honours graduate in Mathematics. She went on to study at Berlin. She was the first woman to plead a case before the House of Lords. She became active in the Women's Suffrage Movement and went on to become a lawyer.
A Millennial plaque is at Kings Buildings (West Mains Road), in Edinburgh. It reads:
In honour of
Suffragist, founder of Women's International League for Peace and Freedom,
first woman science graduate of the University (1896).

1876 William S. Gosset (June 13, 1876–October 16, 1937) This brew-master/statistician published under the name “student.”.   He developed the "small sample" or t-test for statistical testing.  Among many things of interest is a remark in Section 1 in the Comment by Persi Diaconis and Erich Lehmann indicating that Laplace was on the verge of first finding the t pdf but 'fell for the easy normal approximation' (quotation and discussion from the 1998 book A History of Mathematical Statistics From 1750 to 1930 by Anders Hald)

1876 William Sealy Gosset(13 June 1876; Canterbury, England- 16 October 1937 in Beaconsfield, England)
Gosset was the eldest son of Agnes Sealy Vidal and Colonel Frederic Gosset who came from Watlington in Oxfordshire. William was educated at Winchester, where his favourite hobby was shooting, then entered New College Oxford where he studied chemistry and mathematics. While there he studied under Airy. He obtained a First Class degree in both subjects, being awarded his mathematics degree in 1897 and his chemistry degree two years later.
Gosset obtained a post as a chemist with Arthur Guinness Son and Company in 1899. Working in the Guinness brewery in Dublin he did important work on statistics. In 1905 he contacted Karl Pearson and arranged to go to London to study at Pearson's laboratory, the Galton Eugenics Laboratory, at University College in session 1906-07. At this time he worked on the Poisson limit to the binomial and the sampling distribution of the mean, standard deviation, and correlation coefficient. He later published three important papers on the work he had undertaken during this year working in Pearson's laboratory.
Many people are familiar with the name "Student" but not with the name Gosset. In fact Gosset wrote under the name "Student" which explains why his name may be less well known than his important results in statistics. He invented the t-test to handle small samples for quality control in brewing. Gosset discovered the form of the t distribution by a combination of mathematical and empirical work with random numbers, an early application of the Monte-Carlo method.

McMullen says:-
To many in the statistical world "Student" was regarded as a statistical advisor to Guinness's brewery, to others he appeared to be a brewer devoting his spare time to statistics. ... though there is some truth in both these ideas they miss the central point, which was the intimate connection between his statistical research and the practical problems on which he was engaged. ... "Student" did a very large quantity of ordinary routine as well as his statistical work in the brewery, and all that in addition to consultative statistical work and to preparing his various published papers.

From 1922 he acquired a statistical assistant at the brewery, and he slowly built up a small statistics department which he ran until 1934.
Gosset certainly did not work in isolation. He corresponded with a large number of statisticians and he often visited his father in Watlington in England and on these occasions he would visit University College, London, and the Rothamsted Agricultural Experiment Station. He would discuss statistical problems with Fisher, Neyman and Pearson. *SAU

1911 Luis Walter Alvarez (June 13, 1911 – September 1, 1988) was an American experimental physicist, inventor, and professor who was awarded the Nobel Prize in Physics in 1968. The American Journal of Physics commented, "Luis Alvarez was one of the most brilliant and productive experimental physicists of the twentieth century.
In 1940 Alvarez joined the MIT Radiation Laboratory, where he contributed to a number of World War II radar projects, from early improvements to Identification Friend or Foe (IFF) radar beacons, now called transponders, to a system known as VIXEN for preventing enemy submarines from realizing that they had been found by the new airborne microwave radars. The radar system for which Alvarez is best known and which has played a major role in aviation, most particularly in the post war Berlin airlift, was Ground Controlled Approach (GCA). Alvarez spent a few months at the University of Chicago working on nuclear reactors for Enrico Fermi before coming to Los Alamos to work for Robert Oppenheimer on the Manhattan project. Alvarez worked on the design of explosive lenses, and the development of exploding-bridgewire detonators. As a member of Project Alberta, he observed the Trinity nuclear test from a B-29 Superfortress, and later the bombing of Hiroshima from the B-29 The Great Artiste.
After the war Alvarez was involved in the design of a liquid hydrogen bubble chamber that allowed his team to take millions of photographs of particle interactions, develop complex computer systems to measure and analyze these interactions, and discover entire families of new particles and resonance states. This work resulted in his being awarded the Nobel Prize in 1968. He was involved in a project to x-ray the Egyptian pyramids to search for unknown chambers. With his son, geologist Walter Alvarez, he developed the Alvarez hypothesis which proposes that the extinction event that wiped out the dinosaurs was the result of an asteroid impact. *Wik

1906 Bruno de Finetti (13 June 1906 - 20 July 1985) De Finetti was born in Innsbruck, Austria, and was a big contributor to subjective/personal probability and Bayesian inference along with L.J. ("Jimmie") Savage (1917-1971), both of whom are discussed briefly in Chapter 13 ("The Bayesian Heresy") of David Salsburg's book The Lady Tasting Tea and in Salsburg's concluding Chapter 29.*David Bee

1928 John Forbes Nash, Jr ( June 13, 1928-May 23, 2015) is an American mathematician whose works in game theory, differential geometry, and partial differential equations have provided insight into the forces that govern chance and events inside complex systems in daily life. His theories are used in market economics, computing, evolutionary biology, artificial intelligence, accounting, politics and military theory. Serving as a Senior Research Mathematician at Princeton University  during the later part of his life, he shared the 1994 Nobel Memorial Prize in Economic Sciences with game theorists Reinhard Selten and John Harsanyi.
Nash is the subject of the Hollywood movie A Beautiful Mind. The film, loosely based on the biography of the same name, focuses on Nash's mathematical genius and struggle with paranoid schizophrenia*Wik

1942 Homer Alfred Neal, (June 13, 1942 in Franklin, Kentucky; May 23, 2018 Ann Arbor, Michigan) was an African-American particle physicist and a distinguished professor at the University of Michigan. Neal was President of the American Physical Society in 2016. He was also a board member of Ford Motor Company, a council member of the National Museum of African American History and Culture, and a director of the Richard Lounsbery Foundation. Neal was the interim President of the University of Michigan in 1996. Neal's research group works as part of the ATLAS experiment hosted at CERN in Geneva.

He received his B.S. in Physics from Indiana University in 1961, and earned his Ph.D. from the University of Michigan in 1966. From 1976 to 1981, Neal was Dean for Research and Graduate Development at Indiana University, and from 1981 to 1986 he was provost at the State University of New York at Stony Brook. He held Honorary Doctorates from Indiana University, Michigan State University, and Notre Dame University.

On 14 Nov 2009, Dr. Neal described the discoveries of spin at the University of Michigan (UM) with a presentation: History of Spin at Michigan *Wik

1966 Grigori Yakovlevich Perelman (13 June 1966, - ) is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology.
In 1994, Perelman proved the soul conjecture. In 2003, he proved Thurston's geometrization conjecture. This consequently solved in the affirmative the Poincaré conjecture, posed in 1904, which before its solution was viewed as one of the most important and difficult open problems in topology.
In August 2006, Perelman was awarded the Fields Medal for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow." Perelman declined to accept the award or to appear at the congress, stating: "I'm not interested in money or fame, I don't want to be on display like an animal in a zoo." On 22 December 2006, the journal Science recognized Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first such recognition in the area of mathematics.
On 18 March 2010, it was announced that he had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he turned down the prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. *Wik


1916 Silvanus P. Thomson (19 June 1851 – 12 June 1916) In 1910 he published Calculus Made Easy, which was published anonymously until after his death in 1916. It is still in print. *VFR He was a noted physicist and engineer, and a celebrated teacher and writer on electricity and magnetism. He also wrote popular biographies of Faraday and Lord Kelvin. At his death he was professor at City and Guilds Technical College at Finsbury (London)

1939 Hermann Wiener (15 May 1857 in Karlsruhe, Germany-13 June 1939 in Darmstadt, Germany)
was a German mathematician who worked on the foundations of geometry*SAU

1994 John Leslie Britton (November 18, 1927 – June 13, 1994) was an English mathematician from Yorkshire who worked in combinatorial group theory and was an expert on the word problem for groups. Britton was a member of the London Mathematical Society and was Secretary of Meetings and Membership with that organization from 1973-1976. Britton died in a climbing accident on the Isle of Skye. *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Saturday, 12 June 2021

On This Day in Math - June 12

My work always tried to unite the true
with the beautiful, but when I had to choose... 
I usually chose the beautiful.
~ Hermann Weyl

The 163rd day of the year; 163 is the 38th prime number

\( e^{\pi*\sqrt{163}} \) is an integer. Ok, not quite. 262537412640768743.99999999999925

 .     and      *Wikipedia

Colin Beveridge ‏@icecolbeveridge pointed out that \( (2+\sqrt{3})^{163} \) is also very, very close to an integer. (but it is very large,greater than 1093 , and was not, to my knowledge, ever the source of an April fools joke.)

163 is conjectured to be the largest prime that can be represented uniquely as the sum of three squares \( 163 = 1^2 + 9^2 + 9^2 \).

Most students know that the real numbers can be uniquely factored. . Some other fields can be uniquely factored as well, for instance, the complex field a+bi where i represents the square root of -1 is such a field.  In 1801, Gauss conjectured that there were only nine integers k such that \(a + b\sqrt{-k} \) is a uniquely  factorable field.  The largest of these integers is 163.  Today they are called Heegner numbers after a proof by Kurt Heegner in 1952.

163 is as easy as 1+2*3^4.

163 is the sum 37 + 59 + 67, all prime


1493 First issue of Nuremberg Chronicles published in Latin (A German edition would be issued in December). The journal is said to have printed an image of the 684 passage of Halley's comet. Roberta Olsen and Jay Pasachoff of Wheaton College have written that the same woodblock was used to depict four other comets. They also said the Chronicles use three more prints to depict this same 684 comet in different editions. The one below, from the Library of Congress Collection, is the one which was in the Art Exhibit at the Smithsonian Air and Space Museum in Washington, D.C., entitled: "Fire and Ice - A History of Comets in Art"
For more detail about the Chronicles check out this post by the Renaissance Mathematicus.

1676   a partial solar eclipse which was to be viewed as something of an opening ceremony for the Royal Observatory in Greenwich: it was hoped that the King would attend but he did not, Lord Brouncker, President of the Royal Society, being the guest of honour instead. *Rebekah Higgitt, Telescopos

1689 Although they had corresponded, through Oldenburg, about optics sixteen years earlier (much to Newton’s grief), Newton first met Christiaan Huygens at a Royal Society meeting in London.
[Newton, Mathematical Papers, 6, xxiii] *VFR

In 1837, British inventors William Cooke and Charles Wheatstone received a patent for their electromagnetic telegraph. Their invention was put in public service in 1839, five years before the more famous Morse telegraph.*TIS Wheatstone's telegraph was a five wire/five needle telegraph that had a receiver that pointed out the message letter by letter without a code such as Morse used for his one and two wire models. (Wheatstone was very capable of creating codes as well. He was the creator of the Playfair cipher; an ingenious system which prevented frequency analysis by substituting two letters at a time.)

1891, the Swiss Army Soldier Knife
In 1897, the Swiss Army Knife was patented by Carl Elsener *TIS It was in Ibach, in 1884, where Karl Elsener and his mother, Victoria, opened a cutlery cooperative that would soon produce the first knives sold to the Swiss Army. The original model, called the Soldier Knife, was made for troops who needed a foldable tool that could open canned food and aid in disassembling a rifle. The Soldier Knife included a blade, a reamer, a can opener, a screwdriver, and oak handles. *

In 1908, the Rotherhithe-Stepney tunnel beneath the Thames in South London was opened for road vehicle traffic. It was built by Sir Maurice Fitzmaurice between 1904 and 1908. With a length of 4860 feet (1481 metres) excluding the approaches, it remains the largest iron-lined subaqueous tunnel in the world. It was constructed partly by tunneling and partly by the cut and cover method. The area around the entrances was cleared resulting in 3,000 people being rehoused. It is located close to the Rotherhithe-Wapping Thames Tunnel built (1825-43) by Marc Brunel and his son, Isambad K. Brunel which was the world's first tunnel beneath a navigable river.*TIS

1973 Germany issued a postage stamp picturing a model of the calculator built by Wilhelm Schickard of the University of Tubingen 350 years before. [Scott #1123].

1979 Bryan Allen, age 26, of the U.S. pedaled the Gossamer Albatross on the first human powered flight across the English channel. This 21 mile flight won him a £100,000 prize offered by British industrialist Henry Kremer. Two years earlier Allen was the first to fly an aircraft around a one-mile figure eight course under human power alone. See “Human-powered flight,” Scientific American, November 1985, p. 144. *VFR


1577 Paul Guldin born (original name Habakkuk Guldin) (June 12, 1577 – November 3, 1643) was a Swiss Jesuit mathematician and astronomer. He discovered the Guldinus theorem to determine the surface and the volume of a solid of revolution. This theorem is also known as Pappus–Guldinus theorem and Pappus's centroid theorem, attributed to Pappus of Alexandria. ( simply stated: that the volume = area times distance traveled by the centroid, and surface = arclength times distance travelled by centroid. These nicely produce the surface area and volume of a torus, for example.) He was noted for his association with the German mathematician and astronomer Johannes Kepler. He was born in Mels, Switzerland and was a professor of mathematics in Graz and Vienna.
In Paolo Casati's astronomical work Terra machinis mota (1658), Casati imagines a dialogue between Guldin, Galileo, and Marin Mersenne on various intellectual problems of cosmology, geography, astronomy and geodesy. *Wik
Paul Guldin's critique of Bonaventura Cavalieri's indivisibles is contained in the fourth book of his De Centro Gravitatis (also called Centrobaryca), published in 1641. Cavalieri's proofs, Guldin argued, were not constructive proofs, of the kind that classical mathematicians would approve of. *Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World, by Amir Alexander

1806 John A. Roebling ( June 12, 1806 – July 22, 1869), civil engineer and designer of bridges, was born in Mühlhausen, Prussia. The Brooklyn Bridge, Roebling's last and greatest achievement, spans New York's East River to connect Manhattan with Brooklyn. When completed in 1883, the bridge, with its massive stone towers and a main span of 1,595.5 feet between them, was by far the longest suspension bridge in the world. Today, the Brooklyn Bridge is hailed as a key feature of New York's City's urban landscape, standing as a monument to progress and ingenuity as well as symbolizing New York's ongoing cultural vitality. *Library of Congress

1843 Sir David Gill (12 June 1843 – 24 January 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. From his first training as a watchmaker, he progressed to the timekeeping requirements of astronomy. He designed, equipped, and operated a private observatory near Aberdeen. In 1877, Gill and his wife measured the solar parallax by observing Mars from Ascension Island. 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. He later redetermined the solar parallax to such precision that his value was used for almanacs until 1968. *TIS

1851 Sir Oliver Joseph Lodge, FRS (12 June 1851 – 22 August 1940) was a British physicist and writer involved in the development of key patents in wireless telegraphy. In his 1894 Royal Institution lectures ("The Work of Hertz and Some of His Successors"), Lodge coined the term "coherer" for the device developed by French physicist Édouard Branly based on the work of Italian physicist Temistocle Calzecchi Onesti. In 1898 he was awarded the "syntonic" (or tuning) patent by the United States Patent Office. He was also credited by Lorentz (1895) with the first published description of the length contraction hypothesis, in 1893, though in fact Lodge's friend George Francis FitzGerald had first suggested the idea in print in 1889. *Wik

1855 Eduard Wiltheiss (12 June 1855 Worms, Germany – 7 July 1900 Halle) was a German mathematician who made major contributions to the theory of abelian functions *SAU

1888 Zygmunt Janiszewski, (June 12, 1888, Warsaw - January 3, 1920, Lviv) the father of Polish mathematics, born. At the end of World War I, Janiszewski was the driving force behind the creation of one of the strongest schools of mathematics in the world. This is all the more remarkable, given Poland's difficult situaltion at war's end.
Janiszewski devoted the family property that he had inherited from his father to charity and education. He also donated all the prize money that he received from mathematical awards and competitions to the education and development of young Polish students.
In mathematics, his main interest was topology.
He was the driving force, together with Wacław Sierpiński and Stefan Mazurkiewicz, behind the founding of the mathematics journal Fundamenta Mathematicae. Janiszewski proposed the name of the journal in 1919, though the first issue was published in 1920, after his death. It was his intent that the first issue comprise solely contributions by Polish mathematicians. It was Janiszewski's vision that Poland become a world leader in the field of mathematics—which she did in the interbellum.
His life was cut short by the influenza pandemic of 1918-19, which took his life at Lwów on 3 January 1920 at the age of 31. He willed his body for medical research, and his cranium for craniological study, desiring to be "useful after his death". *Wik

1937 Vladimir Arnold (12 June 1937 – 3 June 2010) won a Wolf prize for his work on dynamical systems, differential equations, and singularity theory.*SAU He died nine days before his birthdate in 2010.


1835 Edward Troughton  (October 1753 - June 12, 1835) English scientist and instrument maker. Troughton established himself as the leading maker of instruments in England. He began his instrument making career with instruments to aid navigation, for example, he designed the 'pillar' sextant, patented in 1788, the dip sector, the marine barometer and the reflecting circle built in 1796. Other instruments which he designed were for use in surveying. He designed the pyrometer, the mountain barometer and the large surveying theodolites. His famous instruments were astronomical ones. He made the Groombridge Transit Circle in 1805 and a six foot Mural Transit Circle in 1810 which was erected at the Observatory in Greenwich in 1812. *TIS  Troughton was awarded the Copley Medal of the Royal Society in 1809. He was elected a Fellow of the Royal Society in March 1810. *Wik

1885 (Henry Charles) Fleeming Jenkin (25 Mar 1833; 12 Jun 1885 at age 52) British engineer noted for his work in establishing units of electrical measurement. After earning an M.A. (1851), he worked for the next 10 years with engineering firms engaged in the design and manufacture of submarine telegraph cables and equipment for laying them. In 1861 his friend William Thomson (later Lord Kelvin) procured Jenkin's appointment as reporter for the Committee of Electrical Standards of the British Association for the Advancement of Science. He helped compile and publish reports that established the ohm as the absolute unit of electrical resistance and described methods for precise resistance measurements. *TIS

1900 Jean Frenet (7 February 1816 – 12 June 1900) was a French mathematician best remembered for the Serret-Frenet formulas for a space-curve and they were presented in his doctoral thesis at Toulouse in 1847. *SAU  He wrote six out of the nine formulas, which at that time were not expressed in vector notation, nor using linear algebra.*Wik

1980 Egon Sharpe Pearson, (Hampstead, 11 August 1895 – Midhurst, 12 June 1980) was the only son of Karl Pearson, and like his father, a leading British statistician.
He went to Winchester School and Trinity College, Cambridge, and succeeded his father as professor of statistics at University College London and as editor of the journal Biometrika.
Pearson is best known for development of the Neyman-Pearson lemma of statistical hypothesis testing.
He was President of the Royal Statistical Society in 1955–56, and was awarded its Guy Medal in Gold in 1955. He was awarded a CBE in 1946.
He was elected a Fellow of the Royal Society in Mar 1966. His candidacy citation read: "Known throughout the world as co-author of the Neyman-Pearson theory of testing statistical hypotheses, and responsible for many important contributions to problems of statistical inference and methodology, especially in the development and use of the likelihood ratio criterion. Has played a leading role in furthering the applications of statistical methods - for example, in industry, and also during and since the war, in the assessment and testing of weapons." *Wik

** Actually,  \( e^{\pi*\sqrt{163}} \) is approximately 262537412640768743.9999999999992

In the April 1975 issue of Scientific American, Martin Gardner wrote (jokingly) that Ramanujan's constant (e^(pi*sqrt(163))) is an integer. The name "Ramanujan's constant" was actually coined by Simon Plouffe and derives from the above April Fool's joke played by Gardner. The French mathematician Charles Hermite (1822-1901) observed this property of 163 long before Ramanujan's work on these so-called "almost integers."

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Friday, 11 June 2021

On This Day in Math - June 11

All truths are easy to understand once they are discovered;
the point is to discover them.
~Galileo Galilei

The 162nd day of the year; 162 is the smallest number that can be written as the sum of 4 positive squares in 9 ways.*What's Special About This Number? (Can you find all nine ways?... Can you find a smaller number that can be written as the sum of four squares in eight ways?)

the 12th prime (12 = 1*6*2) ; p12 = 37, and the number of primes less than 162, \( \pi(162)\) is also 37. There is no smaller number with this property.

162 is the total number of baseball games each team plays during a regular season in Major League Baseball.

Jim Wilder pointed out that 1621= 162 has a digit sum of nine; and 1622= 26244 has a digit sum of 18; and 1623= 4251528 has a digit sum of 27. And 1624 ???

A T Vandermonde should be remembered for the wonderfully useful approach he had for generalizations on the factorial, and in my mind, created the most useful notation ever (and, he seems to be the first to think of 0!=1) His notation included a method for skipping numbers, so that [p/3]n would indicate p(p-3)(p-6)... (p-3(n-1)); and in his notation 162 = [9/3]3 or 9*6*3. Now that's a notation worth having an exclamation point!


1644 Florentine scientist, Evangelista Torricelli described in a letter (to Michelangelo Ricci) the invention of a barometer, or "Torricellian tube.
"Many have said that a vacuum does not exist, others that it does exist in spite of the repugnance of nature and with difficulty; I know of no one who has said that it exists without difficulty and without a resistance from nature. I argued thus: If there can be found a manifest cause from which the resistance can be derived which is felt if we try to make a vacuum, it seems to me foolish to try to attribute to vacuum those operations which follow evidently from some other cause; and so by making some very easy calculations, I found that the cause assigned by me (that is, the weight of the atmosphere) ought by itself alone to offer a greater resistance than it does when we try to produce a vacuum."

"We live submerged at the bottom of an ocean of air.",

1742, Benjamin Franklin invented the Franklin stove. The wood fuel burns on an iron surface over a cold air duct which heats air which then passes through baffles in the back wall. The heated air is released through vents on each side of the stove. Rather than patent it, he chose to write about it in a book so that others could freely copy his design. As he wrote, "That as we enjoy great Advantages from the Inventions of others, we should be glad of an Opportunity to serve others by any Invention of ours, and this we should do freely and generously."*TIS
1795 The Board of Longitude awards a 200 pound payment to Ralph Walker for his invention of a compass/sundial combination. "Comparing this reading with the direction in which the compass needle was pointing gave the magnetic variation. This could, in theory, be used to discover the longitude, by finding where supposed ‘magnetic meridians’ intersected with the observed latitude....Nevil Maskelyne didn’t think it was an effective longitude method" *kmcalpine, Royal Museum Greenwich blog
A letter with the directions for the instruments use is here, and the letter from the board to authorize the payment is here. (with HT to Richard Dunn@Lordoflongitude)

Walt Disney files a trademark application for the image of Mickey Mouse
with the United States Patent Office.

1955 France issued a postage stamp with a portrait of
Pierre Simon de Laplace (1749–1827)


1656 Charles René Reyneau (11 June 1656 in Brissac, Maine-et-Loire, France - 24 Feb 1728 in Paris, France) was a French mathematician who published an influential textbook on the newly invented calculus.*SAU (He) "undertook to reduce into one body, for the use of his scholars, the principal theories scattered here and there in Newton, Descartes, Leibnitz, Bernoulli, the Leipsic Acts, the Memoirs of the Paris Academy, and in other works; treasures which by being so widely dispersed, proved much less useful than they otherwise might have been. The fruit of this undertaking, was his “Analyse Demontree,” or Analysis Demonstrated, which he published in 1708, 2 vols. 4to. He gave it the name of “Analysis Demonstrated,” because he demonstrates in it several methods which had not been handled by the authors of them, with sufficient perspicuity and exactness. The book was so well approved, that it soon became a maxim, at least in France, that to follow him was the best, if not the only way, to make any extraordinary progress in the mathematics and he was considered as the first master, as the Euclid of the sublime geometry." (From the 1812 Chalmer's Biography, vol. 26, p. 151)

1687 Maurice Paul Auguste Charles Fabry (11 June 1867, Marseille – 11 December 1945, Paris) was a French physicist who graduated from the École Polytechnique in Paris.
Together with Henri Buisson, he discovered the ozone layer in 1913. In optics, he discovered an explanation for the phenomenon of interference fringes. Together with his colleague Alfred Pérot he invented the Fabry–Pérot interferometer.
In 1921, he was appointed Professor of General Physics at the Sorbonne and the first director of the new Institute of Optics. He was the first general director of the Institut d'optique théorique et appliquée and director of "grande école" École supérieure d'optique (SupOptique).
During his career Fabry published 197 scientific papers, 14 books, and over 100 popular articles. For his important scientific achievements he received the Rumford Medal from the Royal Society of London in 1918. In the United States his work was recognized by the Henry Draper Medal from the National Academy of Sciences (1919) and the Franklin Medal from the Franklin Institute (1921). In 1927 he was elected to the French Academy of Sciences. *Wik

1723  Johann Georg Palitzsch (June 11, 1723 – February 21, 1788) was born.  As a German farmer and amateur astronomer from the village of Prohlis near Dresden, he would observe a comet on Christmas day in 1758 and confirm one of the most significant scientific theories in history.  See the full story of his Christmas/birthday observation from Thony Christie.

 1862 Lothar Heffter (June 11th 1862 in Koszalin , January 1 1962 in Freiburg )At the age of 99 he published the second edition of his Begr¨undung der Funktionentheorie. *VFR He did research in the theory of linear differential equations , the complex analysis and analytic geometry and worked on the four-color problem. Lazarus Fuchs was his teacher. His main concern was the popularization of mathematics.

1881 Hilda Phoebe Hudson (June 11, 1881 Cambridge – November 26, 1965 London) was an English mathematician who worked on algebraic geometry, in particular on Cremona transformations.
Educated at Newnham College, University of Cambridge, after a year studying at the University of Berlin she returned to Newnham as lecturer in mathematics and later Associate Research Fellow. She was also awarded MA and ScD degrees by Trinity College, Dublin. Most of Hudson's research was in the area of pure mathematics concerned with surfaces and plane curves, her special interest was in cremona transformation. Her monograph Ruler and Compasses was well-received as "a welcome addition to the literature on the boundary between elementary and advanced mathematics". In 1917 she joined an Air Ministry subdivision undertaking aeronautical engineering research, where she applied pioneering work on the application of mathematical modelling to aircraft design for which she was appointed OBE in 1919. As a distinguished mathematician she was one of the few women of her time to serve on the council of the London Mathematical Society. *Wik

1886 David Barnard Steinman (June 11, 1886 - August 21, 1960) Designer of the BIG MAC Bridge between the Upper and Lower Peninsulas of Michigan (top). American engineer whose studies of airflow and wind velocity helped make possible the design of aerodynamically stable bridges. Steinman's thesis for his Ph.D. from Colombia University (1911) was published as "The Design of the Henry Hudson Memorial Bridge as a Steel Arch, and more than 20 years later he built the bridge he had planned over the Harlem River. Steinman designed more than 400 bridges, for instance Sidney Harbor Bridge in Australia, Mackinac Straits Bridge, Carquinez Strait Bridge, San Francisco (1937), Saint Johns Bridge, Portland, Ore, Deer Isle Bridge, Maine, Mount Hope Bridge, Rhode Island. *TIS

1910 Jacques-Yves Cousteau (11 June 1910 – 25 June 1997) French naval officer, oceanographer, marine biologist and ocean explorer, known for his extensive underseas investigations. He was co-inventor of the aqualung which made SCUBA diving possible (1943). Cousteau the developed the Conshelf series of manned habitats, the Diving Saucer, a process of underwater television and numerous other platforms and specialized instruments of ocean science. In 1945 he founded the French Navy's Undersea Research Group. He modified a WWII wooden hull minesweeper into the research vesselCalypso, in 1950. An observation dome added to the foot of Calypso's bow was found to increase the ship's stability, speed and fuel efficiency. *TIS For whom my oldest son is named.

1914 Rufus Philip Isaacs (11 June 1914 in New York City, New York -18 January 1981 in Baltimore) was a game theorist especially prominent in the 1950s and 1960s with his work on differential games.
He worked for the RAND Corporation from 1948 until winter 1954/1955. His investigation stemmed from classic pursuit-evasion type zero-sum dynamic two player games such as the Princess and monster game. In 1942, He married Rose Barcov, and they had two daughters.
His work in pure mathematics included working with monodiffric functions, fractional-order mappings, graph theory, analytic functions, and number theory. In graph theory he constructed the first two infinite families of snarks. In applied mathematics, he worked with aerodynamics, elasticity, optimization, and differential games, which he is most known for. He received his bachelors from MIT in 1936, and received his MA and PhD from Columbia University in 1942 and 1943 respectively. His first post after the war ended was at Notre Dame, but he left in 1947 due to salary issues. While at RAND, much of his work was classified, and thus remained unknown until the publication of his classic text on differential games a decade after leaving RAND. His career after RAND was spent largely in the defense and avionics industries. While at RAND, he worked with researchers including Richard E. Bellman, Leonard D. Berkovitz, David H. Blackwell, John M. Danskin, Melvin Dresher, Wendell H. Fleming, Irving L. Glicksberg, Oliver A. Gross, Samuel Karlin, John W. Milnor, John F. Nash, and Lloyd S. Shapley. His work has significant influence on mathematical optimization including fundamental concepts such as dynamic programming (Richard E. Bellman) and the Pontryagin maximum principle (Breitner 2005) which are widely used in economics and many other fields. *Wik

1921 Rodney Hill FRS (11 June 1921 – 2 February 2011) was an applied mathematician and a former Professor of Mechanics of Solids at Gonville and Caius College, Cambridge.
In 1953 he was appointed Professor of Applied Mathematics at Nottingham University. His 1950 The Mathematical Theory of Plasticity forms the foundation of plasticity theory. Hill is widely regarded as among the foremost contributors to the foundations of solid mechanics over the second half of the 20th century. His early work was central to founding the mathematical theory of plasticity. This deep interest led eventually to general studies of uniqueness and stability in nonlinear continuum mechanics, work which has had a profound influence on the field of solid mechanics—theoretical, computational and experimental alike—over the past decades. Hill was the founding editor of the Journal of the Mechanics and Physics of Solids, still among the principal journals in the field.
His work is recognized worldwide for its concise style of presentation and exemplary standards of scholarship. Publisher Elsevier, in collaboration with IUTAM, established a quadrennial award in the field of solid mechanics, known as the Rodney Hill Prize, first presented at ICTAM in Adelaide in August 2008. The prize consists of a plaque and a cheque for US$25,000. Its first recipient is Michael Ortiz, for his contribution to nonconvex plasticity and deformation microstructures (California Institute of Technology, USA).
He won the Royal Medal in 1993 for his contribution to the theoretical mechanics of soil and the plasticity of solids and was elected a Fellow of the Royal Society in 1961. He was awarded an Honorary Degree (Doctor of Science) by the University of Bath in 1978. *Wik

1937 David Bryant Mumford (11 June 1937-  ) born in Worth, Sussex, England. In 1974 he won a Fields Medal for his work on “problems of the existence and structure of varieties of moduli, varieties whose points parameterize isomorhphism clases of some type of geometric object.” *VFR In the 1980s he turned to applied mathematics with the question "Is there a mathematical approach to understanding thought and the brain?" This is part of "Pattern Theory," as introduced by Ulf Grenander in the 70's to give a theoretical setting for a large number of related ideas, techniques and results from fields such as computer vision, speech recognition, image and acoustic signal processing, pattern recognition and its statistical side, neural nets and parts of artificial intelligence. *TIS


1292 Roger Bacon (Ilchester, Somersetshire, about 1214 -  Oxford, perhaps 11 June, 1294) English scholar who was one of the first to propose mathematics and experimentation as appropriate methods of science. He studied mathematics, astronomy, optics, alchemy, and languages. He elucidated the principles of refraction, reflection, and spherical aberration, and described spectacles, which soon thereafter came into use. He developed many mathematical results concerning lenses, proposed mechanically propelled ships, carriages, and flying machines, and used a camera obscura to observe eclipses of the Sun. Bacon was the first European give a detailed description of the process of making gunpowder.*TIS

1895 Daniel Kirkwood (September 27, 1814 - June 11, 1895) American mathematician and astronomer who noted in about 1860 that there were several zones of low density in the minor-planet population. These gaps in the distribution of asteroid distances from the Sun are now known as Kirkwood gaps. He explained the gaps as resulting from perturbations by Jupiter. An object that revolved in one of the gaps would be disturbed regularly by the planet's gravitational pull and eventually would be moved to another orbit. Thus gaps appeared in the distribution of asteroids where the orbital period of any small body present would be a simple fraction of that of Jupiter. Kirwood showed that a similar effect accounted for gaps in Saturns rings.*TIS

1903 Nikolai Vasilievich Bugaev (September 14, 1837 – June 11, 1903) was a prominent Russian mathematician, the father of Andrei Bely.
Bugaev was born in Georgia, Russian Empire into a somewhat unstable family (his father was an army doctor), and at the age of ten young Nikolai was sent to Moscow to find his own means of obtaining an education. He succeeded, graduating in 1859 from Moscow University, where he majored in mathematics and physics. He went on to study engineering, but in 1863 wrote a Master's thesis on the convergence of infinite series. This document was sufficiently impressive to win him a place studying under Karl Weierstrass and Ernst Kummer in Berlin. He also spent some time in Paris studying under Joseph Liouville. He earned his doctoral degree in 1866 and returned to Moscow, where he taught for the remainder of his career. Some of his most influential papers offered proofs of previously unproven assertions of Liouville, but his most original work centered around the development of formal analogies between arithmetic and analytic operations. *Wik

1931 Franklin H(enry) Giddings (March 23, 1855 – June 11, 1931)  American sociologist, one of the first in the United States to turn sociology from a branch of philosophy into a research science dependent on statistics. He was noted for his doctrine of the "consciousness of kind," which he derived from Adam Smith's conception of "sympathy," or shared moral reactions. His explanation of social phenomena was based this doctrine - his theory that each person has an innate sense of belonging to particular social groups. He encouraged statistical studies in sociology. *TIS

1934 Friedrich Wilhelm Franz Meyer (2 Sept 1856 in Magdeburg, Germany - 11 June 1934 in Königsberg, Germany (now Kaliningrad, Russia) studied algebraic geometry, algebraic curves and invariant theory. *SAU

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell

Thursday, 10 June 2021

On This Day in Math - June 10

Mathematics is one of the essential emanations of the human spirit,
a thing to be valued in and for itself, like art or poetry.
~Oswald Veblen

The 161st day of the year, Every number greater than 161 is the sum of distinct primes of the form 6n - 1.  *Prime Curios (which numbers less than 161 are also the sum of distinct primes of the form 6n-1? or which are not?)

and for the gamblers out there, There are 161 ways to bet on a roulette wheel.
161 is not only a palindrome, when is rotated 180o it gives a palindromic prime, (191) (Such  reversible numbers, or words, which form a different number, or word, are called "ambigrams".)

161 is the sum of five consecutive prime numbers: 23 + 29 + 31 + 37 + 41 = 161

Benjamin West *Wik
1752 This is the most common date given, where one is supplied, for the supposed Electrical kite experiment by Benjamin Franklin. The event is poorly documented. Franklin seems never to have written about it, and the only record seems to come from the pen of Joseph Priestly some fifteen years later who was told about it by Ben. Many now think the entire event never took place.
The standard account of Franklin's experiment was disputed following an investigation and experiments based on contemporaneous records by science historian Tom Tucker, the results of which were published in 2003. According to Tucker, Franklin never performed the experiment, and the kite as described is incapable of performing its alleged role.

Further doubt about the standard account has been cast by an investigation by the television series MythBusters. The team found evidence that Franklin would have received a fatal current through his heart had the event actually occurred. Nevertheless, they confirmed that certain aspects of the experiment were feasible - specifically, the ability of a kite with sufficiently damp string to receive and send to the ground the electrical energy delivered by a lightning strike.

Despite this, mainstream historians still support the view that the experiment was performed by Franklin *Wik

1827 William Rowan Hamilton, age 21, appointed astronomer royal at Dunsink Observatory and Andrews professor of astronomy at Trinity College, Ireland. This was a unique event in that he was still an undergraduate. *VFR

1854 The first known published mention of the Four Color Problem was printed in the Athenaeum on this date, appearing in the Miscellanea portion. The letter was signed with the initials F. G., which many supposed might have been one of the two Guthrie brothers involved in discovering the story and revealing it to DeMorgan, but others suspect it may have been Francis Galton, who had requested admission to the esteemed Athenaeum Club during this period. Certainly many of the members would have heard the story of the four colors problem from DeMorgan who had first circulated it to William R. Hamilton. (see October 23, 1852) *PB Notes (unknown)

1854, G.F. Bernhard Riemann proposed that space is curved in a lecture titled Über die Hypothesen welche der Geometrie zu Grunde liegen. He described the old-fashioned Euclidean plane geometry and solid geometry, respectively, as two-, and three-dimensional examples of what we now call Riemann spaces with zero curvature. Saying that the space is curved, rather than flat or Euclidean, is another way saying that the familiar properties of Euclidean geometry - such as the Pythagorean theorem - do not hold. He went on to suggest that all physical laws become simpler when expressed in higher dimensions. Einstein in 1915 used Rieman’s work in his theory of General Relativity which incorporated time as the fourth dimension.*TIS Weber recounted how with unusual emotion Gauss praised Riemann’s profundity on their way home. John Derbyshire in his Prime Obsession calls it "one of the top ten mathematical papers ever delivered anywhere."

1919 In a letter to Irving Langmuir, Ernest Rutherford writes, "I am a great believer in the simplicity of things and as you probably know I am inclined to hang on to broad & simple ideas like grim death until evidence is too strong for my tenacity." Nelson Ernest Rutherford *Quoted in Nathan Reingold and Ida H. Reingold, Science in America: A Documentary History 1900-1939 (1981), 354.

1924 Oswald Veblen describes his ideas for the Institute for Mathematical Research in a letter to Vernon Kellogg. The senior men would devote themselves “entirely to research, and to the guidance of the research of the younger men.” (History and philosophy of modern mathematics By William Aspray)

1977 The first Apple II computer was delivered. This was the first computer I ever used in a classroom.

In 2000, the Millennium Bridge - a footbridge across the River Thames - was opened by Queen Elizabeth. The radical new design was the work of architect Sir Norman Foster with sculptor Sir Anthony Caro and engineering support from Arup. It was the first new crossing of the River Thames in over 100. As the first few thousand people crossed the bridge, it developed an unexpected and potentially dangerous lateral "wobble". This caused people to unwittingly walk "in step", which increased the oscillation. The design had been adapted from a computer model typical for a car bridge, but which did not take into account the lateral forces associated with human walking. After structural damping was added to stop the oscillation, the bridge re-opened in 2002*TIS


940 Abu’l-Wafa (June 10, 940 AD, Buzhgan - July 1, 998 AD, Baghdad) He worked with a rusty compass.*VFR The professors cryptic remark about a "rusty compass" refers to Abu'l wafa's preference, when possible, to do his geometric constructions with a compass with a fixed opening.
Abu'l-Wafa is best known for the first use of the tan function and compiling tables of sines and tangents at 15' intervals. This work was done as part of an investigation into the orbit of the Moon, written down in Theories of the Moon. He also introduced the sec and cosec and studied the interrelations between the six trigonometric lines associated with an arc. He is also often credited as one of the likely originators of the spherical law of sines and established several trigonometric identities such as sin(a ± b) in their modern form, where the Ancient Greek mathematicians had expressed the equivalent identities in terms of chords.

\(\sin(\alpha \pm \beta) = \sin \alpha \cos \beta \pm \cos \alpha \sin \beta \)
"A text written by Abu'l-Wafa for practical use was A book on those geometric constructions which are necessary for a craftsman. This was written much later than his arithmetic text, certainly after 990. The book is in thirteen chapters and it considered the design and testing of drafting instruments, the construction of right angles, approximate angle trisections, constructions of parabolas, regular polygons and methods of inscribing them in and circumscribing them about given circles, inscribing of various polygons in given polygons, the division of figures such as plane polygons, and the division of spherical surfaces into regular spherical polygons.
Another interesting aspect of this particular work of Abu'l-Wafa's is that he tries where possible to solve his problems with ruler and compass constructions. When this is not possible he uses approximate methods. However, there are a whole collection of problems which he solves using a ruler and fixed compass, that is one where the angle between the legs of the compass is fixed. It is suggested in Dictionary of Scientific Biography that:-
Interest in these constructions was probably aroused by the fact that in practice they give more exact results than can be obtained by changing the compass opening.

 His trigonometric tables are accurate to 8 decimal places (converted to decimal notation) while Ptolemy's were only accurate to 3 places." *SAU
In 2015, Google celebrated his 1075th birthday with a Google Doodle, and included, "contributions to science include one of the first known introductions to negative numbers, and the development of the first quadrant, a tool used by astronomers to examine the sky."

1710 James Short (June 10, 1710, Edinburgh, Scot. -  June 14, 1768, London, Eng) British optician and astronomer who produced the first truly
parabolic and elliptic (hence nearly distortionless) mirrors for reflecting telescopes. During his working life of over 35 years, Short made about 1,360 instruments - not only for customers in Britain but also for export: one is still preserved in Leningrad, another at Uppsala and several in America. Short was principal British collator and computer of the Transit of Venus observations made throughout the world on 6th June 1761. His instruments travelled on Endeavour with Captain Cook to observe the next Transit of Venus on 3rd June 1769, but Short died before this event took place.

1803 Henri-Philibert-Gaspard Darcy (June 10, 1803 – January 3, 1858) French hydraulic engineer who first derived the equation (now known as Darcy's law) that governs the laminar (nonturbulent) flow of fluids in homogeneous, porous media. In 1856, modern studies of groundwater began when Darcy was commissioned to develop a water-purification system for the city of Dijon, France. He constructed the first experimental apparatus to study the flow characteristics of water through the earth. From his experiments, he derived the Darcy's Law equation, describing the flow of water in nature, which is fundamental to understanding groundwater systems.

1861 Pierre(-Maurice-Marie) Duhem (10 June 1861 – 14 September 1916)French physicist, mathematician, and philosopher of science who emphasized a history of modern science based on evolutionary metaphysical concepts. He had a wide variety of mathematical interests from mechanics and physics to philosophy and the history of mathematics. Duhem studied magnetism following the work of Gibbs and Helmholtz and also worked on thermodynamics and hydrodynamics producing over 400 papers. He maintained that the role of theory in science is to systematize relationships rather than to interpret new phenomena.  *TIS

1887 Vladimir Ivanovich Smirnov (10 June 1887 – 11 February 1974) was a Russian mathematician who made significant contributions in both pure and applied mathematics, and also in the history of mathematics.
Smirnov worked on diverse areas of mathematics, such as complex functions and conjugate functions in Euclidean spaces. In the applied field his work includes the propagation of waves in elastic media with plane boundaries (with Sergei Sobolev) and the oscillations of elastic spheres.
Smirnov is also widely known among students for his five volume book A Course in Higher Mathematics (the first volume was written jointly with Jacob Tamarkin).*Wik

1904 John Semple (10 June 1904 in Belfast, Ireland - 23 October 1985 in London, England) studied at Queen's University Belfast and Cambridge. He held a post in Edinburgh for a year before becoming Professor of Pure Mathematics at Queen's College Belfast. He moved to King's College London where he spent the rest of his career. His most important work was in Algebraic geometry. *SAU

1932 Pierre Emile Jean Cartier (10 June 1932 in Sedan , Ardennes - ) is a French mathematician . His main interest is the algebraic geometry , presentation and category theory . 1957-1959 he worked at the Institute for Advanced Study . From 1961 he was a professor at the University of Strasbourg (then Faculté de Science). In 1971 he was appointed professor at the Institut des Hautes Études Scientifiques in Paris. He was also from 1974 Director of Research CNRS. In 1982 he became a professor at the Ecole Polytechnique and 1988 at the ENS.
Pierre Cartier led the Cartier operator and is the namesake of the Cartier divisor . *Wik


1836 Andre-Marie Ampere. (20 January 1775 – 10 June 1836)French mathematician and physicist 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.

1903 (Antonio) Luigi (Gaudenzio Giuseppe) Cremona ( Pavia , 7 December 1830 - Rome , 10 June 1903 ) was an Italian mathematician who was an originator of graphical statics (the use of graphical methods to study forces in equilibrium) and work in projective geometry. Cremona's work in statics is of great importance and he gave, in a clearer form, some theorems due to Maxwell. In a paper of 1872 Cremona took an idea of Maxwell's on forces in frame structures that had appeared in an engineering journal in 1867 and interpreted Maxwell's notion of reciprocal figures as duality in projective 3-space. These reciprocal figures, for example, have three forces in equilibrium in one figure represented by a triangle while in the reciprocal figure they are represented by three concurrent lines.*TIS

1948 Philippa Garrett Fawcett (4 April 1868 - 10 June 1948)
Fawcett's performance in the Trinity Intercollege Examination which she sat after two years at Cambridge was outstanding and it was clear that she would excel in the Tripos Examinations of 1890. At this time only the men were ranked in the Tripos Examination but women who took the examination were made aware of their place by being told they were placed between the nth and (n+1)st man or equal to the nth man. Expectations were high that Fawcett would perform well and her mother wrote in a letter to a friend):-

I am going to Cambridge tomorrow week and shall have my last sight of [Philippa] till after the exam. I have made up my mind not to be too anxious about it. There are a great many better things in the world than beating other people in examinations.

However, beat other people is exactly what Fawcett did in the twelve three hour examination papers. The Senior Moderator of the Mathematical Tripos Examinations of 1890 was Walter Rouse Ball and it was his duty to read the women's list after the men's ranked list had been read. When Rouse Ball came to read the women's list he read out first:-
Miss Philippa Garrett Fawcett - above the Senior Wrangler.
Fawcett had become the first woman at Cambridge to come top in the Mathematical Tripos Examinations. A description of the event is recorded in the North Hall Diary of Newnham College:-
The great event of the year was Philippa Garrett Fawcet's achievement in the Mathematical Tripos. For the first time a woman has been placed above the Senior Wrangler. The excitement in the Senate House when the lists were read was unparalleled. The deafening cheers of the throng of undergraduates redoubled as Miss Fawcett left the Senate House by the side of the Principal. On her arrival at the College she was enthusiastically greeted by a crowd of fellow-students, and carried in triumph into Clough Hall. Flowers, letters, and telegrams poured in upon her throughout the day. The College was profusely decorated with flags. In the evening the whole College dined in Clough Hall. After dinner toasts were proposed: the healths drunk were those of the Principal, Miss Fawcett, her Coach (Mr Hobson) and Senior and Junior Optimes. At 9.30 p.m. the College gardens were illuminated, and a bonfire was lighted on the hockey-ground, round which Miss Fawcett was three times carried amid shouts of triumph and strains of "For she's a jolly good fellow." *SAU
Following Fawcett's great achievement in the Mathematical Tripos, she won a scholarship at Cambridge through which she conducted research in Fluid Dynamics. Her published papers include "Note on the Motion of Solids in a Liquid".

She went on to be a College Lecturer in Mathematics at Newnham College, Cambridge a position she held for 10 years. In this capacity, her teaching abilities received considerable praise. One student wrote:
“ What I remember most vividly of Miss Fawcett's coaching was her concentration, speed, and infectious delight in what she was teaching. She was ruthless towards mistakes and carelessness... My deepest debt to her is a sense of the unity of all truth, from the smallest detail to the highest that we know. ”
Fawcett left Cambridge in 1902, when she was appointed as a lecturer to train mathematics teachers at the Normal School, Johannesburg, South Africa. Here, she remained until 1905, setting up schools in South Africa. She then returned to England to take a position in the administration of education for London County Council. Here, she attained the highest LCC rank ever for a woman, in her work developing secondary schools.
Philippa Fawcett maintained strong links with Newnham College throughout her life. The Fawcett building (1938) was named in recognition of her contribution to Newnham, and that of her family. She died on 10 June 1948, two months after her 80th birthday, just one month after the Grace that allowed women to be awarded the Cambridge BA degree received royal assent, and fifty eight years after coming above the `Senior Wrangler'. *Wik

1974 Jaroslav Hájek (4 Feb 1926 in Podebrady, Bohemia (now Czech Republic) - 10 June 1974 in Prague, Czechoslovakia) He was among the pioneers of unequal probability sampling. The name "Hájek predictor" now labels his contributions to the use of auxiliary data in estimating population means. In 1967 Hájek published (jointly with Z Sidak) Theory of rank tests but it was a work which had in fact been written four years before in 1963. Their methods use three lemmas of Le Cam in order to treat rank statistics under local alternatives and they established the efficiency of rank tests. *SAU

1992 Morris Kline (May 1, 1908 – June 10, 1992) was a Professor of Mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
Kline grew up in Brooklyn and in Jamaica, Queens. After graduating from Boys High School in Brooklyn, he studied mathematics at New York University, earning a bachelor's degree in 1930, a master's degree in 1932, and a doctorate in 1936. He continued at NYU as an instructor until 1942.
During World War II, Kline was posted to the Signal Corps (United States Army) stationed at Belmar, New Jersey. Designated a physicist, he worked in the engineering lab where radar was developed. After the war he continued investigating electromagnetism, and from 1946 to 1966 was director of the division for electromagnetic research at the Courant Institute of Mathematical Sciences.
Kline resumed his mathematical teaching at NYU, becoming a full professor in 1952. He taught at New York University until 1975, and wrote many papers and more than a dozen books on various aspects of mathematics and particularly mathematics teaching. He repeatedly stressed the need to teach the applications and usefulness of mathematics rather than expecting students to enjoy it for its own sake. Similarly, he urged that mathematical research concentrate on solving problems posed in other fields rather than building structures of interest only to other mathematicians. *Wik

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell