## Wednesday, 29 March 2017

### On This Day in Math - March 29

 von Mädler Map of Moon, *www.RareMaps.com

Natural selection is a mechanism for generating an exceedingly high degree of improbability.
~R. A. Fisher

The 88th day of the year; 882 = 7744, it is one of only 5 numbers known whose square has no isolated digits. (Can you find the others?) [Thanks to Danny Whittaker @nemoyatpeace for a correction on this.]

There are only 88 narcissistic numbers  in base ten, (an n-digit number that is the sum of the nth power of its digits, 153=13 + 53 + 33

88 is also a chance to introduce a new word (new for me).  88 is strobogrammatic, a number that is the same when it is rotated 180o about its center... 69 is another example. If they make a different number when rotated, they are called invertible (109 becomes 601 for example). *Prime Curios

And with millions (billions?) of stars in the sky, did you ever wonder how many constellations there are?  Well, according to the Internationals Astronomical Union, there are 88.
Currently, 14 men and women, 9 birds, two insects, 19 land animals, 10 water creatures, two centaurs, one head of hair, a serpent, a dragon, a flying horse, a river and 29 inanimate objects are represented in the night sky (the total comes to more than 88 because some constellations include more than one creature.)
And if you chat with Chinese friends, the cool way to say bye-bye is with 88, from Mandarin for 88, "bā ba".

Not too far from my home near Possum Trot, Ky, there is a little place called Eighty-eight, Kentucky. One strory of the naming (there could be as many as 88 of them) is that the town was named in 1860 by Dabnie Nunnally, the community's first postmaster. He had little faith in the legibility of his handwriting, and thought that using numbers would solve the problem. He then reached into his pocket and came up with 88 cents.
In the 1948 presidential election, the community reported 88 votes for Truman and 88 votes for Dewey, which earned it a spot in Ripley's Believe It or Not.

And expanding the "88 is strobogrammatic" theme, INDER JEET TANEJA came up with this beautiful magic square with a constant of 88 that was used in a stamp series in Macao in 2014 and 2015. This image shows the reflections both horizontally and vertically, as well as the 180 degree rotation, each is a magic square.

The stamps had denominations of 1 through 9 pataca and when  two sheets were  printed you could do your own Luo Shu magic square with the denominations. The Luo Shu itself was featured on the 12 pataca stamp.

EVENTS
1796 Gauss achieved the construction of the 17-gon and a week later he would obtain his first proof of the quadratic reciprocity law. These two accomplishments mark the emergence from the ingenious manipulations of his youth, to the polished proofs of the mature mathematician. *Merzbach, An Early Version of Guass' Disquisitiones Arithmeticae, Mathematical Perspectives Academic Press 1981

 first image obtained by NASA’s Dawn spacecraft .
In 1807, Vesta 4, the only asteroid visible to the naked eye, thus the brightest on record, was first observed by the amateur astronomer Heinrich Wilhelm Olbers from Bremen. Vesta is a main belt asteroid with a diameter of 525-km and a rotation period of 5.34 hours. Pictures taken by the Hubble Space Telescope in 1995 show Vesta's complex surface, with a geology similar to that of terrestrial worlds - such as Earth or Mars - a surprisingly diverse world with an exposed mantle, ancient lava flows and impact basins. Though no bigger than the state of Arizona, it once had a molten interior. This contradicts conventional ideas that asteroids essentially are cold, rocky fragments left behind from the early days of planetary formation. *TIS Since the discovery of Ceres in 1801,  and the asteroid Pallas in 1802, he had corresponded and became close friends with Gauss.  For that reason he allowed Gauss to name the new "planet".

1933 Italy issued the world’s ﬁrst postage stamp portraying Galileo. [Scott #D16] *VFR
Galileo Galilei (1564–1642) made his first appearance on this stamp in 1933 for use in pneumatic postal systems (hence the wording “Posta Pneumatica” on the stamp). Pneumatic post involved placing letters in canisters which were then shot along pipes by compressed air from one Post Office to another. Pneumatic postal systems were set up in several European and American cities, including Rome, Naples, and Milan. Italy was the only country to issue stamps specifically for pneumatic postal use. Two of the designs showed Galileo – this one and a modified version with different face value and colour issued in 1945. The portrait is based on one by Justus Sustermans painted in 1636 when Galileo was aged 72. *Ian Ridpath, World's Oldest Astro Stamps page.

1989 Pixar Wins Academy Award for "Tin Toy":
Pixar wins an Academy Award for "Tin Toy," the first entirely computer-animated work to win in the best animated short film category. Pixar, now a division of Disney, continued its success with a string of shorts and the first entirely computer-animated feature-length film, the best-selling "Toy Story." *CHM

2012 Buzz Lightyear that flew in space joins Smithsonian collection. Launched May 31, 2008, aboard the space shuttle Discovery with mission STS-124 and returned on Discovery 15 months later with STS-128, the 12-inch action figure is the longest-serving toy in space. Disney Parks partnered with NASA to send Buzz Lightyear to the International Space Station and create interactive games, educational worksheets and special messages encouraging students to pursue careers in science, technology, engineering and mathematics (STEM). The action figure will go on display in the museum’s "Moving Beyond Earth" gallery in the summer. The Toy Story character became part of the National Air and Space Museum’s popular culture collection. *http://airandspace.si.edu [I still have a Buzz Lightyear toy on my book case given to me by some students because I used to use his trademark quote in (my very questionable) Latin, "ad infinitum, et ultra." ]

BIRTHS
1794 Johann Heinrich von Mädler (29 May 1794, 14 Mar 1874 at age 79) German astronomer who (with Wilhelm Beer) published the most complete map of the Moon of the time, Mappa Selenographica, 4 vol. (1834-36). It was the first lunar map to be divided into quadrants, and it remained unsurpassed in its detail until J.F. Julius Schmidt's map of 1878. Mädler and Beer also published the first systematic chart of the surface features of the planet Mars (1830). *TIS

1825 Francesco Faà di Bruno (29 March 1825–27 March 1888) was an Italian mathematician and priest, born at Alessandria. He was of noble birth, and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula. In 1988 he was beatified by Pope John Paul II. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the determinant form of this formula. However, his work is mainly related to elimination theory and to the theory of elliptic functions.
He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.*Wik

1830 Thomas Bond Sprague (29 March 1830 in London, England - 29 Nov 1920 in Edinburgh, Scotland) studied at Cambridge and went on to become the most important actuary of the late 19th Century. He wrote more than 100 papers including many in the Proceedings of the EMS. *SAU

1873 Tullio Levi-Civita (29 Mar 1873, 29 Dec 1941) Italian mathematician who was one of the founders of absolute differential calculus (tensor analysis) which had applications to the theory of relativity. In 1887, he published a famous paper in which he developed the calculus of tensors. In 1900 he published, jointly with Ricci, the theory of tensors Méthodes de calcul differential absolu et leures applications in a form which was used by Einstein 15 years later. Weyl also used Levi-Civita's ideas to produce a unified theory of gravitation and electromagnetism. In addition to the important contributions his work made in the theory of relativity, Levi-Civita produced a series of papers treating elegantly the problem of a static gravitational field. *TIS

1890 Sir Harold Spencer Jones (29 Mar 1890, 3 Nov 1960) English astronomer who was 10th astronomer royal of England (1933–55). His work was devoted to fundamental positional astronomy. While HM Astronomer at the Cape of Good Hope, he worked on poper motions and parallaxes. Later he showed that small residuals in the apparent motions of the planets are due to the irregular rotation of the earth. He led in the worldwide effort to determine the distance to the sun by triangulating the distance of the asteroid Eros when it passed near the earth in 1930-31. Spencer Jones also improved timekeeping and knowledge of the Earth’s rotation. After WW II he supervised the move of the Royal Observatory to Herstmonceux, where it was renamed the Royal Greenwich Observatory.*TIS

1893 Jason John Nassau (29 March 1893 in Smyrna, (now Izmir) Turkey - 11 May 1965 in Cleveland, Ohio, USA) was an American astronomer.
He performed his doctoral studies at Syracuse, and gained his Ph.D. mathematics in 1920. (His thesis was Some Theorems in Alternants.) He then became an assistant professor at the Case Institute of Technology in 1921, teaching astronomy. He continued to instruct at that institution, becoming the University's first chair of astronomy from 1924 until 1959 and chairman of the graduate division from 1936 until 1940. After 1959 he was professor emeritus.
From 1924 until 1959 he was also the director of the Case Western Reserve University (CWRU) Warner and Swasey Observatory in Cleveland, Ohio. He was a pioneer in the study of galactic structure. He also discovered a new star cluster, co-discovered 2 novae in 1961, and developed a technique of studying the distribution of red (M-class or cooler) stars.*Wik

1896 Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.*Wik

1912 Martin Eichler (29 March 1912 – 7 October 1992) was a German number theorist. He received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.
Eichler once stated that there were five fundamental operations of mathematics: addition, subtraction, multiplication, division, and modular forms. He is linked with Goro Shimura in the development of a method to construct elliptic curves from certain modular forms. The converse notion that every elliptic curve has a corresponding modular form would later be the key to the proof of Fermat's last theorem.*Wik

1912 Caius Jacob (29 March 1912 , Arad - 6 February 1992 , Bucharest ) was a Romanian mathematician and member of the Romanian Academy. He made ​​contributions in the fields of fluid mechanics and mathematical analysis , in particular vigilance in plane movements of incompressible fluids, speeds of movement at subsonic and supersonic , approximate solutions in gas dynamics and the old problem of potential theory. His most important publishing was Mathematical introduction to the mechanics of fluids. *Wik

1941 Joseph Hooton Taylor, Jr. (March 29, 1941, ) is an American astrophysicist and Nobel Prize in Physics laureate for his discovery with Russell Alan Hulse of a "new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation." *Wi

DEATHS
1772 Emanuel Swedenborg (29 Jan 1688; 29 Mar 1772) Swedish scientist, philosopher and theologian. While young, he studied mathematics and the natural sciences in England and Europe. From Swedenborg's inventive and mechanical genius came his method of finding terrestrial longitude by the Moon, new methods of constructing docks and even tentative suggestions for the submarine and the airplane. Back in Sweden, he started (1715) that country's first scientific journal, Daedalus Hyperboreus. His book on algebra was the first in the Swedish language, and in 1721 he published a work on chemistry and physics. Swedenborg devoted 30 years to improving Sweden's metal-mining industries, while still publishing on cosmology, corpuscular philosophy, mathematics, and human sensory perceptions. *TIS

1806 John Thomas Graves (4 December 1806, Dublin, Ireland–29 March 1870, Cheltenham, England) was an Irish jurist and mathematician. He was a friend of William Rowan Hamilton, and is credited both with inspiring Hamilton to discover the quaternions and with personally discovering the octonions, which he called the octaves. He was the brother of both the mathematician Charles Graves and the writer and clergyman Robert Perceval Graves.
In his twentieth year (1826) Graves engaged in researches on the exponential function and the complex logarithm; they were printed in the Philosophical Transactions for 1829 under the title An Attempt to Rectify the Inaccuracy of some Logarithmic Formulæ. M. Vincent of Lille claimed to have arrived in 1825 at similar results, which, however, were not published by him till 1832. The conclusions announced by Graves were not at first accepted by George Peacock, who referred to them in his Report on Algebra, nor by Sir John Herschel. Graves communicated to the British Association in 1834 (Report for that year) on his discovery, and in the same report is a supporting paper by Hamilton, On Conjugate Functions or Algebraic Couples, as tending to illustrate generally the Doctrine of Imaginary Quantities, and as confirming the Results of Mr. Graves respecting the existence of Two independent Integers in the complete expression of an Imaginary Logarithm. It was an anticipation, as far as publication was concerned, of an extended memoir, which had been read by Hamilton before the Royal Irish Academy on 24 November 1833, On Conjugate Functions or Algebraic Couples, and subsequently published in the seventeenth volume of the Transactions of the Royal Irish Academy. To this memoir were prefixed A Preliminary and Elementary Essay on Algebra as the Science of Pure Time, and some General Introductory Remarks. In the concluding paragraphs of each of these three papers Hamilton acknowledges that it was "in reflecting on the important symbolical results of Mr. Graves respecting imaginary logarithms, and in attempting to explain to himself the theoretical meaning of those remarkable symbolisms", that he was conducted to "the theory of conjugate functions, which, leading on to a theory of triplets and sets of moments, steps, and numbers" were foundational for his own work, culminating in the discovery of quaternions.
For many years Graves and Hamilton maintained a correspondence on the interpretation of imaginaries. In 1843 Hamilton discovered the quaternions, and it was to Graves that he made on 17 October his first written communication of the discovery. In his preface to the Lectures on Quaternions and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. After the discovery of quaternions, Graves employed himself in extending to eight squares Euler's four-square identity, and went on to conceive a theory of "octaves" (now called octonions) analogous to Hamilton's theory of quaternions, introducing four imaginaries additional to Hamilton's i, j and k, and conforming to "the law of the modulus".
Graves devised also a pure-triplet system founded on the roots of positive unity, simultaneously with his brother Charles Graves, the bishop of Limerick. He afterwards stimulated Hamilton to the study of polyhedra, and was told of the discovery of the icosian calculus. *Wik

1873 Francesco Zantedeschi (born 1797, 29 Mar 1873) Italian priest and physicist, who published papers (1829, 1830) on the production of electric currents in closed circuits by the approach and withdrawal of a magnet, preceding Faraday's classic experiment of 1831. Studying the solar spectrum, Zantedeschi was among the first to recognize the marked absorption by the atmosphere of the red, yellow, and green light. Though not confirmed, he also thought he detected a magnetic action on steel needles by ultra-violet light (1838), at least suspecting a connection between light and magnetism many years before Clerk-Maxwell's announcement (1867) of the electromagnetic theory of light. He experimented on the repulsion of flames by a strong magnetic field.*TIS

1912 Robert Falcon Scott, (6 June 1868 - 29 March 1912) was a Royal Navy officer and explorer who led two expeditions to the Antarctic regions: the Discovery Expedition, 1901–04, and the ill-fated Terra Nova Expedition, 1910–13. During this second venture, Scott led a party of five which reached the South Pole on 17 January 1912, only to find that they had been preceded by Roald Amundsen's Norwegian expedition. On their return journey, Scott and his four comrades all died from a combination of exhaustion, starvation and extreme cold.  *Wik

1944 Grace Chisholm Young (née Chisholm; 15 March 1868 – 29 March 1944) was an English mathematician. She was educated at Girton College, Cambridge, England and continued her studies at Göttingen University in Germany. Her early writings were published under the name of her husband, William Henry Young, and they collaborated on mathematical work throughout their lives. For her work on calculus (1914–16), she was awarded the Gamble Prize.
Her son, Laurence Chisholm Young, was also a prominent mathematician. One of her living granddaughters, Sylvia Wiegand (daughter of Laurence), is also a mathematician (and a past president of the Association for Women in Mathematics.)*Wik

1980 William Gemmell Cochran (15 July 1909, Rutherglen – 29 March 1980, Orleans, Massachusetts)In 1934 R A Fisher left Rothamsted Experimental Station to accept the Galton chair at University College, London and Frank Yates became head at Rothamsted. Cochran was offered the vacant post but he had not finished his doctoral course at Cambridge. Yates later wrote:-
... it was a measure of good sense that he accepted my argument that a PhD, even from Cambridge, was little evidence of research ability, and that Cambridge had at that time little to teach him in statistics that could not be much better learnt from practical work in a research institute.
Cochran accepted the post at Rothamsted where he worked for 5 years on experimental designs and sample survey techniques. During this time he worked closely with Yates. At this time he also had the chance to work with Fisher who was a frequent visitor at Rothamsted.
Cochran visited Iowa Statistical Laboratory in 1938, then he accepted a statistics post there in 1939. His task was to develop the graduate programe in statistics within the Mathematics Department. In 1943 he joined Wilks research team at Princeton.
At Princeton he was involved in war work examining probabilities of hits in naval warfare. By 1945 he was working on bombing raid strategies.
He joined the newly created North Carolina Institute of Statistics in 1946, again to develop the graduate programe in statistics. From 1949 until 1957 he was at Johns Hopkins University in the chair of biostatistics. Here he was more involved in medical applications of statistics rather than the agricultural application he had studied earlier.
From 1957 until he retired in 1976 Cochran was at Harvard. His initial task was to help set up a statistics department, something which he had a great deal of experience with by this time. He had almost become a professional at starting statistics within universities in the USA. *SAU

1983 Sir Maurice George Kendall, FBA (6 September 1907 – 29 March 1983) was a British statistician, widely known for his contribution to statistics. The Kendall tau rank correlation is named after him.*Wik He was involved in developing one of the first mechanical devices to produce (pseudo-) random digits, eventually leading to a 100,000-random-digit set commonly used until RAND's (once well-known) "A Million Random Digits With 100,000 Normal Deviates" in 1955.
Kendall was Professor of Statistics at the London School of Economics from 1949 to 1961. His main work in statistics involved k-statistics, time series, and rank-correlation methods, including developing the Kendall's tau stat, which eventually led to a monograph on Rank Correlation in 1948. He was also involved in several large sample-survey projects. For many, what Kendall is best known for is his set of books titled The Advanced Theory of Statistics (ATS), with Volume I first appearing in 1943 and Volume II in 1946. Kendall later completed a
rewriting of ATS, which appeared in three volumes in 1966, which were updated by collaborator Alan Stuart and Keith Ord after Kendall's death, appearing now as "Kendall's Advanced Theory of Statistics". *David Bee

1999 Boris A. Kordemsky ( 23 May 1907 – 29 March, 1999) was a Russian mathematician and educator. He is best known for his popular science books and mathematical puzzles. He is the author of over 70 books and popular mathematics articles.
Kordemsky received Ph.D. in education in 1956 and taught mathematics at several Moscow colleges.
He is probably the best-selling author of math puzzle books in the history of the world. Just one of his books, Matematicheskaya Smekalka (or, Mathematical Quick-Wits), sold more than a million copies in the Soviet Union/Russia alone, and it has been translated into many languages. By exciting millions of people in mathematical problems over five decades, he influenced generations of solvers both at home and abroad. *Age of Puzzles, by Will Shortz and Serhiy Grabarchuk (mostly)

1908 John Bardeen (23 May 1908; 30 Jan 1991 at age 82) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS

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

## Tuesday, 28 March 2017

### On This Day in Math - March 28

 *George W. Hart, Sculpture

`The introduction of the cipher 0 or the group concept was general nonsense too, and mathematics was more or less stagnating for thousands of years because nobody was around to take such childish steps ...'.
Alexandre Grothendieck in a letter in 1982 to Ronald Brown

The 87th day of the year; the sum of the squares of the first four primes is 87. $87 = 2^2 + 3^2 + 5^2 + 7^2$

87 = 3 * 29, $87^2 + 3^2 + 29^2 and 87^2 - 3^2 - 29^2$are both primes

Among Australian cricket players, it seems, 87 is an unlucky score and is referred to as "the devil's number", supposedly because it is 13 runs short of 100.

And 87 is, of course, the number of years between the signing of the U.S. Declaration of Independence and the Battle of Gettysburg, immortalized in Abraham Lincoln's Gettysburg Address with the phrase "fourscore and seven years ago..."

EVENTS

In 1747, the fascination with electricity upon reaching the American colonies was the subject of Benjamin Franklin's first of the famous series of letters in which he described his experiments on electricity to Peter Collinson, Esq., of London. He thanked Collison for his “kind present of an electric tube with directions for using it” with which he and others did electrical experiments. “For my own part I never was before engaged in any study that so totally engrossed my attention and my time as this has lately done; for what with making experiments when I can be alone, and repeating them to my friends and acquaintances, who, from the novelty of the thing, come continually in crowds to see them, I have, during some months past, had little leisure for anything else.”*TIS

1764 In a second trial of John Harrison's marine timekeeper, his son William departed for Barbados aboard the Tartar. As with the first trial, William used H4 to predict the ship's arrival at Madeira with extraordinary accuracy. The watch's error was computed to be 39.2 seconds over a voyage of 47 days, three times better than required to win the maximum reward of £20,000. *Royal Museum Greenwich

1802 Olbers, while observing the constellation Virgo, had observed a "star" of the seventh-magnitude not found on the star charts. Over the following week he would observe the motion and determined that it was a planet. In early April he sent the data to Gauss to compute the orbit. On the 18th of April, Gauss computed the orbit in only three hours, placing the orbit between Mars and Jupitor. Olbers named the new planetoid Pallas, and predicted there would be others found in the same area. John Herschel dismissed this speculation as "dreams in which astronomers... indulge" but over 1000 such planetoids have been observed. *Dunnington, Gray, & Dohse; Carl Friedrich Gauss: Titan of Science

1809 Gauss ﬁnished work on his Theoria Motus. It explains his methods of computing planetary orbits using least squares. [Springer’s 1985 Statistics Calendar] *VFR

In 1946, the Census Bureau and the National Bureau of Standards met to discuss the purchase of a computer. The agencies agreed to buy UNIVAC, the world's first general all-purpose business computer, from Presper Eckert and John Mauchly for a mere $225,000. Unfortunately, UNIVAC cost far more than that to develop. Eckert and Mauchly's venture floundered as the company continued to build and program UNIVACs for far less than the development cost. Eventually, the company was purchased by Remington Rand. *TIS 1949 The phrase "Big Bang" is created. Shortly after 6:30 am GMT on BBC's The Third Program, Fred Hoyle used the term in describing theories that contrasted with his own "continuous creation" model for the Universe. "...based on a theory that all the matter in the universe was created in one big bang ... ". *Mario Livio, Brilliant Blunders 1959 Germany issued a stamp commemorating the 400th anniversary of the death of Adam Riese [Scott #799] *VFR I understand that the German expression "nach Adam Riese", is still used today. It means "according to Adam Ries" and it is used in saying something is exactly correct. In 2006, a substantial "lost" book of manuscripts by Robert Hooke in his own handwriting was bought for the Royal Society by donations of nearly £1 million. The book was just minutes before going on the auction block when a last-minute purchase agreement was made and kept the precious document in Britain. Hooke is now often overlooked, except for his law of elasticity, although in his time, he was a prolific English scientist and contributed greatly to planning the rebuilding of London after the Great Fire of 1666. The document of more than 520 pages of manuscripts included the minutes of the Royal Society from 1661-82. It had been found in a cupboard in a private house by an antiques expert there to value other items. *TIS BIRTHS 1847 Gyula Farkas (28 March 1847 in Sárosd, Fejér County, Hungary - 27 Dec 1930 in Pestszentlorinc, Hungary) He is remembered for Farkas theorem which is used in linear programming and also for his work on linear inequalities. In 1881 Gyula Farkas published a paper on Farkas Bolyai's iterative solution to the trinomial equation, making a careful study of the convergence of the algorithm. In a paper published three years later, Farkas examined the convergence of more general iterative methods. He also made major contributions to applied mathematics and physics, particularly in the areas of mechanical equilibrium, thermodynamics, and electrodynamics.*SAU 1923 Israel Nathan Herstein (March 28, 1923, Lublin, Poland – February 9, 1988, Chicago, Illinois) was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books. He is known for his lucid style of writing, as exemplified by the classic and widely influential Topics in Algebra, an undergraduate introduction to abstract algebra that was published in 1964, which dominated the field for 20 years. A more advanced classic text is his Noncommutative Rings in the Carus Mathematical Monographs series. His primary interest was in noncommutative ring theory, but he also wrote papers on finite groups, linear algebra, and mathematical economics.*Wik 1928 Alexander Grothendieck (28 Mar 1928-13 November 2014) In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. Within algebraic geometry itself, his theory of schemes is used in technical work. His generalization of the classical Riemann-Roch theorem started the study of algebraic and topological K-theory. His construction of new cohomology theories has left consequences for algebraic number theory, algebraic topology, and representation theory. His creation of topos theory has appeared in set theory and logic. One of his results is the discovery of the first arithmetic Weil cohomology theory: the ℓ-adic étale cohomology. This result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre Deligne. To this day, ℓ-adic cohomology remains a fundamental tool for number theorists, with applications to the Langlands program. Grothendieck influenced generations of mathematicians after his departure from mathematics. His emphasis on the role of universal properties brought category theory into the mainstream as an organizing principle. His notion of abelian category is now the basic object of study in homological algebra. His conjectural theory of motives has been behind modern developments in algebraic K-theory, motivic homotopy theory, and motivic integration. *Wik DEATHS 1678 Claude François Milliet Dechales (1621 in Chambéry, France - 28 March 1678 in Turin, Italy) Dechales is best remembered for Cursus seu mundus mathematicus published in Lyons in 1674, a complete course of mathematics. Topics covered in this wide ranging work included practical geometry, mechanics, statics, magnetism and optics as well as topics outwith the usual topics of mathematics such as geography, architecture, astronomy, natural philosophy and music. In 1678 he published in Lausanne his edition of Euclid, The Elements of Euclid Explained in a New but Most Easy Method: Together with the Use of Every Proposition through All Parts of the Mathematics, written in French by That Most Excellent Mathematician, F Claude Francis Milliet Dechales of the Society of Jesus. This work covers Books 1 to 6, together with Books 11 and 12, of Euclid's Elements. A second edition was published in 1683, then an edition revised by Ozanam was published in Paris in 1753. An English translation was published in London by M Gillyflower and W Freeman, the translation being by Reeve Williams. A second edition of this English translation appeared in 1696. Schaap writes, "Dechales's separate edition of Euclid, long a favourite in France and elsewhere on the Continent, never became popular in England." *SAU 1794 Marie Jean Antoine Nicolas de Caritat, marquis de Condorcet (17 September 1743 – 28 March 1794), known as Nicolas de Condorcet, was a French philosopher, mathematician, and early political scientist whose Condorcet method in voting tally selects the candidate who would beat each of the other candidates in a run-off election. Unlike many of his contemporaries, he advocated a liberal economy, free and equal public education, constitutionalism, and equal rights for women and people of all races. His ideas and writings were said to embody the ideals of the Age of Enlightenment and rationalism, and remain influential to this day. He died a mysterious death in prison after a period of being a fugitive from French Revolutionary​ authorities.*Wik Condorcet committed suicide by poisoning while in jail so that the republican terrorists could not take him to Paris. *VFR (The St Andrews site has the date of his death one day later.) 1840 Simon Antoine Jean Lhuilier (24 April 1750 in Geneva, Switzerland - 28 March 1840 in Geneva, Switzerland) His work on Euler's polyhedra formula, and exceptions to that formula, were important in the development of topology. Lhuilier also corrected Euler's solution of the Königsberg bridge problem. He also wrote four important articles on probability during the years 1796 and 1797. His most famous pupil was Charles-François Sturm who studied under Lhuilier during the last few years of his career in Geneva. *SAU 1850 Bernt Michael Holmboe (23 March 1795 – 28 March 1850) was a Norwegian mathematician. Holmboe was hired as a mathematics teacher at the Christiania Cathedral School in 1818, where he met the future renowned mathematician Niels Henrik Abel. Holmboe's lasting impact on mathematics worldwide has been said to be his tutoring of Abel, both in school and privately. The two became friends and remained so until Abel's early death. Holmboe moved to the Royal Frederick University in 1826, where he worked until his own death in 1850. Holmboe's significant impact on mathematics in the fledgling Norway was his textbook in two volumes for secondary schools. It was widely used, but faced competition from Christopher Hansteen's alternative offering, sparking what may have been Norway's first debate about school textbooks. *Wik 1874 Peter Andreas Hansen (8 Dec 1795; 28 Mar 1874) Danish astronomer whose most important work was the improvement of the theories and tables of the orbits of the principal bodies in the solar system. At Altona observatory he assisted in measuring the arc of meridian (1821). He became the director (1825) of Seeberg observatory, which was removed to Gotha in a new observatory built for him (1857). He worked on theoretical geodesy, optics, and the theory of probability. The work in celestial mechanics for which he is best known are his theories of motion for comets, minor planets, moon and his lunar tables (1857) which were in use until 1923. He published his lunar theory in Fundamenta ("Foundation") in 1838, and Darlegung ("Explanation") in 1862-64.*TIS 1950 Ernst David Hellinger (0 Sept 1883 in Striegau, Silesia, Germany (now Strzegom, Poland) - 28 March 1950 in Chicago, Illinois, USA) introduced a new type of integral: the Hellinger integral . Jointly with Hilbert he produced an important theory of forms. From 1907 to 1909 he was an assistant at Göttingen and, during this time, he ".. edited Hilbert's lecture notes and Felix Klein's influential Elementarmathematik vom höheren Standpunkte aus (Berlin, 1925) which was translated into English (New York, 1932). Years later the story is told that, Shortly after his arrival at Northwestern, one of the professors in describing Northwest's mathematics program to him remarked that in the honours course Felix Klein's 'Elementary mathematics from an advanced standpoint' was used as a text and "perhaps Hellinger was familiar with it". At this Hellinger ... replied "familiar with it, I wrote it!". *SAU 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 ## Monday, 27 March 2017 ### On This Day in Math - March 27  Charles Minard's Napoleon's March, Modern science, as training the mind to an exact and impartial analysis of facts, is an education specially fitted to promote citizenship. ~Karl Pearson The 86th day of the year; 86 is conjectured to be the largest number n such that 2n (in decimal) doesn't contain a 0. *Tanya Khovanova, Number Gossip The 86th prime is 443, and 4433 = 86,938,307. There is no other two digit n, such that the nth prime starts with n. 86 is the sum of four consecutive integers, 86= 20 + 21 + 22 + 23 and of four consecutive squares, 86= 32 + 42 + 52 + 62 The multiplicative persistence of a number is the number of times the iteration of finding the product of the digits takes to reach a one digit number. For 86, with persistence of three, we produce 8*6= 48, 4*8 = 32, and 3*2 = 6.... and 48+32+6 = 86. (how frequently does that occur?) EVENTS In 1827, Charles Darwin, aged 18, submitted his first report of an original scientific discovery to the Plinian Society in Edinburgh, Scotland. Darwin had discovered several things about the biology of tiny marine organisms found along the Scottish coast. *TIS 1921 On the morning of Easter Sunday, Otto Loewi awoke with the memory he had had an important dream during the night and written down some notes, but when he tried to retrieve them, the writing was hopelessly illegible. After trying to recall the dream all day, he retired early in the evening and eventually the dream came again. The dream was about a way to determine if transmissions between nerve cells was chemical or not. He immediately got out of bed and went to his laboratory. With a single experiment on a frog's heart he confirmed his own thesis of seventeen years before, that the transfer was indeed a chemical process. *Michael Brooks, Free Radicals (pg 24-25) 1958 The ﬁrst national high-school mathematics competition in the U.S. was held. Since 1983 it has been known as the American High School Mathematics Examination (AHSME). [The College Mathematics Journal, 16 (1985), p. 331] *VFR 1976 20-Year Old Bill Gates Gives Opening Address to Hobbyists: Bill Gates gives the opening address at the First Annual World Altair Computer Convention in Albuquerque, N.M. MITS, the company that developed the Altair, had set up shop in the southwestern city to develop its kit computer, which was a hit among hobbyists after it graced the cover of "Popular Mechanics" magazine. Gates, then a 20-year-old erstwhile Harvard student, had helped develop the form of BASIC sold with the Altair. *CHM BIRTHS 1781 Charles Joseph Minard (27 Mar 1781; 24 Oct 1870 at age 89) French civil engineer who made significant contributions to the graphical representations of data. His best-known work, Carte figurative des pertes successives en hommes de l'Armee Français dans la campagne de Russe 1812-1813, dramatically displays the number of Napoleon's soldiers by the width of an ever-reducing band drawn across a map from France to Moscow. At its origin, a wide band shows 442,000 soldiers left France, narrowing across several hundred miles to 100,000 men reaching Moscow. With a parallel temperature graph displaying deadly frigid Russian winter temperatures along the way, the band shrinks during the retreat to a pathetic thin trickle of 10,000 survivors returning to their homeland. *TIS 1824 Johann Wilhelm Hittorf (27 Mar 1824, 28 Nov 1914) German physicist who was a pioneer in electrochemical research. His early investigations were on the allotropes (different physical forms) of phosphorus and selenium. He was the first to compute the electricity- carrying capacity of charged atoms and molecules (ions), an important factor in understanding electrochemical reactions. He investigated the migration of ions during electrolysis (1853-59), developed expressions for and measured transport numbers. In 1869, he published his laws governing the migration of ions. For his studies of electrical phenomena in rarefied gases, the Hittorf tube has been named for him. Hittorf determined a number of properties of cathode rays, including (before Crookes) the deflection of the rays by a magnet. *TIS 1845 Wilhelm Conrad Röntgen (27 Mar 1845 - 10 Feb 1923 at age 77) was a German physicist who discovered the highly penetrating form of radiation that became known as X-rays on 8 Nov 1895. He received the first Nobel Prize for Physics (1901), “in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him.” This high-energy radiation, though first called Röngen rays, became known as X-rays. His discovery initiated revolutionary improvements in making medical diagnoses and enabled many new advances in modern physics. *TIS "In 1901 he became the ﬁrst physicist to receive a Nobel prize." *VFR 1855 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 1857 Karl Pearson (27 Mar 1857; 27 Apr 1936 at age 79) English mathematician who was one of the founders of modern statistics. His lectures as professor of geometry evolved into The Grammar of Science (1892), his most widely read book and a classic in the philosophy of science. Stimulated by the evolutionary writings of Francis Galton and a personal friendship with Walter F.R. Weldon, Pearson became immersed in the problem of applying statistics to biological problems of heredity and evolution. The methods he developed are essential to every serious application of statistics. From 1893 to 1912 he wrote a series of 18 papers entitled Mathematical Contributions to the Theory of Evolution, which contained much of his most valuable work, including the chi-square test of statistical significance. *TIS 1897 Douglas Rayner Hartree PhD, FRS (27 March 1897 – 12 February 1958) was an English mathematician and physicist most famous for the development of numerical analysis and its application to the Hartree-Fock equations of atomic physics and the construction of the meccano differential analyser. *Wik 1905 László Kalmár (27 March 1905 in Edde (N of Kaposvar), Hungary - 2 Aug 1976 in Mátraháza, Hungary) worked on mathematical logic and theoretical computer science. He was ackowledged as the leader of Hungarian mathematical logic. *SAU 1928 Alexander Grothendieck In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. *VFR DEATHS 1850 Wilhelm Beer (4 Jan 1797, 27 Mar 1850 at age 53) German banker and amateur astronomer who owned a fine Fraunhofer refractor which he used in his own a private observatory. He worked jointly with Johann Heinrich von Mädler, to produce the first large-scale moon map to be based on precise micrometric measurements. Their four-year effort was published as Mappa Selenographica (1836). This fine lithographed map provided the most complete details of the Moon's surface in the first half of the 19th century. It was the first lunar map divided in quadrants, and recorded the Moon's face in great detail detail. It was drawn to a scale of scale of just over 38 inches to the moon's diameter. Mädler originated a convention for naming minor craters with Roman letters appended to the name of the nearest large crater (ex. Egede A,B, and C). 1888 Francesco Faà di Bruno (29 March 1825–27 March 1888) was an Italian mathematician and priest, born at Alessandria. He was of noble birth, and held, at one time, the rank of captain-of-staff in the Sardinian Army. He is the eponym of Faà di Bruno's formula. In 1988 he was beatified by Pope John Paul II. Today, he is best known for Faà di Bruno's formula on derivatives of composite functions, although it is now certain that the priority in its discovery and use is of Louis François Antoine Arbogast: Faà di Bruno should be only credited for the determinant form of this formula. However, his work is mainly related to elimination theory and to the theory of elliptic functions. He was the author of about forty original articles published in the "Journal de Mathématiques" (edited by Joseph Liouville), Crelle's Journal, "American Journal of Mathematics" (Johns Hopkins University), "Annali di Tortolini", "Les Mondes", "Comptes rendus de l'Académie des sciences", etc.*Wik 1923 Sir James Dewar (20 Sep 1842; 27 Mar 1923) British chemist and physicist. Blurring the line between physics and chemistry, he advanced the research frontier in several fields at the turn of the century, and gave dazzling lectures. His study of low-temperature phenomena entailed making an insulating double-walled flask of his own design by creating a vacuum between the two silvered layers of steel or glass (1892). This Dewar flask that has been named for him led to the domestic Thermos bottle. In June 1897, The Scientific American reported that "Dewar has just succeeded in liquefying fluorine gas at a temperature of -185 degrees C." He obtained liquid hydrogen in 1898. Dewar also invented cordite, the first smokeless powder.*TIS 1925 Carl Gottfried Neumann,(7 May 1832 in Königsberg, Germany (now Kaliningrad, Russia) - 27 March 1925 in Leipzig, Germany) He worked on a wide range of topics in applied mathematics such as mathematical physics, potential theory and electrodynamics. He also made important pure mathematical contributions. He studied the order of connectivity of Riemann surfaces. During the 1860s Neumann wrote papers on the Dirichlet principle and the 'logarithmic potential', a term he coined. In 1890 Émile Picard used Neumann's results to develop his method of successive approximation which he used to give existence proofs for the solutions of partial differential equations.*SAU 1929 Samuil Shatunovsky (25 March 1859 – 27 March 1929) was a Russian mathematician. focused on several topics in mathematical analysis and algebra, such as group theory, number theory and geometry. Independently from Hilbert, he developed a similar axiomatic theory and applied it in geometry, algebra, Galois theory and analysis.[1] However, most of his activity was devoted to teaching at Odessa University and writing associated books and study materials.*Wik 1972 Maurits Cornelius Escher (17 June 1898 in Leeuwarden, Netherlands - 27 March 1972 in Laren, Netherlands) an artist whose works have included a considerable mathematical content. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations. *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 ## Sunday, 26 March 2017 ### On This Day in Math - March 26  “Have you seen the world go around?" Every human activity, good or bad, except mathematics, must come to an end. ~Paul Erdos The 85th day of the year; 85 is the largest number for which the sum of 12 + 22+32+42+...+n2= 1+2+3+4+.... +M for some n,M, can you find that M? 85 is the largest such n, with a total of 208,335; but can you find some solutions n,M that are smaller? (Reminder for students, the sums of first n consecutive squares are called pyramidal numbers, the sums of the first n integers are called triangular numbers.) and a bonus I found at the Prime Curios web site, (8511 - 85)/11 ± 1 are twin primes. (too cool) 85 is the second smallest n such that n, n+1 and n+2 are products of two primes. (called pronic, or oblong numbers) *Don S McDonald There are 85 five-digit primes that begin with 85. And 85 is the sum of consecutive integers, and the difference of their squares $42+43= 43^2 - 42^2 = 85$, and can be expressed as the sum of two squares in two different ways, 92+ 2 2 = 72 + 62 =85 EVENTS 1619 Descartes reported (to Beekman) his ﬁrst glimpse of “an entirely new science, by which all problems that can be posed, concerning any kind of quantity, continuous or discrete, can be generally solved” which was to become his analytic geometry (published 1637). Descartes relies on the “single motions” of his “new types of compasses (often referred to by commentators as “proportional compasses”), which [he says] are no less exact and geometrical…than the common ones used to draw circles” in order to mark out a new class of problems that have legitimate geometrical solutions. He would apply them to to the problems of (1) dividing a given angle into any number of equal parts, (2) constructing the roots of three types of cubic equations, and (3) describing a conic section. *Stanford Encyclopedia of Philosophy 1760 Guillaume le Gentil sailed from France planning to view the transit of Venus the following year from the east coast of India. Monsoons blew his ship off course, and on the day of the transit, he was becalmed in the Indian Ocean, unable to make any useful observations. Determined to redeem his expedition he books passage to India and builds an observatory to await the 1769 transit in Pondecherry. "The sky remained marvelously clear throughout May, only to cloud over on June 4, the morning of the transit, then clear again as soon as the transit was over." His ordeal of a decade was not yet over. Stricken with dysentery he had to stay nine months more in India, and then booked passage on a Spanish warship. The ship lost its mast in a hurricane off the Cape of Good Hope, and finally limped into Cadiz. Le Gentil set out across the Pyrenees and returned to Paris after a total absence of eleven years, six months, and thirteen days, only to find that he had been presumed dead and his estate divided among his heirs. *Timothy Ferris, Coming of Age in the Milky Way (Thony Christie, The Renaissance Mathematicus, has a more detailed, and perhaps somewhat more accurate, version of Guillame's great adventure. See it here 1851 French Science reporter Terrien wrote in “le National, “Have you seen the world go around? Would you like to see it rotate? Go to the Parthenon on Thursday…the experiment devised by M. Leon Foucault is carried out there, in the presence of the public, under the finest conditions in the world.” *Amir D Aczel, Pendulum, pg 152 Foucault’s most famous pendulum . He suspended a 28 kg brass-coated lead bob with a 67 meter long wire from the dome of the Panthéon, Paris. The plane of the pendulum's swing rotated clockwise 11° per hour, making a full circle in 32.7 hours. *Wik In 1859, Edmond Modeste Lescarbault, a French medical doctor and amateur astronomer, reported sighting a new planet in an orbit inside that of Mercury which he named Vulcan. He had seen a round black spot on the Sun with a transit time across the solar disk 4 hours 30 minutes. He sent this information and his calculations on the planet's movements to Jean LeVerrier, France's most famous astronomer. Le Verrier had already noticed that Mercury had deviated from its orbit. A gravitational pull from Vulcan would fit in nicely with what he was looking for. However, it was not consistently seen again and it is now believed to have been a "rogue asteroid" making a one-time pass close to the sun.*TIS (It was just pointed out to me by @Astroguyz,David Dickinson, that Leonard Nimoy, the actor who is best remembered for his role as the half-Vulcan character of Dr. Spock in the Star Trek series and films was also born on this day in 1931.) 1900 the Roentgen Society of the United States was organised a meeting of doctors from nine states held in Dr. Herber Robarts' office in St. Louis. Dr. Robarts was founder and editor of the American X-Ray Journal, and had been active in radiology since exposing his first X-ray plates in Feb 1896. Robarts was elected as president of the new society and and Dr. J. Rudis-Jicinsky as secretary. They arranged to hold the first annual meeting at the Grand Central Palace in New York City on 13-14 Dec 1900. In 1901, it was renamed as the Roentgen Society of America to include Canadians. It was reorganised at the next annual meeting on 10-11 Dec 1902 as the American Roentgen Ray Society.*TIS 1936 The 200" Hale mirror was SHIPPED, it had been cast in 1934. Still a great video: *David Dickinson ‏@Astroguyz The 200-inch (5.1 m) Hale Telescope (f/3.3) was the world's largest effective telescope for 45 years (1948 - 1993). It is still a workhorse of modern astronomy. It is used nightly for a wide range of astronomical studies. On average the weather allows for at least some data collection about 290 nights a year. *Caltech Astronomy 1985 Alexander's Star is a puzzle similar to the Rubik's Cube, in the shape of a great dodecahedron. Alexander's Star was invented by Adam Alexander, an American mathematician, in 1982. It was patented on 26 March 1985, with US patent number 4,506,891, and sold by the Ideal Toy Company. It came in two varieties: painted surfaces or stickers. Since the design of the puzzle practically forces the stickers to peel with continual use, the painted variety is likely a later edition. *Wik 1994, A picture was released showing the first moon discovered to be in orbit around an asteroid. The potato-shaped asteroid Ida and its newly-discovered moon, Dactyl was imaged by NASA's Galileo spacecraft, about 14 minutes before its closest approach to the asteroid on 28 Aug 1993. Ida appears to be about about 36 miles long and 14 miles wide. It shows numerous craters, including many degraded craters, indicating Ida's surface is older than previously thought. The tiny moon is about one mile (1.5-km) across. The names are derived from the Dactyli, a group of mythological beings who lived on Mount Ida, where the infant Zeus was hidden (and raised, in some accounts) by the nymph Ida and protected by the Dactyli. 2010 Crocheting Adventures with Hyperbolic Planes by Dr Daina Taimina has won the 2009 Diagram Prize, having received the majority of the public vote for the oddest titled book of the year at thebookseller.com. The first award was given in 1978 for Proceedings of the Second International Workshop on Nude Mice BIRTHS 1516 Conrad Gessner (Konrad Gessner, Conrad Geßner, Conrad von Gesner, Conradus Gesnerus, Conrad Gesner; 26 March 1516 – 13 December 1565) was a Swiss naturalist and bibliographer. His five-volume Historiae animalium (1551–1558) is considered the beginning of modern zoology, and the flowering plant genus Gesneria (Gesneriaceae) is named after him. He is denoted by the author abbreviation Gesner when citing a botanical name. Gessner in 1551 was the first to describe adipose tissue; and in 1565 the first to document the pencil. *Wik See more at The Renaissance Mathematicus blog. 1753 Count Benjamin Thompson Rumford (26 Mar 1753, 21 Aug 1814) American-born British physicist, government administrator, and a founder of the Royal Institution of Great Britain, London. Because he was a Redcoat officer and an English spy during the American revolution, he moved into exile in England. Through his investigations of heat he became one of the first scientists to declare that heat is a form of motion rather than a material substance, as was popularly believed until the mid-19th century. Among his numerous scientific contributions are the development of a calorimeter and a photometer. He invented a double boiler, a kitchen stove and a drip coffee pot. *TIS 1773 Nathaniel Bowditch (26 Mar 1773, 16 Mar 1838 at age 65) Self-educated American mathematician and astronomer. He learned Latin to study Newton's Principia and later other languages to study mathematics in these languages. Between 1795 and 1799 he made four sea voyages and in 1802 he was in command of a merchant ship. He was author of the best book on navigation of his time, New American Practical Navigator (1802), and his translation (assisted by Benjamin Peirce) of Laplace's Mécanique céleste gave him an international reputation. Bowditch was the discoverer of the Bowditch curves (more often called Lisajous figures for their co-discoverer), which have important applications in astronomy and physics.*TIS Bowditch was a navigator on the Wilkes Expedition and an island in the Stork Archipelago in the South Pacific is named for him (and sometimes called Fakaofu) *TIS Nathaniel Bowditch acquired his knowledge of mathematics through self-study while apprenticed to a ship’s chandler. He is most noted for his translation of Laplace’s M´ecanique c´eleste. [DSB 2, 368] *VFR 1789 William C. Redfield (26 Mar 1789, 12 Feb 1857 at age 67) American meteorologist who observed the whirlwind character of tropical storms. Following a hurricane that struck New England on 3 Sep 1821, he noted that in central Connecticut trees had toppled toward the northwest, but in the opposite direction 80-km further west. He found that hurricanes are generated in a belt between the Equator and the tropics, then veer eastward when meeting westerly winds at about latitude 30ºN. In 1831, he published his evidence that storm winds whirl counterclockwise about a centre that moves in the normal direction of the prevailing winds. He also promoted railroads and steamships. He co-founded the American Association for the Advancement of Sciences and was president at its first meeting (Sep 1848).*TIS 1803 Sir John William Lubbock, (London, England, 26 March 1803 - Downe, Kent, England, 20 June 1865 )English astronomer and mathematician. He made a special study of tides and of the lunar theory and developed a method for calculating the orbits of comets and planets. In mathematics he applied the theory of probability to life insurance problems. He was a strong proponent of Continental mathematics and astronomy. Lubbock, third Baron Lubbock, was born into a London banking family. After attending Eton, he moved to Trinity College, Cambridge, where he became a student of William Whewell.(it was at the request of Lubbock that Whewell created the term "biometry".) He excelled in mathematics and traveled to France and Italy to deepen his knowledge of the works of Pierre-Simon de Laplace and Joseph Lagrange. Entering his father’s banking firm as a junior partner, he devoted his free time to science. Lubbock strongly supported Lord Brougham’s Society for the Diffusion of Useful Knowledge [SDUK], which produced scientific and technical works designed for the working class. His articles on tides for the Society’s publications resulted in a book, *An Elementary Treatise on the Tides, in 1839. *Biographical Encyclopedia of Astronomers 1821 Ernst Engel (26 Mar 1821, 8 Dec 1896) German statistician, the head of the Prussian Statistical Bureau (1860-82), known for the "Engel curve," or Engel's law, which states that the proportion of expenditure on food will fall as income rises, i.e. food is a necessary good. Engel's law applies to goods as a whole. Demand for food, clothing and shelter - and for most manufactured products - doesn't keep pace with increases in incomes. Engel curves are useful for separating the effect of income on demand from the effects of changes in relative prices. Engel also examined the relationship between the size of the Prussian rye harvest and the average price of rye over a number of years prior to 1860, probably the first empirical study of the relationship between price and supply. *TIS 1848 Konstantin Alekseevich Andreev (26 March 1848 in Moscow, Russia - 29 Oct 1921 Near Sevastopol, Crimea) Andreev is best known for his work on geometry, although he also made contributions to analysis. In the area of geometry he did major pieces of work on projective geometry. Let us note one particular piece of work for which he has not received the credit he deserves. Gram determinants were introduced by J P Gram in 1879 but Andreev invented them independently in the context of problems of expansion of functions into orthogonal series and the best quadratic approximation to functions. *SAU 1862 Philbert Maurice d'Ocagne (26 March 1862 in Paris, France - 23 Sept 1938 in Le Havre, France) In 1891 he began publishing papers on nomography, the topic for which he is most remembered today. Nomography consists in the construction of graduated graphic tables, nomograms, or charts, representing formulas or equations to be solved, the solutions of which were provided by inspection of the tables. An advertisement for a colloquium at the Edinburgh Mathematical Society gave the following description of d'Ocagne's course: It is now generally recognised that for most purposes the nomographic methods are superior to the older graphical methods of calculation. The introduction of some nomographic teaching in British Universities (and schools, for much of it is not too hard for schoolboys) is much to be desired. *SAU Nomographs are still used in wide areas of science and technology. The book below is an excellent coverage of the history and modern usage. 1875 Max Abraham (26 Mar 1875, 16 Nov 1922) German physicist whose life work was almost all related to Maxwell's theory. The text he wrote was the standard work on electrodynamics in Germany for a long time. Throughout his life, he remained strongly opposed to Einstein's Theory of Relativity, objecting to its postulates which he felt were contrary to classical common sense. He further held that the experimental evidence did not support that theory. In 1902, he had developed a theory of the electron in which he held that an electron was a perfectly rigid sphere with a charge distributed evenly over its surface. He also believed in the ether theory, thought that future astronomical data would validate it, and thus relativity was not in fact a good description of the real world. *TIS 1902 Marion Gray (26 March 1902, 16 Sept 1979) graduated from Edinburgh University and then went to Bryn Mawr College in the USA. She completed her doctorate there and returned to posts at Edinburgh and Imperial College London. She returned to the USA and worked for AT&T for the rest of her career. The Gray graph is named after her.*SAU The Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph: every vertex touches exactly three edges. The Gray graph is interesting as the first known example of a cubic graph having the algebraic property of being edge but not vertex transitive *Wik 1903 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 1908 Theodore Samuel Motzkin (26 March 1908–15 December 1970) was an Israeli-American mathematician. Motzkin received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski. He was appointed at UCLA in 1950 and worked there until retirement. The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[3] He was the first to prove the existence of principal ideal domains that are not Euclidean domains. The quote "complete disorder is impossible," describing Ramsey theory is attributed to him. *Wik 1913 Paul Erdös (26 Mar 1913; 20 Sep 1996 at age 83) Hungarian mathematician, who was one of the century's top math experts and pioneered the fields of number theory and combinatorics. The type of mathematics he worked on were beautiful problems that were simple to understand, but notoriously difficult to solve. At age 20, he discovered a proof for a classic theorem of number theory that states that there is always at least one prime number between any positive integer and its double. In the 1930s, he studied in England and moved to the USA by the late 1930s when his Jewish origins made a return to Hungary impossible. Affected by McCarthyism in the 1950s, he spent much of the next ten years in Israel. Writing his many hundreds of papers made him one of history's most prolific mathematicians. *TIS His forte is posing and solving problems. One of his customs is to offer cash prizes for problems he poses. These awards range from$5 to \$10,000 depending on how difficult he judges them to be. Erdos has written over 1,000 research papers, more than any other mathematician. The previous record was held by Arthur Cayley, who wrote 927. [Gallian, Contemporary Abstract Algebra, p 378]*VFR
McGill University Professor Willy Moser, a friend and collaborator of Erdos, tells of the "trial" of hosting Erdos. Once when Erdos was staying with him, Moser set up five dinners for him with five of erdos' old friends. Moser's wife pointed out that after the many times he had visited these homes and never brought a gift, perhaps Moser should remind him to bring candy or flowers. When he suggested the idea to Erdos, he thought it was a great idea and asked Moser, "Would you pick me up five boxes of chocolates?"

1922 Guido Stampacchia (March 26, 1922 - April 27, 1978) was a 20th century mathematician. Stampacchia was active in research and teaching throughout his career. He made key contributions to a number of fields, including calculus of variation and differential equations. In 1967 Stampacchia was elected President of the Unione Matematica Italiana. It was about this time that his research efforts shifted toward the emerging field of variational inequalities, which he modeled after boundary value problems for partial differential equations.
Stampacchia accepted the position of Professor Mathematical Analysis at the University of Rome in 1968 and returned to Pisa in 1970. He suffered a serious heart attack in early 1978 and died of heart arrest on April 27 of that year *Wik

1938 Sir Anthony James (Tony) Leggett (26 March 1938, ), has been a Professor of Physics at the University of Illinois at Urbana-Champaign since 1983.
Professor Leggett is widely recognized as a world leader in the theory of low-temperature physics, and his pioneering work on superfluidity was recognized by the 2003 Nobel Prize in Physics. He has shaped the theoretical understanding of normal and superfluid helium liquids and strongly coupled superfluids. He set directions for research in the quantum physics of macroscopic dissipative systems and use of condensed systems to test the foundations of quantum mechanics. *Wik

DEATHS

1609 John Dee (13 July 1527– *SAU gives 26 March 1609 in Mortlake, London, England) was an English mathematician, astronomer, astrologer, occultist, navigator, imperialist[4] and consultant to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination and Hermetic philosophy.
Dee straddled the worlds of science and magic just as they were becoming distinguishable. One of the most learned men of his age, he had been invited to lecture on advanced algebra at the University of Paris while still in his early twenties. Dee was an ardent promoter of mathematics and a respected astronomer, as well as a leading expert in navigation, having trained many of those who would conduct England's voyages of discovery.
Simultaneously with these efforts, Dee immersed himself in the worlds of magic, astrology and Hermetic philosophy. He devoted much time and effort in the last thirty years or so of his life to attempting to commune with angels in order to learn the universal language of creation and bring about the pre-apocalyptic unity of mankind. A student of the Renaissance Neo-Platonism of Marsilio Ficino, Dee did not draw distinctions between his mathematical research and his investigations into Hermetic magic, angel summoning and divination. Instead he considered all of his activities to constitute different facets of the same quest: the search for a transcendent understanding of the divine forms which underlie the visible world, which Dee called "pure verities".
In his lifetime Dee amassed one of the largest libraries in England. His high status as a scholar also allowed him to play a role in Elizabethan politics. He served as an occasional adviser and tutor to Elizabeth I and nurtured relationships with her ministers Francis Walsingham and William Cecil. Dee also tutored and enjoyed patronage relationships with Sir Philip Sidney, his uncle Robert Dudley, 1st Earl of Leicester, and Edward Dyer. He also enjoyed patronage from Sir Christopher Hatton.*Wik
I have Woolley's book, and enjoyed it.

1797 James Hutton (3 June 1726 in Edinburgh, Scotland - 26 March 1797 in Edinburgh, Scotland) geologist who initiated the principle of uniformitarianism with his Theory of the Earth (1785). He asserted that geological processes examined in the present time explain the formation of older rocks. John Playfair effectively championed Hutton's theory. Hutton, in effect, was the founder of modern geology, replacing a belief in the role of a biblical flood forming the Earth's crust. He introduced an understanding of the action of great heat beneath the Earth's crust in fusing sedimentary rocks, and the elevation of land forms from levels below the ocean to high land in a cyclical process. He established the igneous origin of granite (1788). He also had early thoughts on the evolution of animal forms and meterology. *TIS

1914 John S Mackay (22 Oct 1843 in Auchencairn near Kirkudbright, Kirkcudbrightshire, Scotland - 26 March 1914 in Edinburgh, Scotland)graduated from St Andrews University and taught at Perth Academy and Edinburgh Academy. He was a founder member of the EMS and became the first President in 1883 and an honorary member in 1894. He published numerous papers on Geometry in the EMS Proceedings.*SAU

1933 József Kürschák (14 March 1864 – 26 March 1933) was a Hungarian mathematician noted for his work on trigonometry and for his creation of the theory of valuations. He proved that every valued field can be embedded into a complete valued field which is algebraically closed. In 1918 he proved that the sum of reciprocals of consecutive natural numbers is never an integer. Extending Hilbert's argument, he proved that everything that can be constructed using a ruler and a compass, can be constructed by using a ruler and the ability of copying a fixed segment. He was elected a member of the Hungarian Academy of Sciences in 1897. *Wik

1974 Edward Uhler Condon (March 2, 1902 – March 26, 1974) was a distinguished American nuclear physicist, a pioneer in quantum mechanics, and a participant in the development of radar and nuclear weapons during World War II as part of the Manhattan Project. The Franck–Condon principle and the Slater–Condon rules are named after him.
He was the director of the National Bureau of Standards (now NIST) from 1945 to 1951. In 1946, Condon was president of the American Physical Society, and in 1953 was president of the American Association for the Advancement of Science.
During the McCarthy period, when efforts were being made to root out communist sympathizers in the United States, Edward Condon was a target of the House Un-American Activities Committee on the grounds that he was a 'follower' of a 'new revolutionary movement', quantum mechanics; Condon defended himself with a famous commitment to physics and science.
Condon became widely known in 1968 as principal author of the Condon Report, an official review funded by the United States Air Force that concluded that unidentified flying objects (UFOs) have prosaic explanations. The lunar crater Condon is named for him.
Years later, Carl Sagan reported how Condon described one encounter with a loyalty review board. A board member stated his concern: "Dr. Condon, it says here that you have been at the forefront of a revolutionary movement in physics called...quantum mechanics. It strikes this hearing that if you could be at the forefront of one revolutionary movement...you could be at the forefront of another". Condon said he replied: "I believe in Archimedes' Principle, formulated in the third century B.C. I believe in Kepler's laws of planetary motion, discovered in the seventeenth century. I believe in Newton's laws...." and continued with a catalog of scientists from earlier centuries, including the Bernoulli, Fourier, Ampère, Boltzmann, and Maxwell.[35] He once said privately: "I join every organization that seems to have noble goals. I don't ask whether it contains Communists".*Wik

1996 Hewlett-Packard Co-Founder David Packard Dies:
Hewlett-Packard Company co-founder David Packard dies after several weeks of illness. With fellow Stanford graduate Bill Hewlett, Packard founded Hewlett-Packard in a Palo Alto garage in 1938, spurring the development of what has come to be known as Silicon Valley. The company's first product was an oscillator, eight of which Disney used in its groundbreaking film ""Fantasia."" Since then, HP has made a name in personal computers, laser printers, calculators, accessories, and test equipment.*CHM

1966 Anna Johnson Pell Wheeler (5 May 1883 in Calliope (now Hawarden), Iowa, USA - 26 March 1966 in Bryn Mawr, Pennsylvania, USA) In 1899 she entered the University of South Dakota where she showed great promise in mathematics. The professor of mathematics, Alexander Pell, recognised her talents and helped persuade Anna Johnson that she should follow a career in mathematics. She received an A.B. degree in 1903.
After winning a scholarship to study for her master's degrees at the University of Iowa, she was awarded the degree for a thesis The extension of Galois theory to linear differential equations in 1904. A second master's degree from Radcliffe was awarded in 1905 and she remained there to study under Bôcher and Osgood.
Anna Johnson was awarded the Alice Freeman Palmer Fellowship from Wellesley College to study for a year at Göttingen University. There she attended lectures by Hilbert, Klein, Minkowski, Herglotz and Schwarzschild. She worked for her doctorate at Göttingen. While there Alexander Pell, her former mathematics professor came to Göttingen so that they could marry.
After returning to the United States, where her husband was by now Dean of Engineering, she taught courses in the theory of functions and differential equations. In 1908 Anna Pell returned to Göttingen where she completed the work for her doctorate but, after a disagreement with Hilbert, she returned to Chicago, where her husband was now on the university staff, without the degree being awarded.
At Chicago she became a student of Eliakim Moore and received her Ph.D. in 1909, her thesis Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations being the one written originally at Göttingen. From 1911 Anna Pell taught at Mount Holyoke College and then at Bryn Mawr from 1918. Anna Pell's husband Alexander, who was 25 years older than she was, died in 1920. In 1924 Anna Pell became head of mathematics when Scott retired, becoming a full professor in 1925.
After a short second marriage to Arthur Wheeler, during which time they lived at Princeton and she taught only part-time, her second husband died in 1932. After this Anna Wheeler returned to full time work at Bryn Mawr where Emmy Noether joined her in 1933. However Emmy Noether died in 1935. The period from 1920 until 1935 certainly must have been one with much unhappiness for Anna Wheeler since during those years her father, mother, two husbands and close friend and colleague Emmy Noether died. Anna Wheeler remained at Bryn Mawr until her retirement in 1948.
The direction of Anna Wheeler's work was much influenced by Hilbert. Under his guidance she worked on integral equations studying infinite dimensional linear spaces. This work was done in the days when functional analysis was in its infancy and much of her work has lessened in importance as it became part of the more general theory.
Perhaps the most important honour she received was becoming the first woman to give the Colloquium Lectures at the American Mathematical Society meetings in 1927.
*SAU

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 & Campbel

## Saturday, 25 March 2017

### On This Day in Math - March 25

 *http://agutie.homestead.com/

Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.
~Girolamo Cardano

The 84th day of the year, with nine points equally placed around a circle there are 84 different triangles using three of these points as vertices. Are any of them right triangles?

84 is the only number that is spelled with ten letters that are all different.

Litttle is known of the life of Diophantus, but this problem, supposedly on his tomb, will reveal his age.
**If you get stuck, I posted the answer at the bottom of the blog.

Keith numbers are much rarer than the primes, with only 84 Keith numbers with digits.
Here is a Numberphile video explaining Keith numbers.

A hepteract is a seven-dimensional hypercube with 84 penteract 5-faces.

EVENTS
1539 Tartaglia tells Cardano about his method of solving cubic equations and Cardano signs an oath to keep the method secret, according to Tartaglia. *B L van der Waerden, History of Algebra
"Scipio Ferro of Bologna well-nigh thirty years ago discovered this rule and handed it on to Antonio Maria Fior of Venice, whose contest with Niccolo Tartaglia of Brescia gave Niccolo

occasion to discover it. He [Tartaglia] gave it to me in response to my entreaties, though withholding the demonstration. Armed with this assistance, I sought out its demonstration in [various] forms. This was very difficult." Cardano in Ars Magna (Basel, 1545)

1655 Christiaan Huygens was the first to discover a moon of Saturn, when he viewed Titan (the largest and easiest to see) on 25 Mar 1655. However, the moon wasn't named until almost two centuries later when Sir John Herschel, discoverer of Uranus, assigned names to the seven moons of Saturn that were known at that time. Saturn's largest moon was named simply "Titan," since the word means "one that is great in size, importance, or achievement." *TIS

1792 D’Alembert wrote: “I would like to see our friend Condorcet, who assuredly has great talent and wisdom, express himself in another manner.” Reading Condorcet’s mathematical works is a thankless task, for the notation is inconsistent, the expression of ideas often imprecise and obscure, and the proofs labored. Perhaps this helps explain why he is not a well known mathematician. [DSB 3, 384]*VFR

1822 Gauss reveals plans to contact aliens: Gauss wrote of the heliotrope's potential (an instrument invented by Gauss in 1821 that uses a mirror to reflect sunlight over great distances) as a celestial signaling device in a March 25, 1822 letter to Heinrich Olbers, by which he reveals a belief and interest in finding a method to contact extraterrestrial life: "With 100 separate mirrors, each of 16 square feet, used conjointly, one would be able to send good heliotrope-light to the moon.... This would be a discovery even greater than that of America, if we could get in touch with our neighbors on the moon."
Some have suggested Gauss may have also proposed the constructing an immense right triangle and three squares on the surface of the earth to signal to aliens from the Moon or Mars. See more on that story here.*Wik

In 1857, Frederick Laggenheim took the first photograph of a solar eclipse. This is often reported but seems not to be the first. I found a note on Wikipedia that "The first correctly-exposed photograph of the solar corona was made during the total phase of the solar eclipse of 28 July 1851 by a local daguerreotypist named Berkowski at the Royal Observatory in Königsberg, Prussia (now Kalinigrad in Russia). Berkowski, whose first name was never published, observed at the Royal Observatory. A small 6-cm refracting telescope was attached to the 15.8-cm Fraunhofer heliometer and a 84-second exposure was taken shortly after the beginning of totality. *Wik

In 1903, The Times newspaper reported that the French physicist, Pierre Curie assisted by Marie Curie, communicated to the Academy of Sciences that the recently discovered Radium “possesses the extraordinary property of continuously emitting heat, without combustion, without chemical change of any kind, and without any change to its molecular structure, which remains spectroscopically identical after many months of continuous emission of heat ... such that the pure Radium salt would melt more than its own weight of ice every hour ... A small tube containing Radium, if kept in contact with the skin for some hours ... produces an open sore, by destroying the epidermis and the true skin beneath ... and cause the death of living things whose nerve centres do not lie deep enough to be shielded from their influence.” *TIS

1992 Excel 4.0 Spreadsheet Software Released: Microsoft Corporation releases its Excel 4.0 spreadsheet program. Excel was one in a long line of practical applications that Microsoft and other companies developed for personal computers, making them more appealing to home and office users. The earliest commercial computerized spreadsheet was VisiCalc, written by Ed Frankston and Dan Bricklin and released for the Apple II personal computer in 1979.*CHM

BIRTHS
1538 Christopher Clavius (March 25, 1538 – February 6, 1612) was a German Jesuit mathematician and astronomer who was the main architect of the modern Gregorian calendar. In his last years he was probably the most respected astronomer in Europe and his textbooks were used for astronomical education for over fifty years in Europe and even in more remote lands (on account of being used by missionaries). As an astronomer Clavius held strictly to the geocentric model of the solar system, in which all the heavens rotate about the Earth. Though he opposed the heliocentric model of Copernicus, he recognized problems with the orthodox model. He was treated with great respect by Galileo, who visited him in 1611 and discussed the new observations being made with the telescope; Clavius had by that time accepted the new discoveries as genuine, though he retained doubts about the reality of the mountains on the Moon. Later, a large crater on the Moon was named in his honour.*Wik
Called the Euclid of the sixteenth-century, born in the German town of Bamberg, the see of the prince-bishop of Franconia. He was also the leader of the Gregorian calendar reform. Perhaps his greatest contribution was as an educational reformer.
In his Astrolabium (Rome,1593) he uses a dot to separate whole numbers from decimal fractions, but it would be 20 more years before the decimal point would be widely accepted. Carl Boyer mentions "the Jesuit friend of Kepler" who was the first to use the decimal point with a clear idea of its significance. In the same work, Clavius originated a way of dividing a scale for precise measurements. His idea was adopted by Vernier 42 years later.
In his Algebra (Rome, 1608) Clavius was the first to use parenthesis to express aggregation and the first to use a symbol for an unknown quantity. Other innovations were also seen in the symbols attributed to him by Florian Cajori such as the radical sign, plus and minus signs.

Clavius proposed a proof that there can be no more than three dimensions in geometry, based on the fact that only three concurrent lines can be drawn from a point so that they are mutually perpendicular. He discovered and proved a theorem for a regular polygon with an odd number of sides which two centuries later enabled Carl Friedrich Gauss to construct a 17-sided polygon by ruler and compass.
In hisTriangula sphaerica (Mainz 1611) Clavius summarized all contemporary knowledge of plane and spherical trigonometry. His prostlaphaeresis , the grandparent of logarithms, relied on the sine of the sum and differences of numbers. In this way he was able to substitute addition and subtraction for multiplication, by solving the identity with which we are familiar today: 2 sin x sin y = cos(x-y)-cos(x+y). D. E. Smith gives the details of the proof and emphasizes the impact Clavius' work had on the discovery of logarithms. Smith also underlines the modesty of Clavius in generously giving to one of his contemporaries more credit than is due for his own prostlaphaeresis . *Joseph MacDonnell, S.J., Fairfield Univ webpage
Some really nice detail about Clavius is at Renaissance Mathematicus

1798 Christoph Gudermann (March 25, 1798, September 25, 1852) was born in Vienenburg. He was the son of a school teacher and became a teacher himself after studying at the University of Göttingen, where his advisor was Karl Friedrich Gauss. He began his teaching career in Kleve and then transferred to a school in Münster.
He is most known today for being the teacher of Karl Weierstrass, who took Gudermann's course in elliptic functions, 1839–1840, the first to be taught in any institute. Weierstrass was greatly influenced by this course, which marked the direction of his own research.
Gudermann originated the concept of uniform convergence, in an 1838 paper on elliptic functions, but only observed it informally, neither formalizing it nor using it in his proofs. Instead, Weierstrass elaborated and applied uniform convergence.
His researches into spherical geometry and special functions focused on particular cases, so that he did not receive the credit given to those who published more general works. The Gudermannian function, or hyperbolic amplitude, is named after him.Gudermann died in Münster. *Wik

1833 (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

1859 Samuil Shatunovsky (25 March 1859 – 27 March 1929) was a Russian mathematician. focused on several topics in mathematical analysis and algebra, such as group theory, number theory and geometry. Independently from Hilbert, he developed a similar axiomatic theory and applied it in geometry, algebra, Galois theory and analysis. However, most of his activity was devoted to teaching at Odessa University and writing associated books and study materials.*Wik

1865 Pierre-Ernest Weiss (25 Mar 1865, 24 Oct 1940) French physicist who investigated magnetism and determined the Weiss magneton unit of magnetic moment. Weiss's chief work was on ferromagnetism. Hypothesizing a molecular magnetic field acting on individual atomic magnetic moments, he was able to construct mathematical descriptions of ferromagnetic behaviour, including an explanation of such magnetocaloric phenomena as the Curie point. His theory succeeded also in predicting a discontinuity in the specific heat of a ferromagnetic substance at the Curie point and suggested that spontaneous magnetization could occur in such materials; the latter phenomenon was later found to occur in very small regions known as Weiss domains. His major published work was Le magnetisme ( 1926).*TIS

1923 Kenneth Linn Franklin (25 Mar 1923, ) American astronomer who discovered that the giant planet Jupiter emits radio waves (1955). Dr. Bernard F. Burke and Franklin, astronomers at the Carnegie Institution in Washington, were scanning the sky for radio waves from galaxies. By chance, they found a radio signal that resembled short bursts of static, similar to interference by lightning on home radios. After weeks of study, finding the signals were periodic, four minutes earlier each day, they pin-pointed Jupiter as the source. Never before had radio sounds from a planet in our solar system been detected. Later it was discovered that the radio waves were circularly polarized, so a magnetic field was involved.*TIS

1939 Richard Alfred Tapia (March 25, 1939 - ) is a renowned American mathematician and champion of under-represented minorities in the sciences. In recognition of his broad contributions, in 2005, Tapia was named "University Professor" at Rice University in Houston, Texas, the University's highest academic title. The honor has been bestowed on only six professors in Rice's ninety-nine year history. On September 28, 2011, President Barack Obama announced that Tapia was among twelve scientists to be awarded the National Medal of Science, the top award the United States offers its researchers. Tapia is currently the Maxfield and Oshman Professor of Engineering; Associate Director of Graduate Studies, Office of Research and Graduate Studies; and Director of the Center for Excellence and Equity in Education at Rice University.
Tapia's mathematical research is focused on mathematical optimization and iterative methods for nonlinear problems. His current research is in the area of algorithms for constrained optimization and interior point methods for linear and nonlinear programming.*Wik

DEATHS
1818 Caspar Wessel (8 Jun 174525 Mar 1818 at age 72) was a Norwegian mathematician who invented a geometric way of representing complex numbers which pre-dated Argand. *SAU
His fundamental paper, Om directionens analytiske betegning, was published in 1799 by the Royal Danish Academy of Sciences and Letters. Since it was in Danish, it passed almost unnoticed, and the same results were later independently found by Argand and Gauss.
One of the more prominent ideas presented in "On the Analytical Representation of Direction" was that of vectors. Even though this wasn't Wessel's main intention with the publication, he felt that a geometrical concept of numbers, with length and direction, was needed. Wessel's approach on addition was: "Two straight lines are added if we unite them in such a way that the second line begins where the first one ends and then pass a straight line from the first to the last point of the united lines. This line is the sum of the united lines". This is the same idea as used today when summing vectors. Wessel's priority to the idea of a complex number as a point in the complex plane is today universally recognized. His paper was re-issued in French translation in 1899, and in English in 1999 as On the analytic representation of direction (ed. J. Lützen et al.).*Wik

1995 James S(amuel) Coleman (12 May 1926, 25 Mar 1995 at age 68) was a U.S. sociologist, a pioneer in mathematical sociology whose studies strongly influenced education policy. In the early 1950s, he was as a chemical engineer with Eastman-Kodak Co. in Rochester, N.Y. He then changed direction, fascinated with sociology and social problems. In 1966, he presented a report to the U.S. Congress which concluded that poor black children did better academically in integrated, middle-class schools. His findings provided the sociological underpinnings for widespread busing of students to achieve racial balance in schools. In 1975, Coleman rescinded his support of busing, concluding that it had encouraged the deterioration of public schools by encouraging white flight to avoid integration. (We can never control the law of unintended consequences)*TIS

* Diophantus died at 84, why else would I have it on the 84th day of the year?

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