## Sunday, 20 November 2016

### On This Day in Math - November 20

The history of astronomy is a history of receding horizons.

— Edwin Powell Hubble

The 325th day of the year; 325 is the smallest number that can be written as the sum of two squares in three different ways. (What is the next such number?)

325 is last year day that is the sum of the first n^2 integers, $325 = \sum\limits_{i=1}^{5^2} i$

On an infinite chessboard, there are 325 different squares that can be reached in 5 knight moves.

EVENTS

1629 In a letter to Marin Mersenne, Descartes … went on to postulate another kind of language in which ideas would be represented so clearly that errors of judgment would be 'almost impossible'. To realize such a language, all of our thoughts would first have to be given a proper order 'like the natural order of the numbers'; and this presupposes the 'true philosophy', by which the analysis and ordering of thoughts would be carried out. Although Descartes pursues the plan no further, he is optimistic that 'such a language is possible and that the knowledge on which it depends can be discovered'. *Donald Rutherford,

1711 Robert Simson submitted to a simple test of his mathematical knowledge and was duly admitted as professor of mathematics at the University of Glasgow. His most inﬂuential work was a definitive edition of Euclid’s Elements in 1749. *VFR  The pedal line of a triangle is sometimes called the "Simson line" after him, although it does not actually appear in any work of Simson.

1843 Sylvester departs US for England and describes his life as "Pretty much a blank." After resigning from Un of Va. after only four months, J. J. Sylvester lived with a brother in New York City while trying to find work in the US. Finally giving up, her returned to England with no job or prospects for one. *James Joseph Sylvester: Life and Work in Letters
edited by Karen Hunger Parshall

1980, Steve Ptacek in Solar Challenger piloted its first solar-powered flight. The aircraft was designed and built by AeroVironment, Inc. (founded in 1971 by ultra-light airplane innovator, Dr. Paul MacCready). An earlier, 71-ft wingspan, solar-powered design, the Gossamer Penguin, after test flights, flew about 1.95 miles at a public demonstration on 7 Aug 1980. Solar Challenger built upon this experience to be a piloted, solar-powered aircraft strong enough to handle both long and high flights when encountering normal turbulence. With only a 46.5-ft wingspan, it had a huge horizontal stabilizer and had enough wing area for 16,128 solar cells. After design modifications, Ptacek flew across the English Channel flight on 7 July 1981.*VFR

2008 Conficker, also known as Downup, Downadup and Kido, is a computer worm targeting the Microsoft Windows operating system that was first detected on this day in November 2008. It uses flaws in Windows software and dictionary attacks on administrator passwords to propagate while forming a botnet, and has been unusually difficult to counter because of its combined use of many advanced malware techniques. The Conficker infected millions of computers including government, business and home computers in over 200 countries, making it the largest known computer worm infection since the 2003 Welchia. *Wik

BIRTHS

1602 Otto von Guericke (20 Nov 1602; 11 May 1686) German physicist who investigated the properties of a vacuum invented (1654) the first piston air pump to produce a vacuum. While mayor of Madgeburg, in 1663, he demonstrated that two 51 cm diameter copper hemispheres with air pumped out of their interior would be so strongly held together by the force of air pressure that teams of horses harnessed to each hemisphere were not able to pull the hemispheres apart. He studied the role of air in combustion and respiration. With his invention of the first electrostatic machine - a rotating ball of sulphur electrified by friction against his hand - he produced sizeable sparks and showed that like charges repel each other.*TIS

1792 Nikolai Ivanovich Lobachevsky born. (November 20, 1792 – February 12, 1856 (O.S.)) was a Russian mathematician and geometer, renowned primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry. William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work. Russia did not convert to the Gregorian Calendar until after the communist revolution in 1918. The new style dates were (December 1, 1792 – February 24, 1856 *Wik
And if you've never heard Tom Lehrer's fantastic musical creation about Lobachevsky. He admits the topic has no relation to the man, but the name just fit so well.

1873 William W(eber) Coblentz (20 Nov 1873; 15 Sep 1962) an American physicist and astronomer whose work lay primarily in infrared spectroscopy. In 1905 he founded the radiometry section of the National Bureau of Standards, which he headed for 40 years. Coblentz measured the infrared radiation from stars, planets, and nebulae and was the first to determine accurately the constants of blackbody radiation, thus confirming Planck's law. *TIS

1889 Edwin Powell Hubble (20 Nov 1889; 28 Sep 1953) American astronomer, born in Marshfield, Mo., who is considered the founder of extragalactic astronomy and who provided the first evidence of the expansion of the universe. In 1923-5 he identified Cepheid variables in "spiral nebulae" M31 and M33 and proved conclusively that they are outside the Galaxy. His investigation of these objects, which he called extragalactic nebulae and which astronomers today call galaxies, led to his now-standard classification system of elliptical, spiral, and irregular galaxies, and to proof that they are distributed uniformly out to great distances. Hubble measured distances to galaxies and their redshifts, and in 1929 he published the velocity-distance relation which is the basis of modern cosmology. *TIS
The late Bill Buegsen was a resident who was proud of the achievements of Marshfield's native son, so he designed a one-fourth replica of the original Hubble Space Telescope. The Hubble Telescope replica was dedicated on July 4, 1994 and is located on Clay Street, on the west side of the Webster County Courthouse in Marshfield, Mo. It took approximately three months to build, is approximately twelve feet long, ten feet wide and weighs twelve hundred pounds. There is also an Elementary school named for Hubble. The city is on the famous Route 66 just 30 minutes east of Springfield, Mo. *Marshfield Tourist Office web site

1893 André Bloch (20 Nov 1893 in Besançon, France - 11 Oct 1948 in Paris, France) attended the École Polytechnique in 1913 then was drafted in 1914. An accident at the front made him unfit for military service. On 17 Nov 1917, at a family meal, he murdered one of his brothers, his uncle and his aunt. He was confined to a psychiatric hospital (Saint-Maurice Hospital) where he worked on a large range of topics, function theory, geometry, number theory, algebraic equations and kinematics.
Bloch wrote many important papers, corresponding with Hadamard, Mittag-Leffler, Pólya and Henri Cartan (Élie Cartan's son). He was a model patient who refused to go out saying Mathematics is enough for me. Bloch explained the murders to his doctor saying It's a matter of mathematical logic. There had been mental illness in my family. He saw it as his eugenic duty! The Académie awarded him the Becquerel Prize just before his death. *SAU

1917 Leonard Jimmie Savage (20 November 1917 – 1 November 1971) was an American mathematician and statistician. Nobel Prize-winning economist Milton Friedman said Savage was "one of the few people I have met whom I would unhesitatingly call a genius." His most noted work was the 1954 book Foundations of Statistics, in which he put forward a theory of subjective and personal probability and statistics which forms one of the strands underlying Bayesian statistics and has applications to game theory.
During World War II, Savage served as chief "statistical" assistant to John von Neumann, the mathematician credited with building the first electronic computer.
One of Savage's indirect contributions was his discovery of the work of Louis Bachelier on stochastic models for asset prices and the mathematical theory of option pricing. Savage brought the work of Bachelier to the attention of Paul Samuelson. It was from Samuelson's subsequent writing that "random walk" (and subsequently Brownian motion) became fundamental to mathematical finance.
In 1951 he introduced the minimax regret criterion used in decision theory.
The Hewitt–Savag *Wik

1924 Benoit Mandelbrot (20 Nov 1924 in Warsaw, Poland - 14 Oct 2010 in Cambridge, Massachusetts, USA) was largely responsible for the present interest in Fractal Geometry. He showed how Fractals can occur in many different places in both Mathematics and elsewhere in Nature.*SAU

1955 Ray Ozzie, who designed the Lotus Notes office management software for Lotus Development Corporation, is born in Chicago, IL. Ozzie graduated from the University of Illinois at Urbana-Champaign (UIUC) in 1979. During this time Ray worked at the Computer-based Education Research Lab (CERL) on the PLATO operating system. He was impressed with PLATO’s real-time communications and has often publicly credited his CERL experience as the inspiration for Lotus Notes. In 1984 Mitch Kapor, founder of Lotus Development Corporation, supported the idea to develop a PLATO-like product for PC by funding Iris Associates, Inc. In August 1986 Lotus Notes was complete becoming the first example of groupware and a commercial success. In 1997 Ozzie left Iris Associates to start a new venture, Rythmix Corp.*CHM

1963 Sir William Timothy Gowers, FRS (20 November 1963, ) is a British mathematician. He is a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, where he also holds the Rouse Ball chair, and is a Fellow of Trinity College, Cambridge. In 1998 he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.*Wik

DEATHS

1713 Thomas Tompion (baptised 25 Jul 1639, 20 Nov 1713) Most famous English clockmaker of his time, especially known for watchmaking improvements. He worked closely with experimental physicist Robert Hooke, and in 1675, following Hooke's design, Tompion made one of the first English watches regulated by a balance spring. In 1695, with Edward Barlow and William Houghton, he patented the cylinder escapement (a controlling device) that allowed use of a horizontal wheel, enabling Tompion to make the first of the flat and more compact watches.*TIS

1764 Christian Goldbach (18 Mar 1690, 20 Nov 1764)Russian mathematician whose contributions to number theory include Goldbach's conjecture, formulated in a letter to Leonhard Euler dated 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 1014 - but still remains unproved. Goldbach made another conjecture that every odd number is the sum of three primes, on which Vinogradov made progress in 1937. (It has been checked by computer for vast numbers, but remains unproved.) Goldbach also studied infinite sums, the theory of curves and the theory of equations. *TIS

1856 Farkas Bolyai (9 Feb 1775, 20 Nov 1856) Hungarian mathematician, poet, and dramatist who spent a lifetime trying to prove Euclid's (fifth) postulate that parallel lines do not meet. While studying at the University of Göttingen, he met as a fellow student, the noted German mathematician Carl F. Gauss, with whom he corresponded as a life-long friend. Bolyai taught mathematics, physics and chemistry at Marosvásárhely all his life. He discouraged his son, János Bolyai, from studying the parallel axiom as he had, writing in a letter to him: "For God's sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life." *TIS

1882 Henry Draper (7 Mar 1837, 20 Nov 1882) American physician and amateur astronomer who made the first photograph of the spectrum of a star (Vega), in 1872. He was also the first to photograph a nebula, the Orion Nebula, in 1880. For his photography of the transit of Venus in 1874, Congress ordered a gold medal struck in his honour. His father, John William Draper, in 1840 had made the first photograph of the Moon.*TIS

1934 Willem de Sitter (6 May 1872, 20 Nov 1934) Dutch mathematician, astronomer, and cosmologist who developed theoretical models of the universe based on Albert Einstein's general theory of relativity. He worked extensively on the motions of the satellites of Jupiter, determining their masses and orbits from decades of observations. He redetermined the fundamental constants of astronomy and determined the variation of the rotation of the earth. He also performed statistical studies of the distribution and motions of stars, but today he is best known for his contributions to cosmology. His 1917 solution to Albert Einstein's field equations showed that a near-empty universe would expand. Later, he and Einstein found an expanding universe solution without space curvature.*TIS

1960 Hidehiko Yamabe (山辺 英彦 Yamabe Hidehiko?, August 22, 1923 in Ashiya, Hyōgo, Japan – November 20, 1960 in Evanston, Illinois) was a Japanese mathematician. His most notable work includes the final solution of Hilbert's fifth problem.
After graduating from the University of Tokyo in 1947, Yamabe became an assistant at Osaka University. From 1952 until 1954 he was an assistant at Princeton University, receiving his Ph.D. from Osaka University while at Princeton. He left Princeton in 1954 to become assistant professor at the University of Minnesota. Except for one year as a professor at Osaka University, he stayed in Minnesota until 1960. Yamabe died suddenly of a stroke in November 1960, just months after accepting a full professorship at Northwestern University. *Wik

1986 Arne Carl-August Beurling (February 3, 1905 – November 20, 1986) was a Swedish mathematician and professor of mathematics at Uppsala University (1937–1954) and later at the Institute for Advanced Study in Princeton, New Jersey.
Beurling worked extensively in harmonic analysis, complex analysis and potential theory. The "Beurling factorization" helped mathematical scientists to understand the Wold decomposition, and inspired further work on the invariant subspaces of linear operators and operator algebras.
In the summer of 1940 he single-handedly deciphered and reverse-engineered an early version of the Siemens and Halske T52 also known as the Geheimfernschreiber (secret teletypewriter) used by Nazi Germany in World War II for sending ciphered messages.[1] The T52 was one of the so-called "Fish cyphers", that using, transposition, created nearly one quintillion (893 622 318 929 520 960) different variations. It took Beurling two weeks to solve the problem using pen and paper. Using Beurling's work, a device was created that enabled Sweden to decipher German teleprinter traffic passing through Sweden from Norway on a cable. In this way, Swedish authorities knew about Operation Barbarossa before it occurred. Not wanting to reveal how this knowledge was attained the Swedish warning was not treated as credible by Soviets. *Wik

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*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