Tuesday, 21 November 2017

On This Day in Math - November 21

The shortest math joke ever: let $\epsilon < 0 $

found on Mathematical humor collected by Andrej and Elena Cherkaev

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.


1675 Leibniz completes the product rule. In a manuscript only days earlier Leibniz had struggled with the product and quotient rules for differentiation. At first he thought d(uv)= du dv. *F Cajori, History of Mathematics, (pg 208)

1751 “The weather was exceedingly tempestuous, and the sky was overcast with clouds..” so begins An Account of the Eclipse of the Moon, Which Happened Nov. 21, 1751; Observed by Mr. James Short, F. R. S. in Surry-Street *Philosophical Transactions 1751-1752 XLIX

1783 The first manned free balloon flight, often credited to the brothers Montgolfier was actually the work of J. A. C. Charles, for whom Charles Law is named. This was a hydrogen filled balloon, and not the hot air type promoted by the Montgolfiers. It carried chemist Jean Pilatre de Rozier and the Marquis d’Arlandes on a flight that wafted across Paris for 25 minutes, reached a height of 500 feet and traveled five and a half miles. The Montgolfier brothers had unmanned launches on June 5 and September 19, 1783. Among the onlookers was Benjamin Franklin, American emissary to the court of Louis XVI. When asked of what use is ballooning, Franklin replied with emphatic simplicity, “Of what use is a newborn baby?” [Air & Space, vol. 1, p. 72 and Williams, p. 43]  Charles and the hydrogen promoters were rivals of the Montgolfiers until Charles' partner,  King Louis XVI had offered to send two prisoners on the flight, but Rozier, a professor of physics and chemistry, wanted to deny criminals the glory of being the first men to go into the atmosphere.  *TIS  Pilatre would become the first aviation casualty the following year when he tried to mix the hot air and hydrogen techniques together to cross the English Channel.

1811 Gauss to Bessel: “One should never forget that the functions, like all mathematical constructions, are only our own constructions.” *VFR

1877 Thomas Edison announced the invention of what he called “The Talking Machine”—the phonograph. *VFR  He appears to have envisioned it as a business dictation machine. In Sep 1877, he wrote that its purpose was "to record automatically the speech of a very rapid speaker upon paper; from which he reproduces the same Speech immediately or years afterwards preserving the characteristics of the speakers voice so that persons familiar with it would at once recognize it." The indented tin foil, however, would survive only a few playings. By the first public showing of a phonograph, which took place in New York City in early Feb 1878, its practical applications had not yet been realized.*TIS

 1963 Denmark and Greenland issued almost identical stamps to commemorate the 50th anniversary of the atomic theory of Niels Bohr (1885–1962)*VFR

1969 First ARPANET Link Put Into Service ARPANAT was an early computer network developed by J.C.R. Licklider, Robert Taylor, and other researchers for the U.S. Department of Defense’s Advanced Research Projects Agency​ (ARPA). It connected a computer at UCLA with a computer at the Stanford Research Institute​, Menlo Park, CA. In 1973, the government commissioned Vinton Cerf​ and Robert E. Kahn to create a national computer network for military, governmental, and institutional use. The network used packet-switching, flow-control, and fault-tolerance techniques developed by ARPANET. Historians consider this worldwide network to be the origin of the Internet. *CHM

1973 Mexico issued a stamp portraying an Aztec calendar stone and another with the mathematician and astronomer Carlos de Siguenza y Gongora (1645–1700). *VFR

1983 A special purpose computer built by Lee Sallows generated the following self-documenting pangram (it contains each letter of the alphabet and what it asserts about itself is true): This pangram contains four a’s, one b, two c’s, one d, thirty e’s, six f’s, five g’s, seven h’s, eleven i’s, one j, one k, two l’s, two m’s, eighteen n’s, fifteen o’s, two p’s, one q, five r’s, twenty-seven s’s, eighteen t’s, two u’s, seven v’s, eight w’s, two x’s, three y’s and one z. See Scientific American, October 1984, p. 26. *VFR


1694  (François Marie Arouet) Voltaire (21 Nov 1694; 30 May 1778) was a French author who popularized Isaac Newton's work in France by arranging a translation of Principia Mathematica to which he added his own commentary (1737). The work of the translation was done by the marquise de Châtelet who was one of his mistresses, but Voltaire's commentary bridged the gap between non-scientists and Newton's ideas at a time in France when the pre-Newtonian views of Descartes were still prevalent. Although a philosopher, Voltaire advocated rational analysis. He died on the eve of the French Revolution. *TIS

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


1652 Jan Brożek (Ioannes Broscius, Joannes Broscius or Johannes Broscius;) (1 November 1585 – 21 November 1652) was a Polish polymath: a mathematician, astronomer, physician, poet, writer, musician and rector of the Kraków Academy.
Brożek was born in Kurzelów, Sandomierz Province, and lived in Kraków, Staszów, and Międzyrzec Podlaski. He studied at the Kraków Academy (now Jagiellonian University) and at the University of Padua. He served as rector of Jagiellonian University.
He was the most prominent Polish mathematician of the 17th century, working on the theory of numbers (particularly perfect numbers) and geometry. He also studied medicine, theology and geodesy. Among the problems he addressed was why bees create hexagonal honeycombs; he demonstrated that this is the most efficient way of using wax and storing honey.
He contributed to a greater knowledge of Nicolaus Copernicus' theories and was his ardent supporter and early prospective biographer. Around 1612 he visited the chapter at Warmia and with the knowledge of Prince-Bishop Simon Rudnicki took from there a number of letters and documents in order to publish them, which he never did. He contributed to a better version of a short biography of Copernicus by Simon Starowolski. "Following his death, his entire collection was lost"; thus "Copernicus' unpublished work probably suffered the greatest damage at the hands of Johannes Broscius."
Brożek died at Bronowice, now a district of Kraków. One of the Jagiellonian University's buildings, the Collegium Broscianum, is named for him. *Wik

1782 Jacques de Vaucanson (24 Feb 1709, 21 Nov 1782) French inventor of automata - robot devices of later significance for modern industry. In 1737-38, he produced  a transverse flute player, a pipe and tabor player, and a mechanical duck, which was especially noteworthy, not only imitating the motions of a live duck, but also the motions of drinking, eating, and "digesting." He made improvements in the mechanization of silk weaving, but his most important invention was ignored for several decades - that of automating the loom by means of perforated cards that guided hooks connected to the warp yarns (later reconstructed and improved by J.-M. Jacquard, it became one of the most important inventions of the Industrial Revolution.) He also invented many machine tools of permanent importance.*TIS

1866 Gustav Roch (9 Dec 1839 in Dresden, Germany, 21 Nov 1866 in Venice, Italy) was a German mathematician known for the Riemann-Roch theorem which relates the genus of a topological surface to algebraic properties of the surface. As presented by Roch, the Riemann-Roch theorem related the topological genus of a Riemann surface to purely algebraic properties of the surface. The Riemann-Roch theorem was so named by Max Noether and Alexander von Brill in a paper they jointly wrote 1874 when they refined the information obtained from the theorem. It was extended to algebraic curves in 1929 and then in the 1950s an n-dimensional version, the Hirzebruch-Riemann-Roch theorem, was proved by Hirzebruch and a version for a morphism between two varieties, the Grothendieck-Riemann-Roch theorem, was proved by Grothendieck.
Over the three academic years 1863-64, 1864-65 and 1865-66 Roch gave a number of courses at Halle. These included: Differential and Integral Calculus; Analytic Geometry; and Elliptic and Abelian Functions. Up to this time Roch was still a privatdozent at Halle but in the spring of 1866 the University began to take up referees' reports with a view to appointing him as an extraordinary professor. Heine wrote a strong letter of support and Roch was appointed extraordinary professor at the University of Halle-Wittenberg on 21 August.
However Roch's health was failing and on 13 October he was granted leave for the winter semester of 1866-67 to allow him to regain his health. Roch went to Venice where he hoped the warmer weather would aid his recovery. Sadly, however, it was not to be and he died of consumption in Venice in November at the age of 26 years. Roch's name will live on through the fundamental Riemann-Roch theorem, but it is a tragedy that the young man with so much mathematical promise died when he had only just commenced his career. *SAU

1970 Sir Chandrasekhara Venkata Raman (7 Nov 1888, 21 Nov 1970)Indian physicist whose work was influential in the growth of science in India. He was the recipient of the 1930 Nobel Prize for Physics for the 1928 discovery now called Raman scattering: a change in frequency observed when light is scattered in a transparent material. When monochromatic or laser light is passed through a transparent gas, liquid, or solid and is observed with the spectroscope, the normal spectral line has associated with it lines of longer and of shorter wavelength, called the Raman spectrum. Such lines, caused by photons losing or gaining energy in elastic collisions with the molecules of the substance, vary with the substance. Thus the Raman effect is applied in spectrographic chemical analysis and in the determination of molecular structure. *TIS

1978 Francesco Giacomo Tricomi studied differential equations which became very important in the theory of supersonic flight. *SAU 

1980 László Rédei (Rákoskeresztúr, 15 November, 1900—Budapest, 21 November, 1980) was a Hungarian mathematician.
His mathematical work was in algebraic number theory and abstract algebra, especially group theory. He proved that every finite tournament contains an odd number of Hamiltonian paths. He gave several proofs of the theorem on quadratic reciprocity. He proved important results concerning the invariants of the class groups of quadratic number fields. In several cases, he determined if the ring of integers of the real quadratic field Q(√d) is Euclidean or not. He successfully generalized Hajós's theorem. This led him to the investigations of lacunary polynomials over finite fields, which he eventually published in a book. He introduced a very general notion of skew product of groups, both the Schreier-extension and the Zappa-Szép product are special case of. He explicitly determined those finite noncommutative groups whose all proper subgroups were commutative (1947). This is one of the very early results which eventually led to the classification of all finite simple groups.*Wik

1991 Hans Zassenhaus (28 May 1912 in Koblenz-Moselweiss, Germany - 21 Nov 1991 in Columbus, Ohio, USA) did important work on Group Theory and Lie algebras. His work on computational algebraic number theory seems to have started when he visited Caltec in 1959 and collaborated with Taussky-Todd. He put forward a programme to develop methods for computational number theory which, given an algebraic number field, involved calculating its Galois group, an integral basis, the unit group and the class group. He contributed himself in a major way to all four of these tasks.
Zassenhaus worked on a broad range of topics and, in addition to those mentioned above, he worked on nearfields, the theory of orders, representation theory, the geometry of numbers and the history of mathematics. He loved teaching and wrote several articles on the topic such as On the teaching of algebra at the pre-college level. *SA

1993 Bruno Rossi (13 Apr 1905, 21 Nov 1993)Italian pioneer in the study of cosmic radiation. In the 1930s, his experimental investigations of cosmic rays and their interactions with matter laid the foundation for high energy particle physics. Cosmic rays are atomic particles that enter earth's atmosphere from outer space at speeds approaching that of light, bombarding atmospheric atoms to produce mesons as well as secondary particles possessing some of the original energy. He was one of the first to use rockets to study cosmic rays above the Earth's atmosphere. Finding X-rays from space he became the grandfather of high energy astrophysics, being largely responsible for starting X-ray astronomy, as well as the study of interplanetary plasma.  *TIS

1996 Abdus Salam (29 Jan 1926, 21 Nov 1996) Pakistani nuclear physicist who shared the 1979 Nobel Prize for Physics with Steven Weinberg and Sheldon Lee Glashow. Each had independently formulated a theory explaining the underlying unity of the weak nuclear force and the electromagnetic force. His hypothetical equations, which demonstrated an underlying relationship between the electromagnetic force and the weak nuclear force, postulated that the weak force must be transmitted by hitherto-undiscovered particles known as weak vector  bosons, or W and Z bosons. Weinberg and Glashow reached a similar conclusion using a  different line of reasoning. The existence of the W and Z bosons was eventually verified in 1983  by researchers using particle accelerators at CERN. *TIS

*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

Monday, 20 November 2017

On This Day in Math - November 20

The history of astronomy is a history of receding horizons.

— Edwin Powell Hubble

The 324th day of the year; 324 is the largest possible product of positive integers with a sum of 16. (Students, Can you find the integers. Try to find the similar maximum product with a sum of 17)).
324 is also the sum of four consecutive primes, 324 = 73 + 79 + 83 + 89

If you have a square array of 324 dots (that's 18x18) you can carefully paint them each in one of four colors so that no four corners of a rectangle (with sides horizontal and vertical) are the same color. you can also do that for any smaller square, but not for any larger. Here is a 17x17 to ponder


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


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


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

*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

Sunday, 19 November 2017

On This Day in Math - November 19

A visitor to Niels Bohr's country cottage, noticing a horseshoe hanging on the wall, teasing the eminent scientist about this ancient superstition. 'Can it be true that you, of all people, believe it will bring you luck?'
'Of course not,' replied Bohr, 'but I understand it brings you luck whether you believe it or not.'

The 323rd day of the year; If you put drew every possible path from (0,0) to (8,0) that never dropped below the x-axis using only unit vectorial moves with slopes of 1, 0, or -1 there are 323 possible paths. (alternatively this is the number of different ways of drawing non-intersecting chords on a circle with eight points- this is deceptive because it counts each way of drawing a single chord, and drawing no chords at all, students might want to count how many ways this can be done using four chords.) These are called Motzkin numbers, after Theodore Motzkin.

3232 is the sum of nine consecutive primes 323 = 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 *Derek Orr

323 is a palindrome and also the smallest composite number n that divides the (n+1)st Fibonacci number. *What's Special about this Number

When eight labled points are selected around a circle, there are 323 ways of drawing any number of nonintersecting chords joining them, such numbers are called Motzkin numbers


1857 Arhtur Cayley opens a letter to J. J. Sylvester with, "I have just obtained a theorem that appears to be very remarkable." The theorem would be the centerpiece of his Memoire on the Theory of Matrices. The theorem showed that a matrix was the solution of its own characteristic equation. *A. J. Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age

1982 Science has an article describing Friedman’s version of Kruskal’s theorem. The important thing is that this is a mathematical (rather than metamathematical) statement independent of arithmetic. *VFR

2010 Experts confirmed that the remains of the 16th-century Danish astronomer Tycho Brahe, his wife and another eight people, including five children, were buried in Prague's Church of Our Lady before Tyn. The tin coffin, tied up with a red ribbon, was deposited in the tomb in the overcrowded church that afternoon preceded by a church service celebrated by Prague Archbishop Dominik Duka and including prayers in Czech and Danish. *Wik The grave had been previously opened 1901, on the three hundredth anniversary of his death, the bodies of Tycho Brahe and his wife Kirstine were exhumed in Prague. They had been embalmed and were in remarkably good condition, but the astronomer’s artificial nose was missing, apparently filched by someone after his death. It had been made for him in gold and silver when his original nose was sliced off in a duel he fought in his youth at Rostock University after a quarrel over some obscure mathematical point.


1894 Heinz Hopf (19 Nov 1894 in Gräbschen (near Breslau), Germany (now Wrocław, Poland) - 3 June 1971 in Zollikon, Switzerland) work was in algebraic topology. He studied vector fields and extended Lefschetz's fixed point formula. He also studied homotopy classes and defined what is now known as the 'Hopf invariant'.*SAU

1900 Mikhail Lavrentev (19 Nov 1900 in Kazan, Russia
- 15 Oct 1980 in Moscow, Russia) remembered for an outstanding book on conformal mappings and he made many important contributions to that topic.*SAU

1901 Nina Karlovna Bari (November 19, 1901, Moscow – July 15, 1961, Moscow) was a Soviet mathematician known for her work on trigonometric series. She was killed by a train in the Moscow Metro, and her colleagues speculated that she committed suicide, prompted by the death of her mentor Nikolai Luzin ten years earlier, a man who may have been her lover.*Wik

1907 Adrien Albert (19 November 1907, Sydney - 29 December 1989, Canberra) was a leading authority in the development of medicinal chemistry in Australia. Albert also authored many important books on chemistry, including one on selective toxicity.
He was awarded BSc with first class honours and the University Medal in 1932 at the University of Sydney. He gained a PhD in 1937 and a DSc in 1947 from the University of London. His appointments included Lecturer at the University of Sydney (1938-1947), advisor to the Medical Directorate of the Australian Army (1942-1947), research at the Wellcome Research Institute in London (1947-1948) and in 1948 the Foundation Chair of Medical Chemistry in the John Curtin School of Medical Research at the Australian National University in Canberra where he established the Department of Medical Chemistry. He was a Fellow of the Australian Academy of Science.
He was the author of Selective Toxicity: The Physico-Chemical Basis of Therapy, first published by Chapman and Hall in 1951.
The Adrien Albert Laboratory of Medicinal Chemistry at the University of Sydney was established in his honour in 1989.[1] His bequest funds the Adrien Albert Lectureship, awarded every two years by the Royal Society of Chemistry *Wik

1918 Hendrik Christoffel van de Hulst (19 Nov 1918; 31 Jul 2000) Dutch astronomer who predicted theoretically (1944) that in interstellar space the amount of neutral atomic hydrogen, which in its hyperfine transition radiates and absorbs at a wavelength of 21 cm, might be expected to occur at such high column densities as to provide a spectral line sufficiently strong as to be measurable. Shortly after the end of the war several groups set about to test this prediction. The 21-cm line of atomic hydrogen was detected in 1951, first at Harvard University followed within a few weeks by others. The discovery demonstrated that astronomical research, which at that time was limited to conventional light, could be complemented with observations at radio wavelengths, revealing a range of new physical processes.*TIS


1672 John Wilkins FRS (1 January 1614 – 19 November 1672) was an English clergyman, natural philosopher and author, as well as a founder of the Invisible College and one of the founders of the Royal Society, and Bishop of Chester from 1668 until his death. Along with his inventions (almost all of which were destroyed in the Great Fire) and assorted writings on philosophy, mathematics, and cryptography, John Wilkins distinguished himself by planning the first lunar expedition.(in the 17th century??? Yes… learn more here)
He wrote for the common reader the Discovery (1638) and the Discourse (1640) which showed how reason and experience supported Copernicus, Kepler and Galileo rather than Aristotlian or literal biblical doctrines. In 1641, he anonymously published a small but comprehensive treatise on cryptography. In Mathematical Magick (1648) he described and illustrated the balance lever, wheel, pulley, wedge and screw in a part called "Archimedes or Mechanical Powers" and in a second part "Daedalus or Mechanical Motions" such strange devices as flying machines, artificial spiders, a land yacht, and a submarine. *WIS

1998 Tetsuya Theodore Fujita(23 Oct 1920, 19 Nov 1998) was a Japanese-American meteorologist who increased the knowledge of severe storms. In 1953, he began research in the U.S. Shortly afterwards, he immigrated and established the Severe Local Storms Project. He was known as "Mr. Tornado" as a result of the Fujita scale (F-scale, Feb 1971), which he and his wife, Sumiko, developed for measuring tornadoes on the basis of their damage. Following the crash of Eastern flight 66 on 24 Jun 1975, he reviewed weather-related aircraft disasters and verified the downburst and the microburst (small downburst) phenomena, enabling airplane pilots to be trained on how to react to them. Late in his career, he turned to the study of storm tracks and El Nino. *TIS

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

Saturday, 18 November 2017

On This Day in Math - November 18

Predictions can be very difficult—
especially about the future.
— Niels Bohr

The 322nd day of the year; 322 is the 12th Lucas Number. The Lucas Sequence is similar to the Fibonacci sequence with L(1) = 1 and L(2) = 3 and each term is the sum of the two previous terms. L(n) is also the integer nearest to \( \phi ^n \) This is the last day of the year that will be a Lucas Number.

322 is smallest number whose square has 6 diff digits (103684). *Derek Orr
322 is a sphenic number, which means that it is the area of  a rectangular box (parallelepiped) with prime lengths for its length, width, and height.


2349 B.C. Noah’s flood began according to the English mathematician, William Whiston (1667–1752) who felt it was caused by a comet which passed over the equator causing extensive rains. *Claire L. Parkinson, Breakthroughs, p. 131 Whiston would follow Newton as the Lucasian Professor at Cambridge.*RMAT

1690 First use of catenary According to E. H. Lockwood (1961) and the University of St. Andrews website, this term was first used (in Latin as catenaria) by Christiaan Huygens (1629-1695) in a letter to Leibniz dated November 18, 1690. *Earliest Known Uses of Some of the Words of Mathematics The English word catenary is usually attributed to Thomas Jefferson (but see below****), who wrote in a letter to Thomas Paine on the construction of an arch for a bridge"I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to be a very scientifical work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the catenary is in perfect equilibrium."  (Dec. 23, 1788) *Jeff Miller  (Paine had previously used the term "catenarian" in earlier letter to Jefferson. (Sept. 15, 1788).
****Miller's web site now includes a single previous use of Catenary in English in 1725 in Lexicon Technicum: Or, An Universal English Dictionary of ARTS and SCIENCES: Fourth Edition Volume I*****

1752 Goldbach writes Euler with conjecture that every odd number greater than 3 is the sum of an odd number and twice a square (he allowed 02). Euler would reply that it was true for the first 1000 odd numbers, and then later to confirm it for the first 2500. A hundred years later, German mathematician Moritz Stern found two contradictions, 5777 and 5993. The story appears in Alfred S. Posamentier's Magnificent Mistakes in Mathematics, (but gloriously, has a mistake for the date, using 1852, but such a wonderful book can forgive a print error.)

1812 Jean Victor Poncelet , a military engineer, was captured while Napoleon’s army was retreating from Moscow. He profited from this enforced leisure (until his release in June 1814) by resuming his study of mathematics. While there he did important work on projective geometry. *VFR

1825 Birbeck writes to Gilmer regarding the application for professor at U Va of Charles Bonnycastle, son of John Bonneycastle.  “The name of Bonnycastle must be well known in America, and if known, must be highly valued; and the son I am persuaded will extend the fame of the parent. 

1879  After the death of Maxwell, George Stokes writes to offer Lord Rayleigh the position of head of the Cavendish Laboratory in Cambridge.  *Memoir and scientific correspondence of the late Sir George Gabriel Stokes, pg 227

1883 At noon on this day the telegraphic time signals sent out daily from the Naval Observatory at Washington, D.C., were changed to standard time, a system adopted on the initiative of the American Railway Association. Standard time was suggested for the U.S. in 1869 by Charles Ferdinand Dowd, a schoolmaster from Saratoga, N.Y., but was not adopted then. He suggested dividing the continent into four time zones each one hour or fifteen degrees of longitude wide. Standard Railroad Time had four time zones, Eastern, Central, Western, and Pacific. Congress made these official in 1918. Some citizens grumbled about “railroad tyranny” and tampering with “God’s time.” See New York Times, 20 Nov. 1983. *VFR On April 1 of 1967, The Uniform Time Act divided the United States into eight time zones; Eastern, Central, Mountain, Pacific, Yukon, Alaska, Hawaii, and Bering.  *FFF, pg 149

1963 The first push-button telephone goes into service. @yovisto
The first electronic push-button system with Touch-Tone dialing was offered by Bell Telephone to customers in Carnegie and Greensburg, Pennsylvania.
Western Electric experimented as early as 1941 with methods of using mechanically activated reeds to produce two tones for each of the ten digits. But the technology proved unreliable and it was not until long after the invention of the transistor when the technology matured. On 18 November 1963 the Bell System in the United States officially introduced dual-tone multi-frequency (DTMF) technology under its registered Touch-Tone® mark. Over the next few decades Touch-Tone service replaced traditional pulse dialing technology and it eventually became a world-wide standard for telecommunication signaling.
The now standard layout of the keys on the Touch-Tone telephone was the result of research of the human-engineering department at Bell Laboratories in the 1950s under the leadership of South African-born psychologist John Elias Karlin (1918–2013), who was previously a leading proponent in the introduction of all-number-dialing in the Bell System. This research resulted in the design of the DTMF keypad that arranged the push-buttons into 12 positions in a 3-by-4 position rectangular array, and placed the 1, 2, and 3 keys in the top row for most accurate dialing.[18] The remaining digits occupied the lower rows in sequence from left to right, however, placing the 0 into the center of the fourth row, while omitting the lower left, and lower right positions. These two positions were later assigned to the asterisk and pound key when the keypad was expanded for twelve buttons in 1969. *Wik

1991 IBM and Siemens AG Announce 64M DRAM Chip Prototype : IBM and Siemens AG announce they have developed a prototype 64 megabyte DRAM chip. This development was in line with Moore’s Law which predicts a doubling of the number of transistors etched into silicon every 18 months. *CHM


1839 August (Adolph Eduard Eberhard) Kundt (18 Nov 1839; 21 May 1894)  was a German physicist who developed a method (1866) to determine the  velocity of sound in gases and solids. He used a closed glass tube into  which a dry powder (such as lycopodium) has been sprinkled. The source  of sound in the original device was a metal rod clamped at its centre  with a piston at one end, which is inserted into the tube. When the rod  is stroked, sound waves generated by the piston enter the tube. If the  position of the piston in the tube is adjusted so that the gas column is  a whole number of half wavelengths long, the dust will be disturbed by  the resulting stationary waves forming a series of striations, enabling  distances between nodes to be measured. *TIS 

1844 Albert Wangerin (November 18, 1844 – October 25, 1933) worked on potential theory, spherical functions and differential geometry.*SAU He wrote an important two volume treatise on potential theory and spherical functions. Theorie des Potentials und der Kugelfunktionen I was published in 1909 and Theorie des Potentials und der Kugelfunktionen II was published in 1921. Wangerin functions are named for him.
He was also known for writing of textbooks, encyclopaedias and his historical writings.*Wik

1872 Giovanni Enrico Eugenio Vacca (18 November 1872 – 6 January 1953) was an Italian mathematician, Sinologist and historian of science.
Vacca studied mathematics and graduated from the University of Genoa in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved to Turin and became an assistant to Giuseppe Peano. In 1899 he studied, at Hanover, unpublished manuscripts of Gottfried Wilhelm Leibniz, which he published in 1903. Around 1898 Vacca became interested in Chinese language and culture after attending a Chinese exhibition in Turin. He took private lessons of Chinese and continued to study it at the University of Florence. Vacca then traveled to China in 1907-8 and defended a PhD in Chinese studies in 1910. In 1911, he became a lecturer in Chinese literature at the University of Rome. In 1922, he moved to Florence and taught Chinese literature and language at university until 1947.
The interests of Vacca were almost equally split between mathematics, Sinology and history of science, with a corresponding number of papers being 38, 47 and 45. In 1910, Vacca developed a complex number iteration for pi. *Wik

1887 Gustav Theodor Fechner (19 Apr 1801, 18 Nov 1887) German physicist and philosopher who was a key figure in the founding of psychophysics, the science concerned with quantitative relations between sensations and the stimuli producing them. He formulated the rule known as Fechner’s law, that, within limits, the intensity of a sensation increases as the logarithm of the stimulus. He also proposed a mathematical expression of the theory concerning the difference between two stimuli, advanced by E. H. Weber. (These are now known to be only approximately true. However, as long as the stimulus is of moderate intensity, then the laws will give us a good estimate.) Under the name “Dr. Mises” he also wrote humorous satire. In philosophy he was an animist, maintaining that life is manifest in all objects of the universe. *TIS

1897 Patrick M.S. Blackett (18 Nov 1897; 13 Jul 1974) English scientist who won the Nobel Prize for Physics in 1948 for his discoveries in the field of cosmic radiation, which he accomplished primarily with cloud-chamber photographs that revealed the way in which a stable atomic nucleus can be disintegrated by bombarding it with alpha particles (helium nuclei). Although such nuclear disintegration had been observed previously, his data explained this phenomenon for the first time and were useful in explaining disintegration by other means. *TIS

1900 George Bogdanovich Kistiakowsky (November 18, 1900 – December 7, 1982) was a Ukrainian-American physical chemistry professor at Harvard who participated in the Manhattan Project and later served as President Dwight D. Eisenhower's Science Advisor.
Born in Kiev in the old Russian Empire, Kistiakowsky fled Russia during the Russian Civil War. He made his way to Germany, where he earned his PhD in physical chemistry under the supervision of Max Bodenstein at the University of Berlin. He emigrated to the United States in 1926, where he joined the faculty of Harvard University in 1930, and became a citizen in 1933.
During World War II, he was the head of the National Defense Research Committee (NDRC) section responsible for the development of explosives, and the technical director of the Explosives Research Laboratory (ERL), where he oversaw the development of new explosives, including RDX and HMX. He was involved in research into the hydrodynamic theory of explosions, and the development of shaped charges. In October 1943, he was brought into the Manhattan Project as a consultant. He was soon placed in charge of X Division, which was responsible for the development of the explosive lenses necessary for an implosion-type nuclear weapon. He watched an implosion weapon that was detonated in the Trinity test in July 1945. A few weeks later a Fat Man implosion weapon was dropped on Nagasaki.
From 1962 to 1965, he chaired the National Academy of Sciences's Committee on Science, Engineering, and Public Policy (COSEPUP), and was its vice president from 1965 to 1973.
In later years he was active in an antiwar organization, the Council for a Livable World. Kistiakowsky severed his connections with the government in protest against the US involvement in the war in Vietnam. In 1977, he assumed the chairmanship of the Council for Livable World, campaigning against nuclear proliferation. He died of cancer in Cambridge, Massachusetts, on December 17, 1982. His body was cremated, and his ashes were scattered near his summer home on Cape Cod, Massachusetts. His papers are in the Harvard University archives.*Wik

1901 George Horace Gallup (November 18, 1901 – July 26, 1984) was an American pioneer of survey sampling techniques and inventor of the Gallup poll, a successful statistical method of survey sampling for measuring public opinion.
Gallup was born in Jefferson, Iowa, the son of George Henry Gallup, a dairy farmer. His higher education took place at the University of Iowa. He served as a journalism professor at Drake and Northwestern for brief periods. In 1932 he moved to New York City to join the advertising agency of Young and Rubicam as director of research (later as vice president from 1937 to 1947). He was also professor of journalism at Columbia University, but he had to give up this position shortly after he formed his own polling company, the American Institute of Public Opinion (Gallup Poll), in 1935.
In 1936, his new organization achieved national recognition by correctly predicting, from the replies of only 50,000 respondents, that Franklin Roosevelt would defeat Alf Landon in the U.S. Presidential election. This was in direct contradiction to the widely respected Literary Digest magazine whose poll based on over two million returned questionnaires predicted that Landon would be the winner. Not only did Gallup get the election right, he correctly predicted the results of the Literary Digest poll as well using a random sample smaller than theirs but chosen to match it.
Twelve years later, his organization had its moment of greatest ignominy, when it predicted that Thomas Dewey would defeat Harry S. Truman in the 1948 election, by five to fifteen percentage points. Gallup believed the error was mostly due to ending his polling three weeks before Election Day.
Gallup died in 1984 of a heart attack at his summer home in Tschingel, a village in the Bernese Oberland of Switzerland. He was buried in Princeton Cemetery. *Wik

1912 Shigeo Sasaki 佐々木 (18 November 1912 Yamagata Prefecture, Japan – 14 August 1987 Tokyo) was a Japanese mathematician working on differential geometry who introduced Sasaki manifolds. *Wik

1916 Sir David Robert Bates, FRS(18 November 1916, Omagh, County Tyrone, Ireland – 5 January 1994) was an Irish mathematician and physicist.
During the Second World War he worked at the Admiralty Mining Establishment where he developed methods of protecting ships from magnetically activated mines.
His contributions to science include seminal works on atmospheric physics, molecular physics and the chemistry of interstellar clouds. He was knighted in 1978 for his services to science, was a Fellow of the Royal Society and vice-president of the Royal Irish Academy. In 1970 he won the Hughes Medal. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1974.
The Mathematics Building at Queens University Belfast, is named after him. *Wik

1923 Alan B. Shepard, Jr. (18 Nov 1923; 21 Jul 1998) Alan Bartlett Shepard, Jr. was America's first man in space and one of only 12 humans who walked on the Moon. Named as one of the nation's original seven Mercury astronauts in 1959, Shepard became the first American into space on 5 May 1961, riding a Redstone rocket on a 15-minute suborbital flight that took him and his Freedom 7 Mercury capsule 115 miles in altitude and 302 miles downrange from Cape Canaveral, FL. (His flight came three weeks after the launch of Soviet cosmonaut Yuri Gagarin, who on 12 Apr 1961, became the first human space traveler on a one-orbit flight lasting 108 minutes.) Although the flight of Freedom 7 was brief, it  was a major step for U.S. in a  race with the USSR. *TIS

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


1919 Adolf Hurwitz (26 March 1859 in Hildesheim, Lower Saxony, Germany
Died: 18 Nov 1919 in Zurich, Switzerland) Hurwitz studied the genus of the Riemann surface and worked on how class number relations could be derived from modular equations. Hurwitz did excellent work in algebraic number theory. For example he published a paper on a factorisation theory for integer quaternions in 1896 and applied it to the problem of representing an integer as the sum of four squares. A full proof of Hurwitz's ideas appears in a booklet published in the year of his death. This involves studying the ring of integer quaternions in which there are 24 units. He shows that one-sided ideals are principal and introduces prime and primary quaternions. *SAU

1928 Alexander Ziwet (February 8, 1853 -  No
vember 18, 1928) born in Breslau. He became professor at the University of Michigan, an editor of the Bulletin of the AMS, and a collector of mathematics text who enriched the Michigan library. *VFR His early education was obtained in a German gymnasium. He afterwards studies in the universities of Warsaw and Moscow, one year at each, and then entered the Polytechnic School at Karlsruhe, where he received the degree of Civil Engineer in 1880.
He came immediately to the United States and received employment on the United States Lake Survey. Two years later he was transferred to the United States Coast and Geodetic Survey, computing division, where he remained five years.
In 1888 he was appointed Instructor in Mathematics in the University of Michigan. From this position he was advanced to Acting Assistant Professor in 1890, to Assistant Professor in 1891, to Junior Professor in 1896, and to Professor of Mathematics in 1904.
He was a member of the Council of the American Mathematical Society and an editor of the "Bulletin" of the society. In 1893-1894 he published an "Elementary Treatise on Theoretical Mechanics" in three parts, of which a revised edition appeared in 1904. He also translated from the Russian of I. Somoff "Theoretische Mechanik" (two volumes, 1878, 1879).
*Burke A. Hinsdale and Isaac Newton Demmon, History of the University of Michigan (Ann Arbor: University of Michigan Press, 1906), pp. 320-321.

1933 Robert Forsyth Scott (28 July 1849 in Leith, near Edinburgh, Scotland - 18 Nov 1933 in Cambridge, England) studied at Cambridge and was elected to a fellowship. After a short time teaching he studied to be a barrister. He spent most of his career as Bursar and Master of St John's College Cambridge. He published a book on Determinants. *SAU

1949 Frank Baldwin Jewett (5 Sep 1879, 18 Nov 1949) Frank Baldwin Jewett was the U.S. electrical engineer who directed research as the first president of the Bell Telephone Laboratories, Inc., (1925-40). Jewett believed that the best science and technology result from bringing together and nurturing the best minds. Under his tenure Bell Labs laid the foundation for a new scientific discipline, radio astronomy, and transformed movies by synchronizing sound to pictures. Bell Labs was the first to transmit television over a long distance in the U.S. and designed the first electrical digital computer. Bell Labs won its first Nobel Prize in physics for fundamental work demonstrating the wave nature of matter.*TIS

1959 Aleksandr Yakovlevich Khinchin (July 19, 1894, Kondrovo, Kaluga Oblast, Russia - November 18, 1959, Moscow, Russia) was a Russian mathematician who contributed to many fields including number theory and probability. Khinchin made significant contributions to the metric theory of Diophantine approximations and established an important result for simple real continued fractions, discovering a property of such numbers that leads to what is now known as Khinchin's constant. He also published several important works on statistical physics, where he used the methods of probability theory, and on information theory, queuing theory and mathematical analysis.*Wik

*Niels Bohr Institute
1962 Niels Henrik David Bohr (7 Oct 1885, 18 Nov 1962) was a Danish physicist, born in Copenhagen, who was the first to apply the quantum theory, which restricts the energy of a system to certain discrete values, to the problem of atomic and molecular structure. For this work he received the Nobel Prize for Physics in 1922. He developed the so-called Bohr theory of the atom and liquid model of the nucleus. Bohr was of Jewish origin and when the Nazis occupied Denmark he escaped in 1943 to Sweden on a fishing boat. From there he was flown to England where he began to work on the project to make a nuclear fission bomb. After a few months he went with the British research team to Los Alamos in the USA where they continued work on the project. *TIS (Bohr was an excellent athlete in his youth, read more here.)
Niels and his mathematician brother Harald are buried in the same grave site at the Assistens cemetery in Copenhagen. I love the youthful picture of the two brothers shown at right.

1994 Nathan Jacob Fine (22 October 1916 in Philadelphia, USA - 18 Nov 1994 in Deerfield Beach, Florida, USA) He published on many different topics including number theory, logic, combinatorics, group theory, linear algebra, partitions and functional and classical analysis. He is perhaps best known for his book Basic hypergeometric series and applications published in the Mathematical Surveys and Monographs Series of the American Mathematical Society. The material which he presented in the Earle Raymond Hedrick Lectures twenty years earlier form the basis for the material in this text.*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