## Wednesday, 25 November 2015

### On This Day in Math - November 25

The capacity to blunder slightly is the real marvel of DNA.
Without this special attribute, we would still be anaerobic bacteria
and there would be no music.
— Lewis Thomas

The 329th day of the year; 329 is the sum of three consecutive primes. 329 is the number of forests (trees and disconnected trees) possible with ten vertices.
329 is also a happy number, since the iteration of the sums of the squares of its digits includes 1, $3^2 + 2^2 + 9^2 = 94, 9^2 + 4^2 = 97, 9^2 + 7^2 = 130, 1^2 +3^2+0^2 = 10, and 1^2 + 0^2 = 1$

EVENTS

1658 The prize committee for Pascal’s cycloid problems (see 1 October 1658) decided not to give the prize of sixty Spanish gold doubloons to anyone. [DSB 7, 583] *VFR
In 1658, four years after renouncing mathematics as a vainglorious pursuit, Pascal found himself one day suffering from a painful toothache, and in desperation began to think about the cycloid to take his mind off the pain. Quickly the pain abated, and Pascal interpreted this as a sign from the Almighty that he should proceed to study the cycloid, which he did intensively for the next eight days. During this period he rediscovered most of what had already been learned about the cycloid, and several results that were new. Pascal decided to propose a set of challenge problems, with the promise of a first and second prize to be awarded for the best solutions. Roberval was named as one of the judges. Only two sets of solutions were received, one from Antoine de Lalouvere and another from John Wallis, but Pascal and Roberval decided that neither of the entries merited a prize, so no prizes were awarded. Instead, Pascal published his own solutions, along with an essay on the "History of the Cycloid". *www.mathpages.com

1731 A letter from Euler to Goldbach on this day includes the first use by Euler of continued fractions. Prior to his use continued fractions had made only scattered appearences. In the same letter he introduced the letter e as the base for the natural logarithms, "(e denotat hic numerum, cujus logarithmus hyperbolicus est=1.)," which Google translates as "(e denotes here the number of out of which the hyperbolic logarithm is equal to 1.)"
According to Maor's book e: The story of a number,:
Euler had already used the letter e to represent the number 2.71828... in one of his earliest works, a manuscript entitled "Meditation upon Experiments made recently on the firing of Cannon," written in 1727 when he was only twenty years old (it was not published until 1862, eighty years after his death). In a letter written in 1731 the number e appeared again in connection with a certain differential equation; Euler defines it as "that number whose hyperbolic logarithm is=1." The earliest appearance in a published work was in Euler's Mechanica (1736), in which he laid the foundations of analytical mechanics.
(My thanks to Dave Richeson who provided resources and tied all this information together for me.)

1804 Gauss, in a letter to his close friend Farkas Bolyai, explains that he does not agree with Bolyai's claim that he had put Euclidean Geometry on Solid Ground, "Bolyai has communicated to Gauss his claim that he has put Euclidean geometry on solid ground."
You desire only my careful and unfettered judgment: it is that your explanation does not satisfy me. I will try to explain the issue (it belongs to the same set of reefs on which my attempts have run aground) with as much clarity as possible. To be sure, I still have hope that, before my time is up, these reefs will permit passage. For the time being I have so many other tasks at hand that I cannot think about this; believe me, it would really make me happy if you were to pull ahead of me and overcome all obstacles. I would then undertake with the greatest joy, with all that is in my power, to defend your accomplishment and bring it to the light of day.
*Stan Burris, Notes on Non-Euclidean Geometry

1901 Richardson's law; Owen Willans Richardson read a paper before the Cambridge Philosophical Society which first announced his work on thermionic emission (the release of electrons from hot metals) and in particular a law which mathematically described how the amount of electron current increased as the temperature of the hot surface was raised. (He had been working at the Cavendish Laboratory only one year since his graduation from Cambridge University.) As recorded in the published Proceedings, in Richardson's words: "If then the negative radiation is due to the corpuscles coming out of the metal, the saturation current s should obey the law s = AT1/2e-b/T." The discovery of Richardson's law earned him the 1928 Nobel Prize for Physics.*TIS

1906 First Audion tube. The first triode was ordered by Lee de Forest who instructed the New York automobile lamp maker, H. W. Candless, to make a glass bulb containing a "grid" wire between a filament and an electrode plate. These specifications extended the Fleming two-element diode valve design previously published in the Proceedings of the Royal Society. The third element - the grid wire - regulated the flow of electrons between the filament and the anode plate, producing an amplification of the variations in a signal voltage applied to the grid. De Forest named his invention the "Audion." Within a few years (1913-1917) he was able to profit from his patents that he sold to AT&T for a total of $390,000.*TIS 1907 First general meeting of the Warsaw Scientiﬁc Society. Among the 14 founders of the Society were the two mathematicians Samuel Dickstein (1851–1939) and WLladysLlaw Gosiewski (1844– 1911). [Kuratowski, A Half Century of Polish Mathematics, p. 17] *VFR 1915 Albert Einstein completed his general theory of relativity. [A. Hellemans and B. Bunch, The Timetables of Science, p 429].*VFR 1952 Portugal issued two stamps commemorating the centenary of the birth of the mathematician Francisco Gomes Teixeira (1851-1932). [Scott #751-2]. *VFR 1997 Pixar’s A Bug’s Life and Geri’s Game is released. Pixar Animation Studio released their second feature-length animated film, “A Bug’s Life,” on this day in 1997, preceding it with a computer animated short, “Geri’s Game.” A Bug’s Life, following on the success of Pixar’s Toy Story, was the story of a rag-tag group of bugs who band together to defeat a group of invading grasshoppers. The film would make more than$160 million in its initial US release. Geri’s Game would go on to win the Academy Award for Best Animated Short Film. *CHM

BIRTHS

1783 Claude-Louis Mathieu (25 Nov 1783; 5 Mar 1875) French astronomer and mathematician who worked particularly on the determination of the distances of the stars. He began his career as an engineer, but soon became a mathematician at the Bureau des Longitudes in 1817 and later professor of astronomy in Paris. For many years Claude Mathieu edited the work on population statistics L'Annuaire du Bureau des Longitudes produced by the Bureau des Longitudes. His work in astronomy focussed on determining the distances to stars. He published L'Histoire de l'astronomie au XVIII siècle in 1827. *TIS

1814 (Julius) Robert Mayer (25 Nov 1814; 20 Mar 1878) a German physicist. While a ship's doctor sailing to Java, he considered the physics of animal heat. In 1842, he measured the mechanical equivalent of heat. His experiment compared the work done by a horse powering a mechanism which stirred paper pulp in a caldron with the temperature rise in the pulp. He held that solar energy was the ultimate source of all energy on earth, both living and nonliving. Mayer had the idea of the conservation of energy before either Joule or Helmholtz. The prominence of these two scientists, however, diminished credit for Mayer's earlier insights. James Joule presented his own value for the mechanical equivalent of heat. Helmhotlz more systematically presented the law of conservation of energy. *TIS

1816 Lewis Morris Rutherfurd (25 Nov 1816; 30 May 1892) American spectroscopist, astrophysicist and photographer, born in Morrisania, NY, who made the first telescopes designed for celestial photography. He produced a classification scheme of stars based on their spectra as similarly developed by the Italian astronomer. Rutherfurd spent his life working in his own observatory, built in 1856, where he photographed (from 1858) the Moon, Jupiter, Saturn, the Sun, and stars down to the fifth magnitude. While using photography to map star clusters, he devised a new micrometer to measure distances between stars with improved accuracy. When Rutherford began (1862) spectroscopic studies, he devised highly sophisticated diffraction gratings.*TIS

1841 Friedrich Wilhelm Karl Ernst Schröder (25 Nov 1841 in Mannheim, Germany - 16 June 1902 in Karlsruhe, Germany) His important work is in the area of algebra, set theory and logic. His work on ordered sets and ordinal numbers is fundamental to the subject. *SAU

1913 Lewis Thomas (25 Nov 1913; 3 Dec 1993) American physician, researcher, author, and teacher best known for his reflective essays on a wide range of topics in biology. While his specialities are immunology and pathology, in his book, Lives of a Cell, his down-to-earth science writing stresses that what is seen under the microscope is similar to the way human beings live, and he emphasizes the interconnectedness of life. As a research scientist, Thomas made an impact by suggesting that an immunosurveillance mechanism protects us from the possible ravages of mutant cells, an idea later championed by Macfarlane Burnett. He also proposed that viruses have played a major role in the evolution of species by their ability to move pieces of DNA from one individual or species to another. *TIS

1987 Evelyn Merle Nelson (November 25, 1943 – August 1, 1987), born Evelyn Merle Roden, was a Canadian mathematician. Nelson made contributions to the area of universal algebra with applications to theoretical computer science. Nelson's teaching record was, according to one colleague, "invariably of the highest order". However, before earning a faculty position at McMaster, prejudice against her lead to doubts about her teaching ability. Nelson published over 40 papers during her 20-year career before she died from cancer in 1987.
She, along with Cecilia Krieger, is the namesake of the Krieger–Nelson Prize, awarded by the Canadian Mathematical Society for outstanding research by a female mathematician. *Wik

DEATHS

1694 Ismael Boulliau (28 Sept 1605 , 25 Nov 1694) was a French clergyman and amateur mathematician who proposed an inverse square law for gravitation before Newton. Boulliau was a friend of Pascal, Mersenne and Gassendi and supported Galileo and Copernicus. He claimed that if a planetary moving force existed then it should vary inversely as the square of the distance (Kepler had claimed the first power), "As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances that is, 1/d2. *SAU

1913 Sir Robert Stawell Ball​ (1 July 1840 – 25 November 1913) was an Irish astronomer. He worked for Lord Rosse from 1865 to 1867. In 1867 he became Professor of Applied Mathematics at the Royal College of Science in Dublin. In 1874 Ball was appointed Royal Astronomer of Ireland and Andrews Professor of Astronomy in the University of Dublin at Dunsink Observatory. In 1892 he was appointed Lowndean Professor of Astronomy and Geometry at Cambridge University at the same time becoming director of the Cambridge Observatory.[(not exactly at the same time)In 1892 John Couch Adams, the Lowndean Professor of Astronomy and Geometry at Cambridge and the director of the Cambridge Observatory, died. Ball applied ... and was appointed as Lowndean Professor of Astronomy and Geometry but disputes with the university meant that he had to wait a year before he was appointed director of the Cambridge Observatory.*SAU] His lectures, articles and books (e.g. Starland and The Story of the Heavens) were mostly popular and simple in style. However, he also published books on mathematical astronomy such as A Treatise on Spherical Astronomy. His main interest was mathematics and he devoted much of his spare time to his "Screw theory". He served for a time as President of the Quaternion Society. His work The Story of the Heavens is mentioned in the "Ithaca" chapter of James Joyce's Ulysses. *Wik

1936 Édouard (-Jean-Baptiste) Goursat (21 May 1858, 25 Nov 1936) French mathematician and theorist whose contribution to the theory of functions, pseudo- and hyperelliptic integrals, and differential equations influenced the French school of mathematics. The Cauchy-Goursat theorem states the integral of a function round a simple closed contour is zero if the function is analytic inside the contour. Cauchy had established the theorem with the added condition that the derivative of the function was continuous. In 1891, he wrote Leçons sur l'intégration des équations aux dérivées partielles du premier ordre. Goursat's best known work is Cours d'analyse mathématique (1900-10) which introduced many new analysis concepts. *TIS
It is almost certain that l'Hôpital's rule, for finding the limit of a rational function whose numerator and denominator tend to zero at a point, is so named because Goursat named the rule after de l'Hôpital in his Cours d'analyse mathématique . Certainly the rule appears in earlier texts (for example it appears in the work of Euler), but Goursat is the first to attach de l'Hôpital's name to it.*SAU

1937 Alessandro Padoa​ (14 October 1868 – 25 November 1937) was an Italian mathematician and logician, a contributor to the school of Giuseppe Peano. He is remembered for a method for deciding whether, given some formal theory, a new primitive notion is truly independent of the other primitive notions. There is an analogous problem in axiomatic theories, namely deciding whether a given axiom is independent of the other axioms.*Wik

1952 Edward Vermilye Huntington (April 26 1874, Clinton, New York, USA -- November 25, 1952, Cambridge, Massachusetts, USA) was an American mathematician.
Huntington's primary research interest was the foundations of mathematics. He was one of the "American postulate theorists" (the term is Scanlan's), American mathematicians active early in the 20th century (including E. H. Moore and Oswald Veblen) who proposed axiom sets for a variety of mathematical systems. In so doing, they helped found what are now known as metamathematics and model theory.
Huntington was perhaps the most prolific of the American postulate theorists, devising sets of axioms (which he called "postulates") for groups, abelian groups, geometry, the real number field, and complex numbers. His 1902 axiomatization of the real numbers has been characterized as "one of the first successes of abstract mathematics" and as having "filled the last gap in the foundations of Euclidean geometry". Huntington excelled at proving axioms independent of each other by finding a sequence of models, each one satisfying all but one of the axioms in a given set. His 1917 book The Continuum and Other Types of Serial Order was in its day "...a widely read introduction to Cantorian set theory." (Scanlan 1999) Yet Huntington and the other American postulate theorists played no role in the rise of axiomatic set theory then taking place in continental Europe.
In 1904, Huntington put Boolean algebra on a sound axiomatic foundation. He revisited Boolean axiomatics in 1933, proving that Boolean algebra required but a single binary operation (denoted below by infix '+') that commutes and associates, and a single unary operation, complementation, denoted by a postfix prime. The only further axiom Boolean algebra requires is: (a '+b ')'+(a '+b)' = a, now known as Huntington's axiom.
Revising a method from Joseph Adna Hill, Huntington is credited with the Method of Equal Proportions or Huntington-Hill method of apportionment of seats in the U.S. House of Representatives to the states, as a function of their populations determined in the U.S. census. This mathematical algorithm has been used in the U.S. since 1941 and is currently the method used.
In 1919, Huntington was the first President of the Mathematical Association of America, which he helped found. He was elected to the American Academy of Arts and Sciences in 1913, and to the American Philosophical Society in 1933.*Wik

1978 Eduard L. Stiefel (21 April 1909, Zürich – 25 November 1978, Zürich) was a Swiss mathematician. Together with Cornelius Lanczos and Magnus Hestenes, he invented the conjugate gradient method, and gave what is now understood to be a partial construction of the Stiefel–Whitney classes of a real vector bundle, thus co-founding the study of characteristic classes.
Stiefel achieved his full professorship at ETH Zurich in 1948, the same year he founded the Institute for Applied Mathematics. The objective of the new institute was to design and construct an electronic computer (the Elektronische Rechenmaschine der ETH, or ERMETH). *Wik

1988 Dmitrii Evgenevich Menshov (18 April 1892 in Moscow, Russia - 25 Nov 1988)
For his work on the representation of functions by trigonometric series, Menshov was awarded a State Prize in 1951. He was then elected a Corresponding Member of the USSR Academy of Sciences in 1953. In 1958 Menshov attended the International Congress of Mathematicians in Edinburgh and he was invited to address the Congress with his paper On the convergence of trigonometric series. *SAU

2008 Beno Eckmann (March 31, 1917, Bern – November 25, 2008, Zurich) was a Swiss mathematician who was a student of Heinz Hopf.
Born in Bern, Eckmann received his master's degree from Eidgenössische Technische Hochschule Zürich (ETH) in 1931. Later he studied there under Heinz Hopf, obtaining his Ph.D. in 1941. Eckmann was the 2008 recipient of the Albert Einstein Medal.
Calabi–Eckmann manifolds, Eckmann–Hilton duality, the Eckmann–Hilton argument, and the Eckmann–Shapiro lemma are named after Eckmann.*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