Saturday, 2 February 2013

On This Day in Math - February 2

Smooth shapes are very rare in the wild
but extremely important in the ivory tower and the factory.
~Benoit Mandelbrot

The 33rd day of the year; among the infinity of integers, there are only six that can not be formed by the addition of distinct triangular numbers. The largest of these is 33. What are the other five?

1673 From Hooke's Diary: Sir Jonas More & Cox here: compleated arithmeticall engin in ye contrivance for a product of 20 places. He would present the "engin" to the Royal Society three days later.*‏@HookesLondon
1823 Gauss completes the “Gauss-Markov Theorem.” *VFR
In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator of the coefficients is given by the ordinary least squares (OLS) estimator. *Wik

1851 “You are invited to come to see the Earth turn, tomorrow from three to five, at Meridian Hall of the Paris Observatory.” Foucault sent these handwritten invitations to all the known scientists in Paris. *Amir D Aczel, Pendulum, pg 93

In 1962, eight of the nine planets lined up for the first time in 400 years.*TIS On May 12,2011 six planets (Mercury, Venus, Jupiter, Mars, Uranus and Neptune, were essentially in a line. All the planets will not be aligned (at least as closely as they can get) until sometime in the 29th century.

1522 Lodovico Ferrari (2 Feb 1522 in Bologna, Italy - 5 Oct 1565) Italian mathematician who was the first to find an algebraic solution to the biquadratic, or quartic, equation (an algebraic equation that contains the fourth power of the unknown quantity but no higher power).*TIS born in Bologna, Italy. In 1536 he was sent to live with Girolamo Cardano, who taught him Latin, Greek, and mathematics. He collaborated with Cardano in research on third and fourth degree equations. *VFR He began as the servant of Cardano but was extremely bright, so Cardano started teaching him mathematics. Ferrari aided Cardano on his solutions for quadratic equations and cubic equations, and was mainly responsible for the solution of quartic equations that Cardano published. While still in his teens, Ferrari was able to obtain a prestigious teaching post after Cardano resigned from it and recommended him. Ferrari eventually retired young (only 42) and quite rich. He then moved back to his home town of Bologna where he lived with his widowed sister Maddalena to take up a professorship of mathematics at the University of Bologna in 1565. Shortly thereafter, he died of white arsenic poisoning, allegedly murdered by his greedy sister.*Wik

1766 Timofei Fedorovic Osipovsky (February 2, 1766–June 24, 1832) was a Russian mathematician, physicist, astronomer, and philosopher. Timofei Osipovsky graduated from the St Petersburg Teachers Seminary.
He was to became a teacher at Kharkov University. Kharkov University was founded in 1805. The city of Kharkov, thanks to its educational establishments, became one of the most important cultural and educational centers of Ukraine. Osipovsky was appointed to Kharkov University in 1805, the year of the foundation of the University. In 1813 he became rector of the University. However in 1820 Osipovsky was suspended from his post on religious grounds.
His most famous work was the three volume book A Course of Mathematics (1801–1823). This soon became a standard university text and was used in universities for many years. *Wik

1786 Jacques Philippe Marie Binet (2 Feb 1786 in Rennes, Bretagne, France - 12 May 1856 in Paris, France) investigated the foundations of matrix theory which was to set the scene for later work by Cayley and others. He discovered the rule for multiplying matrices in 1812 and it is almost certainly for this that he will be remembered rather than his other work.
He did, however, write a number of important papers which were influential in the development of mathematics, in particular he wrote Mémoire sur les intégrales définies eulériennes in 1840. The following year he wrote on number theory, making a contribution to the theory of the Euclidean algorithm. *SAU

1793 William Hopkins FRS (2 February 1793 – 13 October 1866) was an English mathematician and geologist. He is famous as a private tutor of aspiring undergraduate Cambridge mathematicians, earning him the sobriquet the senior-wrangler maker.
Before graduation, Hopkins had married Caroline Frances Boys (1799–1881) and was, therefore, ineligible for a fellowship. He instead maintained himself as a private tutor, coaching the young mathematicians who sought the prestigious distinction of Senior Wrangler. He was enormously successful in the role, earning the sobriquet senior wrangler maker and grossing £700-800 annually. By 1849, he had coached almost 200 wranglers, of whom 17 were senior wranglers including Arthur Cayley and G. G. Stokes. Among his more famous pupils were Lord Kelvin, James Clerk Maxwell and Isaac Todhunter.
He also made important contributions in asserting a solid, rather than fluid, interior for the Earth and explaining many geological phenomena in terms of his model. However, though his conclusions proved to be correct, his mathematical and physical reasoning were subsequently seen as unsound.In 1833, Hopkins published Elements of Trigonometry and became distinguished for his mathematical knowledge.
There was a famous story that the theory of George Green (1793–1841) was almost forgotten. In 1845, Lord Kelvin (William Thomson, a young man in 1845) got some copies of Green's 1828 short book from William Hopkins. Subsequently, Lord Kelvin helped to make Green's 1828 work famous according to the book "George Green" written by D.M. Cannell. *Wik It is known that he gave one copy of Green's book to Liouville, founder and editor of a popular French Mathematical Journal.

1849 Leopold Bernhard Gegenbauer (2 Feb 1849 - 3 June 1903) was an Austrian mathematician who gave his name to a sequence of orthogonal polynomials. He gave the well-known asymptotic estimate 6n/π2 for the number of square-free integers not exceeding n.*SAU

1881 Gustav Herglotz (2 February 1881 – 22 March 1953) was a German mathematician. He is best known for his works on the theory of relativity and seismology. From 1925 (until becoming Emeritus in 1947) he again was in Göttingen as the successor of Carl Runge on the chair of applied mathematics. One of his students was Emil Artin.
Herglotz made contribution in many fields of applied and pure mathematics. The Theorem of Herglotz is known in differential geometry, and he also contributed to number theory. He worked in the fields of celestial mechanics, theory of electrons, special relativity (where he developed a theory of elasticity), general relativity, hydrodynamics, refraction theory. *Wik

1882 Joseph Henry Maclagen Wedderburn (2 Feb 1882 in Forfar, Angus, Scotland - 9 Oct 1948 in Princeton, New Jersey, USA) studied at Edinburgh, Leipzig, Berlin and Chicago. He returned to Scotland to work at Edinburgh but then moved to a post at Princeton where he spent the rest of his career except for a break for service in World War I. He made far-reaching discoveries in the theory of rings, algebras and matrices. He became an honorary member of the EMS in 1946. *SAU

1893 Cornelius Lanczos (2 Feb 1893 - 25 June 1974) worked on relativity and mathematical physics and invented what is now called the Fast Fourier Transform. *SAU

1896 Kazimierz Kuratowski (2 Feb 1896 in Warsaw, Russian Empire (now Poland) - 18 June 1980 in Warsaw, Poland) He worked in the area of topology and set theory. He is best known for his theorem giving a necessary and sufficient condition for a graph to be planar.*SAU
Kuratowski's theorem:  "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K5 (the complete graph on five vertices) or K3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three)."  (in simpler, but less exact terms,  it can be drawn in such a way that no edges cross each other."  The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is K3,3 (below).  The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other. (1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917)  (see June 21)

1897 Gertrude Blanch (2 Feb, 1897 (sometimes 1898) - 1 Jan,1996) was an American mathematician who did pioneering work in numerical analysis and computation. After the war, Blanch's career was hampered by FBI suspicions that she was secretly a communist. Their evidence for this seems scarce, and included, for example, the observation that she had never married or had children. In what must have been a remarkable showdown, the diminutive fifty-year-old mathematician demanded, and won, a hearing to clear her name.
Subsequently, she worked for the Institute for Numerical Analysis at UCLA and the Aerospace Research Laboratory at Wright-Patterson Air Force Base in Dayton, Ohio. She was one of the founders of the ACM.
She published over thirty papers on functional approximation, numerical analysis and Mathieu functions. In 1962, she was elected a Fellow in the American Association for the Advancement of Science.
Blanch retired in 1967 at the age of 69, but continued working under a consulting contract for the Air Force for another year. Thereafter she moved to San Diego and continued to work on numerical solutions of Mathieu functions until her death in 1996, concentrating on the use of continued fractions to achieve highly accurate results in a small number of computational steps. This work has not been published. The Gertrude Blanch Papers, 1932-1996 are stored at the Charles Babbage Institute, University of Minnesota, Minneapolis. *Wik

1903 Bartel Leendert van der Waerden (2 Feb 1903 - 12 Jan 1996) This famous algebraist is best known for his book Moderne Algebra, but has, more recently, done interesting work on the history of ancient mathematics. *VFR

1704 GGuillaume François Antoine, Marquis de l'Hôpital (?, 1661, Paris – February 2, 1704, Paris) was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞. Although the rule did not originate with l'Hôpital, it appeared in print for the first time in his treatise on the infinitesimal calculus, entitled Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes. This book was a first systematic exposition of differential calculus. Several editions and translations to other languages were published and it became a model for subsequent treatments of calculus. or a while, he was a member of Nicolas Malebranche's circle in Paris and it was there that in 1691 he met young Johann Bernoulli, who was visiting France and agreed to supplement his Paris talks on infinitesimal calculus with private lectures to l'Hôpital at his estate at Oucques. In 1693, l'Hôpital was elected to the French academy of sciences and even served twice as its vice-president. Among his accomplishments were the determination of the arc length of the logarithmic graph, one of the solutions to the brachistochrone problem, and the discovery of a turning point singularity on the involute of a plane curve near an inflection point.
L'Hôpital exchanged ideas with Pierre Varignon and corresponded with Gottfried Leibniz, Christiaan Huygens, and Jacob and Johann Bernoulli. His Traité analytique des sections coniques et de leur usage pour la résolution des équations dans les problêmes tant déterminés qu'indéterminés ("Analytic treatise on conic sections") was published posthumously in Paris in 1707. *Wik

1950 Constantin Carathéodory (or Constantine Karatheodori) (13 September 1873 – 2 February 1950) was a Greek mathematician. He made significant contributions to the theory of functions of a real variable, the calculus of variations, and measure theory. His work also includes important results in conformal representations and in the theory of boundary correspondence. In 1909, Carathéodory pioneered the Axiomatic Formulation of Thermodynamics along a purely geometrical approach. *Wik He is the only modern Greek mathematician “who does not suffer by comparison with the famous names of Greek antiquity.” *VFR.

1911 Hugues Charles Robert Méray (November 12, 1835, Chalon-sur-Saône, Saône-et-Loire - February 2, 1911, Dijon) was a French mathematician. He is noted as the first to publish an arithmetical theory of irrational numbers. His work did not have much of a role in the history of mathematics because France, at that time, was less interested in such matters than Germany.*Wik

1965 George Neville Watson (31 Jan 1886 in Westward Ho!, Devon, England - 2 Feb 1965 in Leamington Spa, Warwickshire, England) studied at Cambridge, and then taught at Cambridge and University College London before becoming Professor at Birmingham. He is best known as the joint author with Whittaker of one of the standard text-books on Analysis. Titchmarsh wrote of Watson's books, "Here one felt was mathematics really happening before one's eyes. ... the older mathematical books were full of mystery and wonder. With Professor Watson we reached the period when the mystery is dispelled though the wonder remains." *SAU

1970 Bertrand Arthur William Russell (18 May 1872 - 2 Feb 1970) (3rd earl) was a Welsh mathematical logician, analytical philosopher and writer. He worked to establish foundations of mathematics and developed contemporary formal logic. He is known for Russell's paradox (concerning the set of all sets that are not members of themselves), his theory of types, and his contributions to the first-order predicate calculus. He believed in logicism, the theory that mathematics was in some important sense reducible to formal logic. With Alfred Whitehead, he co-authored Prinicpia Mathematica (1910). Russell is regarded as one of the most important logicians of the twentieth century. He was active in social and political campaigns, and advocated pacifism and nuclear disarmament. The Nobel Prize for Literature was awarded to Russell in 1950 *TIS

2005 Edward Maitland Wright (13 Feb 1906 in Farnley, near Leeds, England - 2 Feb 2005 in Reading, England) was initially self-taught in Mathematics but was able to go and study at Oxford. He spent a year at Göttingen and returned to Oxford. He was appointed to the Char at Aberdeen where he stayed for the rest of his career, eventually becoming Principal and Vice-Chancellor of the University. He is best known for the standard work on Number Theory he wrote with G H Hardy. One of Wright's first papers, published in 1930, was on Bernstein polynomials. Also among his early work was a series of three papers titled Asymptotic partition formulae. The third in the series Asymptotic partition formulae, III. Partitions into kth powers was published by Acta Mathematica in 1934. *SAU

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

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
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