Friday, 26 October 2012

On This Day in Math - October 26

There are no foolish questions and no man becomes a fool until he has stopped asking questions.
Charles P Steinmetz

The 300th day of the year; 300 is a triangular number, the sum of the integers from 1 to 24. 300 is also the sum of a pair of twin primes (149 + 151). It is also the sum of ten consecutive primes, 300 = 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47.


1676 Newton, through the intermediary of Oldenburg, wrote Leibniz concerning his work on the calculus. An anagram contained the statement of the problem of integrating differential equations. *VFR

1843 John T Graves replies to Hamilton about the invention of Quaternions,
"There is something in the system which gravels me. I have not yet any clear views as to the extent to which we are at liberty arbitrarily to create imaginaries, and to endow them with supernatural properties."
"If with your alchemy you can create three pounds of gold, why should you stop there?
Graves is credited by Hamilton with being a critical inspiration in the Quaternions, and would quickly go on to create the "Octaves", an eight dimensional normed division algebra. Why should you stop there indeed? *Joan Baez Rankin Lecture of September 17, 2008 Glascow
1847 William Whewell wrote to Aubrey De Vere expressing dismay at the influence of Carlyle's pessimism among his friends and in society. *@GalileosBalls, Twitter
1896 Comptes Rendus publishes, "Extension of the Reimann-Roch Theorem to Algebraic Surfaces. A note by M. M. Noether, presented by M. Hermite *Mathematical Intellignecer vol 8 #4
1893 Karl Pearson’s first statistical publication. *VFR In Pearson' s first published statistical paper of 26 October 1893, he introduced the method of moments as a means of curve fitting asymmetrical distributions. One of his aims in developing the method of moments was to provide a general method for determining the values of the parameters of a frequency distribution. *StatProb web site

1960 Saga, a silent shoot-em-up Western playlet made on the TX-0 computer, was run on CBS' special for MIT's 100th anniversary. The TX-0 was the first general purpose transistorized computer. The program for Saga comprised 4,096 words of magnetic core storage. The 13,000 lines of code choreographed the movements of each object. A line of direction was written for each action, even if it went wrong. This led to the high point of the show where sheriff put his gun in the holster of the robber resulting in a never ending loop.
Doug Ross explained the rule-based diagram: If the robber drank from alcohol, his judgement would start to decline, but the program would remain logical.*CHM


1846 Lewis Boss (26 Oct 1846; 12 Oct 1912) American astronomer best known for his compilation of two catalogues of stars (1910, 1937). In 1882 he led an expedition to Chile to observe a transit of Venus. About 1895 Boss began to plan a general catalog of stars, giving their positions and motions. After 1906, the project had support from the Carnegie Institution, Washington, D.C. With an enlarged staff he observed the northern stars from Albany and the southern stars from Argentina. With the new data, he corrected catalogs that had been compiled in the past, and in 1910 he published the Preliminary General Catalogue of 6,188 Stars for the Epoch 1900. The work unfinished upon his death was completed by his son Benjamin in 1937 (General Catalogue of 33,342 Stars for the Epoch 1950, 5 vol.)*TIS

1849 Georg Frobenius (26 Oct 1849; 3 Aug 1917) German mathematician who made major contributions to group theory, especially the concept of abstract groups (with Ludwig Stickleberger) and the theory of finite groups of linear substitutions (with Issai Schur), that later found important uses in the theory of finite groups as it applies to quantum mechanics. He also contributed to means of solving linear homogenous differential equations. The fact so many of Frobenius's papers read like present day text-books on the topics which he studied is a clear indication of the importance that his work, in many different areas, has had in shaping the mathematics which is studied today.*TIS

1877 Max Mason (26 Oct 1877; 23 Mar 1961) American mathematical physicist, educator, and science administrator. During World War I he invented several devices for submarine detection - several generations of the Navy's "M," or multiple-tube, passive submarine sensors. This apparatus focused sound to ascertain its source. To determine the direction from which the sound came, the operator needed only to seek the maximum output on his earphones by turning a dial. The final device had a range of 3 miles. Mason's special interest and contributions lay in mathematics (differential equations, calculus of variations), physics (electromagnetic theory), invention (acoustical compensators, submarine-detection devices), and the administration of universities and foundations. *TIS

1885 Niels Erik Norlund (26 Oct 1885 in Slagelse, near Soro, Sjaelland, Denmark - 4 July 1981 in Copenhagen, Denmark) In 1907 he was awarded a gold medal for an essay on continued fractions and his resulting two publications were in 1908: Sur les différences réciproques; and Sur la convergence des fractions continues both published in Comptes Rendus de l'Academie des Sciences. These publications in the most prestigious French journal earned Norlund an international reputation despite still being an undergraduate. In the summer of 1910 he earned a Master's degree in astronomy and in October of that year he successfully defended his doctoral thesis in mathematics Bidrag til de lineaere differentialligningers Theori. In the same year he published the 100-page paper Fractions continues et différences réciproques as well as Sur les fractions continues d'interpolation, a paper on Halley's comet, and an obituary of his teacher Thorvald Thiele. Norlund's sister Margrethe married Niels Bohr whose brother, Harald, was also an outstanding mathematician. In 1955 Norland reached retirement age. That mathematics was his first love now became clear, for once he gave up the responsibilities of the Geodesic Institute he returned to mathematics research. He published Hypergeometric functions in 1955 which was reviewed by Arthur Erdélyi, "This is one of those rare papers in which sound mathematics goes hand in hand with excellent exposition and style; and the reader is both instructed and delighted. It is likely to become the standard memoir on the generalized hypergeometric series ... " The paper Sur les fonctions hypergéométriques d'ordre supérieur (1956) gives a very full, rigorous and classical treatment of some integrals from generalized hypergeometric function theory.*SAU

1911 Shiing-shen Chern (26 Oct 1911; 3 Dec 2004) Chinese-American mathematician and educator whose researches in differential geometry include the development of the Chern characteristic classes in fibre spaces, which play a major role in mathematics and in mathematical physics. "When Chern was working on differential geometry in the 1940s, this area of mathematics was at a low point. Global differential geometry was only beginning, even Morse theory was understood and used by a very small number of people. Today, differential geometry is a major subject in mathematics and a large share of the credit for this transformation goes to Professor Chern." *TIS

1930 Walter Feit (26 Oct 1930 in Vienna, Austria - 29 July 2004 in Branford, Connecticut, USA) was an Austrian mathematician who (with John Thompson) proved one of the most important theorems about finite simple groups. In 1990 his 60th birthday was celebrated with an 'International Symposium on the Inverse Galois Problem' held in Oxford. His retirement from Yale in October 2003 was marked with the holding of a 'Conference on Groups, Representations and Galois Theory' in his honour. Feit died after a long illness at the Connecticut Hospice in Branford, Connecticut, USA. A memorial service was held on Sunday 10 October 2004 at the New Haven Lawn Club, New Haven, Connecticut. *SAU


1817 Aida Yasuaki was a Japanese mathematician who published about 2000 works. Aida compiled Sampo tensi shinan which appeared in 1788. It is a book of geometry problems, developing formulae for ellipses, spheres, circles etc. Aida explained the use of algebraic expressions and the construction of equations. He also worked on number theory and simplified continued fraction methods due to Seki. *SAU

1923 Charles Proteus Steinmetz (9 Apr 1865- 26 Oct 1923) German-born American inventor and electrical engineer whose theories and mathematical analysis of alternating current systems helped establish them as the preferred form of electrical energy in the United States, and throughout the world. In 1893, Steinmetz joined the newly organized General Electric Company where he was an engineer then consultant until his death. His early research on hysteresis (loss of power due to magnetic resistance) led him to study alternating current, which could eliminate hysteresis loss in motors. He did extensive new work on the theory of a.c. for electrical engineers to use. His last research was on lightning, and its threat to the new AC power lines. He was responsible for the expansion of the electric power industry in the U.S. *TIS

1968 Sergei Natanovich Bernstein (March 5, 1880 – October 26, 1968) was a Russian and Soviet mathematician. His doctoral dissertation, submitted in 1904 to the Sorbonne, solved Hilbert's nineteenth problem on the analytic solution of elliptic differential equations. Later, he published numerous works on Probability theory, Constructive function theory, and mathematical foundations of genetics. From 1906 until 1933, Bernstein was a member of the Kharkov Mathematical Society. *Wik

1970 Marcel Gilles Jozef Minnaert (12 Feb 1893; 26 Oct 1970 at age 77)
Flemish astronomer and solar physicist who was one of the pioneering solar researchers during the first half of the 20th century. Applying solar spectrophotometry, he was one of the first to make quantitative measurements of the intensity distribution inside Fraunhofer lines, and interpret from them information about the outer solar layers. His range of study also included comets, nebulae and lunar photometry. During the time he was director of the observatory at the University of Utrecht, (1937-1963) he created a modern astronomical institute to study solar and stellar spectra with resources including a solar telescope, spectrograph, photometer, and mechanical workshop. Minnaert also maintained a strong interest in the education of physics teachers, and as a univeristy professor gave clear, enthusiastic and well-prepared lectures. *TIS
1983 Alfred Tarski (14 Jan 1902, 26 Oct 1983) Polish-born American mathematician and logician who made important studies of general algebra, measure theory, mathematical logic, set theory, and metamathematics. Formal scientific languages can be subjected to more thorough study by the semantic method that he developed. He worked on model theory, mathematical decision problems and with universal algebra. He produced axioms for "logical consequence", worked on deductive systems, the algebra of logic and the theory of definability. Group theorists study 'Tarski monsters', infinite groups whose existence seems intuitively impossible. *TIS

1984 Mark Kac (3 Aug 1914 in Krzemieniec, Poland, Russian Empire - 26 Oct 1984 in California, USA) pioneered the modern development of mathematical probability, in particular its applications to statistical physics. The method of quantization now in use involves the Feynman-Kac path integral, named after Richard Feynman and Mark Kac. He published a classic text Statistical Independence in Probability, Analysis and Number Theory in 1959. To many Kac will be remembered best for a paper he wrote for the American Mathematical Monthly in 1966. This is the famous paper Can One Hear the Shape of a Drum? and Kac received the Chauvenet Prize from the Mathematical Association of America in 1968 for the, "most outstanding expository article on a mathematical topic by a member of the Association." *SAU

1998 Kenkichi Iwasawa (11 Sept 1917 in Shinshuku-mura (near Kiryu), Gumma Prefecture, Japan - 26 Oct 1998 in Tokyo, Japan ) In the late 1960s Iwasawa made a conjecture for algebraic number fields which, in some sense, was the analogue of the relationship which Weil had found between the zeta function and the divisor class group of an algebraic function field. This conjecture became known as "the main conjecture on cyclotomic fields" and it remained one of the most outstanding conjectures in algebraic number theory until it was solved by Mazur and Wiles in 1984 using modular curves. "it is no exaggeration to say that Iwasawa's ideas have played a pivotal role in many of the finest achievements of modern arithmetical algebraic geometry on such questions as the conjecture of B Birch and H Swinnerton-Dyer on elliptic curve; the conjecture of B Birch, J Tate, and S Lichtenbaum on the orders of the K-groups of the rings of integers of number fields; and the work of A Wiles on the modularity of elliptic curves and Fermat's Last Theorem." *SAU

*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
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