## Monday, 17 October 2016

### On This Day in Math - October 17

To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.

The 291st day of the year; 291 is the largest number that is not the sum of distinct non-trivial powers.

$\phi(291) = 192$  The number of integers less than, and relatively prime to 291 is equal to it's reversal, 192.

EVENTS

1604 In Prague, Kepler first observes the supernova now known as supernova 1604 and Kepler's Star. The first recorded observation of this supernova was in northern Italy on October 9, 1604. It was named after Kepler because his observations tracked the object for an entire year and because of his book on the subject, entitled De Stella nova in pede Serpentarii ("On the new star in Ophiuchus's foot", Prague 1606). Here is an image of Kepler's De Stella Nova, open to the foldout star map placing the supernova of 1604, from the twitter feed of @Libroantiguo . It was the second supernova to be observed in a generation (after SN 1572 seen by Tycho Brahe in Cassiopeia). No further supernovae have since been observed with certainty in the Milky Way, though many others outside our galaxy have been seen since S Andromedae. *Wik

1776 Euler read a paper to the St. Petersburg Academy of Science entitled “De quadratis magicis,” in which he gave a method of constructing magic squares by means of two orthogonal Latin squares. *Peter Ullrich, “An Eulerian square before Euler and an experimental design before R. A. Fisher: On the early history of Latin squares,” Chance, vol. 12, no. 1, Winter 1999, pp. 22–26.

1831 After discovering induced current on October 1st using two electrified coils,  on the 17th of October Michael Faraday  observers the same effect on the galvanometer when he inserts a permanent steel magnet into the electrified coil. *A history of physics in its elementary branches By Florian Cajori

1843 Hamilton Writes to his friend, John Graves, with a description of Quaternions. By December, Graves will have extended the idea to an eight dimensional algebra which will become "octonians".

Observatory, October 17, 1843
My dear Graves,|A very curious train of mathematical speculation occurred to me
yesterday, which I cannot but hope will prove of interest to you. You know that I have long
wished, and I believe that you have felt the same desire, to possess a Theory of Triplets,
analogous to my published Theory of Couplets, and also to Mr. Warren's geometrical representation
of imaginary quantities. Now I think that I discovered1 yesterday a theory of
quaternions which includes such a theory of triplets.

The complete letter is available at this site. *David R. Wilkins, *John Derbyshire, Unkown Quantity
In his preface to the ‘Lectures on Quaternions’ and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. *Wik

1858 DeMorgan writes a letter about Euler’s  prodigious output. *W W Rouse Ball, from The genius of Euler: reflections on his life and work, By William Dunham, pg 89

1933 Albert Einstein seeks asylum in the US, one of many Jewish/left-wing intellectuals fleeing the Nazi govt in Germany and Europe. The Nazi government put a bounty now worth £50,000 on his head while a German magazine included him in a list of the Nazis’ enemies who were 'not yet hanged'.
1952 D. H. Lehmer, University of California, announced that 2n − 1 for n = 2203 and 2281 are Mersenne primes. He was aided by a SWAC computing machine, the ﬁrst result taking 59 minutes. *VFR This may have been predated by Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) at Berkeley may have beaten him by a week or so on October 7th of the same year.
D. H. Lehmer continued his fathers interest in combinatorial computing and in fact wrote the article "Machine tools of Computation," which is chapter one in the book "Applied Combinatorial Mathematics," by Edwin Beckenbach, 1964. It describes methods for producing permutations, combinations etc. This was a uniquely valuable resource and has only been rivaled recently by Volume 4 of Donald Knuth's series. In 1950, Lehmer was one of 31 University of California faculty fired after refusing to sign a loyalty oath, a policy initiated by the Board of Regents of the State of California in 1950 during the Communist scare personified by Senator Joseph McCarthy. (see below)*Wik

1952 The California Supreme Court declared the state loyalty oath unconstitutional and declared that the eighteen faculty members who had refused to sign the oath be reinstated.*VFR

1978 James Burke's history of science series Connections first airs, on BBC Television in the United Kingdom (with accompanying book). *Wik

1983 Gerard Debreu, who holds a joint appointment in Mathematics and Economics at Berkeley, won a Nobel Prize for his work in mathematical economics. For a non-technical description of his work see The Mathematical Intelligencer, 6(1984), no. 2, pp. 61–62. *VFR

2012 Car size pieces of Halley's Comet lit up the skies over the Bay Area in California. Hundreds of residents from Oakland, San Francisco and Santa Cruz called ABC News station KGO-TV, reporting a loud boom, explosions and streaks of light around 7:45 p.m. local time. The Orionids are one of two annual meteor showers produced by icy pieces of Halley's Comet. The other shower, called the Eta Aquarids, peaks each year in early May, according to NASA. Video *ABC News

BIRTHS

1759 Jakob II Bernoulli (17 October 1759, Basel – 3 July 1789, Saint Petersburg), younger brother of Johann III Bernoulli. Having finished his literary studies, he was, according to custom, sent to Neuchâtel to learn French. On his return he graduated in law. This study, however, did not check his hereditary taste for geometry. The early lessons which he had received from his father were continued by his uncle Daniel, and such was his progress that at the age of twenty-one he was called to undertake the duties of the chair of experimental physics, which his uncle’s advanced years rendered him unable to discharge. He afterwards accepted the situation of secretary to count de Brenner, which afforded him an opportunity of seeing Germany and Italy. In Italy he formed a friendship with Lorgna, professor of mathematics at Verona, and one of the founders of the Società Italiana for the encouragement of the sciences. He was also made corresponding member of the royal society of Turin; and, while residing at Venice, he was, through the friendly representation of Nicolaus von Fuss, admitted into the academy of St Petersburg. In 1788 he was named one of its mathematical professors. *Wik
He drowned while bathing in the Neva in July 1789, a few months after his marriage with a granddaughter of Leonhard Euler.  (Can't tell your Bernoulli's without a scorecard?  Check out "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

1788 Paul Isaak Bernays (17 Oct 1888; 18 Sep 1977) Swiss mathematician and logician who is known for his attempts to develop a unified theory of mathematics. Bernays, influenced by Hilbert's thinking, believed that the whole structure of mathematics could be unified as a single coherent entity. In order to start this process it was necessary to devise a set of axioms on which such a complete theory could be based. He therefore attempted to put set theory on an axiomatic basis to avoid the paradoxes. Between 1937 and 1954 Bernays wrote a whole series of articles in the Journal of Symbolic Logic which attempted to achieve this goal. In 1958 Bernays published Axiomatic Set Theory in which he combined together his work on the axiomatisation of set theory. *TIS

1927 Friedrich Ernst Peter Hirzebruch (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as "the most important mathematician in the Germany of the postwar period.
Amongst many other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded him the Order of the Sacred Treasure in 1996. He also won an Einstein Medal in 1999, and received the Cantor medal in 2004.*Wik

DEATHS

1817 John West (10 April 1756 in Logie (near St Andrews), Scotland - 17 Oct 1817 in Morant Bay, Jamaica) The achievements of the little-known Scottish mathematician, John West (1756–1817), deserve recognition: hisElements of Mathematics(1784) shows him to be a skilled expositor and innovative geometer while his manuscript,Mathematical Treatises,unpublished until 1838, reveal him also to be an accomplished exponent of “continental” analysis, familiar with works of Lagrange, Laplace, and Arbogast then little studied in Britain.
First an assistant at St. Andrews University in Scotland, West then worked in isolation in Jamaica, combining mathematics with the duties of an Anglican rector. His life and his pastoral and mathematical works are here described. *abstract for Geometry, Analysis, and the Baptism of Slaves: John West in Scotland and Jamaica, Alex D.D. Craik

1877 Gustav Robert Kirchhoff (12 Mar 1824, 17 Oct 1887) German physicist who, with Robert Bunsen, established the theory of spectrum analysis (a technique for chemical analysis by analyzing the light emitted by a heated material), which Kirchhoff applied to determine the composition of the Sun. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated, which explained the numerous dark lines (Fraunhofer lines) in the Sun's spectrum. In his Kirchhoff's laws (1845) he generalized the equations describing current flow to the case of electrical conductors in three dimensions, extending Ohm's law to calculation of the currents, voltages, and resistances of electrical networks. He demonstrated that current flows in a zero-resistance conductor at the speed of light. *TIS

1923 August Adler (24 Jan 1863 in Opava, Austrian Silesia (now Czech Republic)-17 Oct 1923 in Vienna, Austria) In 1906 Adler applied the theory of inversion to solve Mascheroni construction problems in his book Theorie der geometrischen Konstruktionen published in Leipzig. In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.
Since he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses. However Adler did not simplify Mascheroni proof. On the contrary, his new methods were not as elegant, either in simplicity or length, as the original proof by Mascheroni.
This 1906 publication was not the first by Adler studying this problem. He had published a paper on the theory of Mascheroni's constructions in 1890, another on the theory of geometrical constructions in 1895, and one on the theory of drawing instruments in 1902. As well as his interest in descriptive geometry, Adler was also interested in mathematical education, particularly in teaching mathematics in secondary schools. His publications on this topic began around 1901 and by the end of his career he was publishing more on mathematical education than on geometry. Most of his papers on mathematical education were directed towards teaching geometry in schools, but in 1907 he wrote on modern methods in mathematical instruction in Austrian middle schools. He produced various teaching materials for teaching geometry in the sixth-form in Austrian schools such as an exercise book which he published in 1908. *SAU

1937 Frank Morley (9 Sept 1860 in Woodbridge, Suffolk, England-17 Oct 1937 in Baltimore, Maryland, USA) wrote mainly on geometry but also on algebra.*SAU Morley is remembered most today for a singular theorem which bears his name in recreational literature.  Simply stated, Morley's Theorem says that if the angles at the vertices of any triangle (A, B, and C in the figure) are trisected, then the points where the trisectors from adjacent vertices intersect (D, E, and F) will form an equilateral triangle. In 1899 he observed the relationship described above, but could find  no  proof. It spread from discussions with his friends to become an item  of  mathematical gossip. Finally in 1909 a trigonometric solution was   discovered by M. Satyanarayana. Later an elementary proof was developed.   Today the preferred proof is to begin with the result and work   backward. Start with an equilateral triangle and show that the vertices   are the intersection of the trisectors of a triangle with any given set   of angles. For those interested in seeing the proof, check Coxeter's Introduction to Geometry, Vol 2, pages 24-25. Find more about this unusual man here.  *PB

1941 John Stanley Plaskett (17 Nov 1865, 17 Oct 1941) Canadian astronomer known for his expert design of instruments and his extensive spectroscopic observations. He designed an exceptionally efficient spectrograph for the 15-inch refractor and measured radial velocities and found orbits of spectroscopic binary stars. He designed and supervised construction of the 72-inch reflector built for the new Dominion Astrophysical Observatory in Victoria and was appointed its first director in 1917. There he extended the work on radial velocities and spectroscopic binaries and studied spectra of O and B-type stars. In the 1930s he published the first detailed analysis of the rotation of the Milky Way, demonstrating that the sun is two-thirds out from the center of our galaxy about which it revolves once in 220 million years.*TIS

1952 Ernest Vessiot (8 March 1865 in Marseilles, France-17 Oct 1952 in La Bauche, Savoie, France) applied continuous groups to the study of differential equations. He extended results of Drach (1902) and Cartan (1907) and also extended Fredholm integrals to partial differential equations.  Vessiot was assigned to ballistics during World War I and made important discoveries in this area. He was honoured by election to the Académie des Sciences in 1943. *SAU

1963 Jacques-Salomon Hadamard (8 Dec 1865, 17 Oct 1963) French mathematician who proved the prime-number theorem (as n approaches infinity, the limit of the ratio of (n) and n/ln(n) is 1, where (n) is the number of positive prime numbers not greater than n). Conjectured in the 18th century, this theorem was not proved until 1896, when Hadamard and also Charles de la Vallée Poussin, used complex analysis. Hadamard's work includes the theory of integral functions and singularities of functions represented by Taylor series. His work on the partial differential equations of mathematical physics is important. He introduced the concept of a well-posed initial value and boundary value problem. In considering boundary value problems he introduced a generalization of Green's functions (1932). *TIS

1978 Gertrude Mary Cox (January 13, 1900 – October 17, 1978) was an influential American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of the Consolidated University of North Carolina and the Statistics Research Division of North Carolina State University. Her most important and influential research dealt with experimental design; she wrote an important book on the subject with W. G. Cochran. In 1949 Cox became the first female elected into the International Statistical Institute and in 1956 she was president of the American Statistical Association.*Wik

2008 Andrew Mattei Gleason (November 4, 1921 – October 17, 2008) was an American mathematician and the eponym of Gleason's theorem and the Greenwood–Gleason graph. After briefly attending Berkeley High School (Berkeley, California) he graduated from Roosevelt High School in Yonkers, then Yale University in 1942, where he became a Putnam Fellow. He subsequently joined the United States Navy, where he was part of a team responsible for breaking Japanese codes during World War II. He was appointed a Junior Fellow at Harvard in 1946, and later joined the faculty there where he was the Hollis Professor of Mathematicks and Natural Philosophy. He had the rare distinction among Harvard professors of having never obtained a doctorate. (In graph theory, the Greenwood–Gleason graph (Image at top of page) is also known as the Clebsch graph. It is an undirected graph with 16 vertices and 40 edges. It is named after Alfred Clebsch, a German mathematician who discovered it in 1868. It is also known as the Greenwood–Gleason graph after the work of Robert M. Greenwood and Andrew M. Gleason (1955), who used it to evaluate the Ramsey number R(3,3,3) = 17 *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