Tuesday, 6 October 2015

On This Day in Math - October 6

[after proving Euler's formula e π i + 1 = 0 in a lecture]
Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it is the truth.

~Benjamin Peirce

The 279th day of the year; Every positive integer is the sum of at most 279 eighth powers. See Waring's problem

279 = 3^2 + 3^3 + 3^5 (powers are consecutive primes). *Derek Orr

For more fun with daily calendar math see Dereks Daily Math
and Ben Vitale


1570 Cardano imprisoned for 87 days on charges of impiety (casting a horoscope of Christ). He spent the remaining five years of his life in Rome under the eye of a suspicious pope who nonetheless gave him a pension. See “Girolamo Cardano’s Horoscope of Christ,” pp. 53–90 in Renaissance Curiosa by Wayne Shumaker, especially p. 55 *VFR

1651 Sir Charles Cavendish writes to John Pell about Thomas Harriot’s Doctrine of Triangular Numbers; “Sr. Th Alesburie remembers him to you & desires to know if you would be pleased to shew the use of Mr. Harriots doctrine of triangulare numbers; which if you will doe, he will send you the original; I confess I was so farre in loue with it that I coppied it out; though I doute I vnderstand it not all; much less the many vses which I assure myself you will finde of it.” *Thomas Harriot’s Doctrine of Triangular Numbers, Beery &Stedall, pg 3

1668 (Oct 16 NS) Wallis writes to thank Oldenburg for gift of "Lalovera's book" (La Loubere), veterum geometria promota, in septem de cycloide libris. La Loubere is often cited as the first man to bring the "Siamese" method of solving nxn odd magic squares to the West. *Philip Beeley, Christoph J. Scriba; Correspondence of John Wallis

1729 The first known letter which contains an interpolating function for the factorials was written by Daniel Bernoulli on October 6, 1729. Bernoulli suggests for an arbitrary (positive) x and an infinite number A the infinite product $$ (A + \frac{x}{2})^{x-1} *((\frac{2}{1+x}) *(\frac{3}{2+x})* ... *(\frac{A}{A-1+x})$$

In 1783, the self-winding clock was patented by Benjamin Hanks.*TIS

1807 Humphry Davy first isolated potassium by electrolysis of molten KCl in the basement of Royal Institute.  *Anthony Hardwicke Tweet

1860 J. J. Sylvester, in a dinner invitation for Thomas Archer Hirst to join him with Arthur Cayley and Sylvester's "young French mathematical friend", (Camille Jordan); Sylvester entices him with a bit of mathematics, "I shall have something very striking to tell you about algebraic quantities of any order of irrationality and their representation by multiple definite integrals when we meet." *James Joseph Sylvester: Life and Work in Letters, edited by Karen Hunger Parshall

1983 Lotus Development Corp. went public after recording revenues of $12.8 million for the previous 12 months. The company, founded by Mitch Kapor and Jonathan Sachs in 1982, found its success with Kapor’s spreadsheet program, Lotus 1-2-3​. Lotus 1-2-3 bypassed the operating system of the IBM PC, making it much faster than its competitors. In addition, its combination of spreadsheet capabilities with graphics and data retrieval made the program popular. IBM acquired Lotus in 1995.*CHM

1994 Fermat confirmed, FINALLY. Wiles sends corrected proof. Over the course of three lectures delivered at Isaac Newton Institute for Mathematical Sciences on June 21, 22, and 23 of 1993, Andres Wiles had announced his proof of the Taniyama–Shimura conjecture, and hence of Fermat's Last Theorem. There was a relatively large amount of press coverage afterwards.
(Nick) Katz was a referee on his manuscript and he asked Wiles a series of questions that led Wiles to recognize that the proof contained a gap. There was an error in a critical portion of the proof which gave a bound for the order of a particular group: the Euler system used to extend Flach's method was incomplete. Wiles and his former student Richard Taylor spent almost a year resolving it. Wiles indicates that on the morning of September 19, 1994 he realized that the specific reason why the Flach approach would not work directly suggested a new approach with the Iwasawa theory which resolved all of the previous issues with the latter and resulted in a CNF that was valid for all of the required cases. On 6 October Wiles sent the new proof to three colleagues including Faltings. The new proof was published and, despite its size, widely accepted as likely correct in its major components. *Wik

In 1995, the first discovery of a planet around a star similar to the sun was announced (about 160 times the mass of the Earth around the star 51 Pegasus).*TIS

2008 First Space object observed before it hit the earth. At 06:38 UTC on October 6, astronomers at the University of Arizona discovered an object provisionally called 8TA9D69 that appeared to be on a collision course with Earth. Three other observatories reported sightings within the next few hours -- Sabino Canyon in Arizona and Siding Spring Observatory and a Royal Astronomical Society site, both in Australia. Together these four observers provided enough data on the object so that a Minor Planet Electronic Circular was issued at 14:59 UTC the same day, giving 8TA9D69 the more formal name 2008 TC3, and advising the astronomical community that "The nominal orbit given above has 2008 TC3 coming to within one earth radius around Oct. 7.1. The absolute magnitude indicates that the object will not survive passage through the atmosphere. Steve Chesley (JPL) reports that atmospheric entry will occur on 2008 Oct 07 0246 UTC over northern Sudan."
The object wouldn't be more than a big meteor, but even so, it represented the first time ever that an object had been observed before it was to hit Earth, and, clearly, astronomers around the world scrambled to their telescopes to observe it before it was to pass into Earth's shadow (and, therefore, invisibility) just before 01:50 UTC. *The Planetary Society


1552 Matteo Ricci (6 Oct 1552, 11 May 1610) Matteo Ricci was an Italian Jesuit who went to China as a missionary and introduced the Chinese to Western mathematics.*SAU More detail about this student of Clavius at the Renaissance Mathematicus

1732 Nevil Maskelyne (6 Oct 1732, 9 Feb 1811) (SAU gives 5 Oct for birhtdate)
British astronomer noted for his contribution to the science of navigation. In 1761 the Royal Society sent Maskelyne to the island of St Helena to make accurate measurements of a transit of Venus. This in turn gives the distance from the Earth to the Sun, and the scale of the solar system. During the voyage he also experimented with the lunar position method of determining longitude. In 1764 he went on a voyage to Barbados to carry out trials of Harrison's timepiece, followed by appointment as Astronomer Royal (1765). In 1774, he carried out an experiment on a Scottish mountain with the use of a plumb line to determine the Earth's density. He found it was approximately 4.5 times that of water. *TIS

1735 Jesse Ramsden (6 Oct 1735; 5 Nov 1800) British pioneer in the design of precision tools. At 23, Ramsden chose to apprentice to a maker of mathematical instruments. By age 27 he had his own business in London and was known as the most skilful designer of mathematical, astronomical, surveyingand navigationalinstruments in the 18th Century. He is best known for the design of a telescope and microscope eyepiece (ocular) still commonly used today and bearing his name. The French scientist N. Cassegrain proposed a design of a reflecting telescope in 1672, but Ramsden, however, 100 years later, who found that this design reduces blurring of the image caused by the sphericity of the lenses or mirrors. He also built lathes, barometers, manometers and assay balances.*TIS

1784 Pierre Charles François Dupin (6 Oct 1784, 18 Jan 1873) Dupin made contributions to differential geometry and in particular invented the 'Dupin indicatrix'.*SAU

1795 Benjamin Olinde Rodrigues (6 Oct 1795, 17 Dec 1851) was a French mathematician best known for his formula for the Legendre polynomials.*SAU

1831 (Julius Wilhelm) Richard Dedekind (6 Oct 1831, 12 Feb 1916 at age 84) German mathematician who developed a major redefinition of irrational numbers in terms of arithmetic concepts. Although not fully recognized in his lifetime, his treatment of the ideas of the infinite and of what constitutes a real number continues to influence modern mathematics. *TIS A 1904 academic calendar marked September fourth, 1899 as the day Dedekind died. He wrote the publisher saying that while 4 September might be correct, 1899 certainly was not, for on that day he had enjoyed a stimulating mathematical discussion with his dinner guest and honored friend, Georg Cantor. *VFR

1866 Reginald Aubrey Fessenden (6 Oct 1866, 22 Jul 1932) Canadian inventor and engineer with 300 patents. He broadcast the first program of voice and music. In 1893, Fessenden moved to Pittsburgh as the head of electrical engineering at the university, Fessenden read of Marconi's work and began experimenting himself. Marconi could only transmit Morse code. But Fessenden's goal was to transmit the human voice and music. He invented the "continuous wave": sound superimposed onto a radio wave for transmission. A radio receiver extracts the signal so the listener with the original sound. Fessenden made the first long-range transmissions of voice on Christmas Eve 1906 from a station at Brant Rock, Massachusetts, heard hundreds of miles out in the Atlantic.*TIS

1903 Ernest Thomas Sinton Walton(6 Oct 1903; 25 Jun 1995) Irish physicist, who was corecipient, with Sir John Douglas Cockcroft of England, of the 1951 Nobel Prize for Physics for the development of the first nuclear particle accelerator, known as the Cockcroft-Walton generator. The accelerator was built in a disused room in the Cavendish Laboratory, and supplied with several hundred kilovolts from a voltage multiplier circuit designed and built by Cockroft and Walton. On 14 Apr 1932 Walton turned the proton beam on to a lithium target. Despite all the odds against them, they succeeded in being the first to split the atom, and Walton was the first to see the reaction taking place. They identified the disintegration products as alpha particles (helium nuclei). *TIS

1908 Sergei Lvovich Sobolev (6 October 1908 – 3 January 1989) was a Soviet mathematician working in mathematical analysis and partial differential equations.*Wik

1918 Abraham Robinson (October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics.*Wik

1936 Robert Phelan Langlands (October 6, 1936 - ) is a Canadian mathematician best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study of Galois groups in number theory. He is an emeritus professor at the Institute for Advanced Study. Langlands has received the 1996 Wolf Prize (which he shared with Andrew Wiles), the 2005 AMS Steele Prize, the 1980 Jeffery-Williams Prize, the 1988 NAS Award in Mathematics from the National Academy of Sciences, the 2006 Nemmers Prize in Mathematics, and the 2007 Shaw Prize in Mathematical Sciences (with Richard Taylor) for his work on automorphic forms. *Wik Langlands occupies the office formerly held by Albert Einstein at Princeton.  *Edward Frenkel, Love and Math

1950 Glen David Brin, (born October 6, 1950 - ) is an American scientist and award-winning author of science fiction. He has received the Hugo, Locus, Campbell and Nebula Awards.
Brin was born in Glendale, California in 1950. In 1973, he graduated from the California Institute of Technology with a Bachelor of Science in astrophysics. He followed this with a Master of Science in applied physics in 1978 and a Doctor of Philosophy in space science in 1981, both from the University of California, San Diego. He is a 2010 fellow of the Institute for Ethics and Emerging Technologies.*Wik


1809 Benjamin Peirce (4 Apr 1809, 6 Oct 1880) American astronomer, mathematician and educator who computed the general perturbations of the planets Uranus and Neptune. He was Harvard's Perkins Professor of Astronomy and Mathematics for nearly 40 years, and was largely responsible for introducing mathematics as a subject for research in American institutions. He is known especially for his contributions to analytic mechanics and linear associative algebra, but he is also remembered for his early work in astronomy and for playing a role in the discovery of Neptune. *TIS In number theory, he proved there is no odd perfect number with fewer than four prime factors. In algebra, he was notable for the study of associative algebras. He first introduced the terms idempotent and nilpotent in 1870 to describe elements of these algebras, and he also introduced the Peirce decomposition. *Wik

1840 François Budan de Boislaurent (28 Sept 1761, 6 Oct 1840) was a Haitian born amateur mathematician best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have n real roots between two given numbers. Budan is considered an amateur mathematician and he is best remembered for his discovery of a rule which gives necessary conditions for a polynomial equation to have n real roots between two given numbers. Budan's rule was in a memoir sent to the Institute in 1803 but it was not made public until 1807 in Nouvelle méthode pour la résolution des équations numerique d'un degré quelconque. In it Budan wrote, "If an equation in x has n roots between zero and some positive number p, the transformed equation in (x - p) must have at least n fewer variations in sign than the original." *SAU (Sounds like a nice followup extension to Descartes Rule of signs in Pre-calculus classes. Mention the history, how many times do your students hear about a Haitian mathematician?)

Crelle Memorial in his hometown
1855 August Leopold Crelle (11 Mar 1780; 6 Oct 1855 at age 75). Although always interested in mathematics he lacked the money to enroll at a university and so became an engineer instead. In 1826, when he had the money, he founded the Journal f¨ur die rein und angewandte Mathematik and edited fifty two volumes. Although not a great mathematician he had a gift for recognizing the abilities of such men as Abel, Jacobi, Steiner, Dirichlet, Pl¨ucker, M¨obius, Eisenstein, Kummer, and Weierstrass and offered to publish their papers in his journal. *VFR As a civil engineer in the service of the Prussian Government and worked on the construction and planning of roads and the first railway in Germany (completed in 1838). He founded (1826) the world's oldest mathematical periodical still in existence, Journal für die reine und angewandte Mathematik ("Journal for Pure and Applied Mathematics"), now known as Crelle's Journal,and edited it for the rest of his life. In 1841, he was elected a foreign member of the Royal Swedish Academy of Sciences.*TIS

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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