Monday, 27 June 2011

On This Day in Math - June 27

Every science that has thriven has thriven upon its own symbols: logic, the only science which is admitted to have made no improvements in century after century, is the only one which has grown no symbols.
Augustus de Morgan

EVENTS
432 B.C. Meton observed the summer solstice and began his cycle. Meton was one of the first Greek astronomers to make accurate astronomical observations. It is widely believed that, working with Euctemon, he observed the summer solstice, which marked the Athenian New Year, in 432 BC.
The Metonic cycle appears in the oldest known astronomical device, the Antikythera Mechanism (2nd century BC) together with its multiple the Callippus cycle of 76 years.
The foundations of Meton's observatory in Athens are still visible just behind the podium of the Pnyx, the ancient parliament. Meton found the dates of equinoxes and solstices by observing sunrise from his observatory. The bisectrice of the observatory lies in an easterly direction, between the Acropolis and the Lycabetus hill.*Wik

In 1847, New York and Boston were linked by telegraph wires. This enabled the New York newspapers to receive foreign news brought by Cunard's steamers to the Boston port about 190 miles away. When the Cambria next arrived in Boston, three New York Newspapers on 18 Jul 1846 carried identical brief first-day telegraphic summaries of the Cambia's news*. This telegraph link opened three years after the first U.S. telegraph line was opened on 24 May 1844 with a message sent by Samuel Morse 80 miles from Washington D.C. and Baltimore, Md.*TIS

1908 The academy of sciences of Gottingen announced a prize of one hundred thousand marks, according to the will of Dr. Paul Wolfskehl, of Darmstadt, for the proof of Fermat’s great theorem. A German industrialist and amateur mathematician, Wolfskehl bequeathed 100,000 marks to the Göttingen Academy of Sciences to be offered as a prize for a complete proof of Fermat's Last Theorem. On 27 June 1908, the Academy published nine rules for awarding the prize. Among other things, these rules required that the proof be published in a peer-reviewed journal; the prize would not be awarded for two years after the publication; and that no prize would be given after 13 September 2007, roughly a century after the competition was begun. Wiles collected the Wolfskehl prize money, then worth \$50,000, on 27 June 1997.
Prior to Wiles' proof, thousands of incorrect proofs were submitted to the Wolfskehl committee, amounting to roughly 10 feet (3 meters) of correspondence. In the first year alone (1907–1908), 621 attempted proofs were submitted, although by the 1970s, the rate of submission had decreased to roughly 3–4 attempted proofs per month. According to F. Schlichting, a Wolfskehl reviewer, most of the proofs were based on elementary methods taught in schools, and often submitted by "people with a technical education but a failed career". In the words of mathematical historian Howard Eves, "Fermat's Last Theorem has the peculiar distinction of being the mathematical problem for which the greatest number of incorrect proofs have been published."*Wik

1967 The first ATM in England that was put into use was by Barclays Bank in Enfield Town in North London, United Kingdom, on 27 June 1967. This machine was the first in the UK and was used by English comedy actor Reg Varney, at the time so as to ensure maximum publicity for the machines that were to become mainstream in the UK. This instance of the invention has been credited to John Shepherd-Barron of printing firm De La Rue, who was awarded an OBE in the 2005 New Year's Honours List. His design used special cheques that were matched with a personal identification number, as plastic bank cards had not yet been invented. *Wik (The plaque posted at the sight makes the claim to be the first cash machine in the world, but cash dispensing machines had been installed in Tokyo and another shortly after in Upsalla.)

1977 Italy issued a postage stamp honoring Filippo Brunelleschi (1377–1446). [Scott #1266]. *VFR

1980 Creighton Carvello recited 20,013 digits of π from memory in nine hours and one minute. *VFR

BIRTHS

1767 Alexis Bouvard French astronomer and director of the Paris Observatory, who is noted for discovering eight comets and writing Tables astronomiques of Jupiter and Saturn (1808) and of Uranus (1821). Bouvard's tables accurately predicted orbital locations of Jupiter and Saturn, but his tables for Uranus failed, leading him to hypothesize that irregularities were caused by an unknown perturbing body. This spurred observations leading to the discovery of Neptune by Adams and Leverrier.*TIS

1806 Augustus de Morgan born in Madura (now Madurai), India, son of a colonel in the Indian Army. He is best known for his work in Formal Logic. “De Morgan’s Laws”, are contained in his ﬁrst book (1847), although they were known to Peter of Spain in the fourteenth century. *VFR
In formal logic, De Morgan's laws are rules relating the logical operators "and" and "or" in terms of each other via negation. With two operands A and B:
$\overline{A \cdot B} = \overline A + \overline B$
$\overline{A + B} = \overline {A} \cdot \overline {B}$
In another form:
NOT (P AND Q) = (NOT P) OR (NOT Q)
NOT (P OR Q) = (NOT P) AND (NOT Q)
The rules can be expressed in English as:
"The negation of a conjunction is the disjunction of the negations." and
"The negation of a disjunction is the conjunction of the negations."
*Wik When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked. He originated the use of the slash to represent fractions, as in 1/5 or 3/7. In Trigonometry and Double Algebra (1849) he gave a geometric interpretation of complex numbers. *TIS  A nice blog about De Morgan's life and relationships is at The Renaissance Mathematicus.

1850 Jorgen Pedersen Gram. Danish mathematician. Today he is best known for his criterion of linear independence of functions. The Gram-Schmidt Orthonormal Basis Theorem in Linear Algebra was ﬁrst published by him in 1883.
1940 Daniel G. Quillen bon in Orange, New Jersey. In 1978 he won a Fields Medal as the “prime architect of the higher algebraic K-theory, a new tool that successfully employed geometric and topological methods and ideas to formulate and solve major problems in algebra, particu¬larly ring theory and module theory.” *VFR French mathematician who is known for her work in number theory and contributions to the applied mathematics of acoustics and elasticity. Germain was self-taught from books, and from lecture notes supplied by male friends attending the Ecole Polytechnique which she, as a woman, was not permitted to attend. Using a male pseudonym, M. LeBlanc, she corresponded with Lagrange who recognised her skill, and subsequently sponsored her work. She accomplished a limited proof of Fermat's last theorem, for any prime under 100 where certain conditions were met. In 1816, she won a prize sponsored by Napoleon for a mathematical explanation of Chladni figures, the vibration of elastic plates. She died at age 55, from breast cancer. TIS

DEATHS
1829 James Smithson English scientist who provided funds in his will for the founding of the Smithsonian Institution, Washington, D.C. "for the increase and diffusion of knowledge." He had inherited his fortune chiefly through his mother's family. He was a chemist and minerologist who published 27 scientific papers. The mineral smithsonite (carbonate of zinc) was named for him.*TIS

1831 Sophie Germain died before she could receive the honorary doctorate Gauss had persuaded the University of Gottingen to give her. *VFR

1880 Carl Borchardt was a German mathematician who worked in a variety of areas in analysis. He edited Crelle's Journal for more than 30 years.*SAU

1952 Max Dehn died. He solved Hilbert’s third problem in 1900 (shortly after receiving his Ph.D. un¬der Hilbert on another topic in the foundations of geometry): a tetrahedron cannot be cut up into ﬁnitely many pieces and reassembled into a cube of equal volume. Thus Dehn became the ﬁrst mathematician to join “the honors class” of mathematicians who had solved one of the twenty-three problems Hilbert posed in Paris in 1900.

1975 Sir Geoffrey Ingram Taylor OM (7 March 1886 – 27 June 1975) was a British physicist, mathematician and expert on fluid dynamics and wave theory. His biographer and one-time student, George Batchelor, described him as "one of the most notable scientists of this (the 20th) century". His final research paper was published in 1969, when he was 83. In it he resumed his interest in electrical activity in thunderstorms, as jets of conducting liquid motivated by electrical fields. The cone from which such jets are observed is called the Taylor cone for his namesake. In the same year Taylor was appointed to the Order of Merit. He suffered a stroke in 1972 which effectively put an end to his work; he died in Cambridge in 1975.*Wik

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History