Monday, 30 April 2012

On This Day in Math - April 30

Statue of C. F. Gauss in Braunschweig *Wik

I mean the word proof not in the sense of the lawyers,
who set two half proofs equal to a whole one,
but in the sense of a mathematician, 
where half a proof is zero,
and it is demanded for proof that 
every doubt becomes impossible.
Karl Friedrich Gauss As quoted in Calculus Gems (1992) by George F. Simmons

The 121st day of the year; 121 will be the largest year day for which n!+1 is a square number. Brocard conjectured in 1904 that the only solutions of n! + 1 = m2 are n = 4, 5, and 7. There are no other solutions with n < 10^ 9. 121 is also the only square of the form 1 + n + n2+ n3 + n4. *What's So Special About This Number

121 is also a Smith Number, a composite number for which the sum of its digits is equal to the sum of the digits in its prime factorization. Smith numbers were named by Albert Wilansky of Lehigh University. He noticed the property in the phone number (493-7775) of his brother-in-law Harold Smith:
4937775 = 3 × 5 × 5 × 65837, while 4 + 9 + 3 + 7 + 7 + 7 + 5 = 3 + 5 + 5 + 6 + 5 + 8 + 3 + 7 = 42.
There are 49 Smith numbers below 1000, collect the whole set.

In 1006, Chinese and Arabic astronomers noted a supernova. The speed of the still-expanding shock wave was measured nearly a millenium later. This was history's brightest "new star" ever recorded, at first seen to be brighter than the planet Venus. It occurred in our Milky Way galaxy, appearing in the southern constellation Lupus, near the star Beta Lupi. It was also recorded by observers in Switzerland, Italy, Japan, Egypt and Iraq. From the careful descriptions of the Chinese astronomers of how the light varied, that it was of apparently yellow color and visible for over a year, it is possible that the supernova reached a magnitude of up to -9. Modern measurements of the speed of the shock wave have been used to estimate its distance. *TIS The associated supernova remnant from this explosion was not identified until 1965, when Doug Milne and Frank Gardner used the Parkes radio telescope to demonstrate that the previously known radio source PKS 1459-41, near the star Beta Lupi, had the appearance of a 30-arcminute circular shell.

1633 Galileo was forced to recant his scientific findings related to the Copernican Theory as “abjured, cursed and detested” by the Inquisition. He was placed under house arrest for the remaining nine years of his life. Legend had it that when Galileo rose from knealing before his inquisitors, he murmured, “e pur, si mouve”—“even so, it does move.” *VFR [church doctrine held that the Earth, God's chosen place, was the center of the universe and everything revolved around it. Copernicans believed that the sun was the center of the solar system, and "the earth moves" around it.]

In 1683, the Boston Philosophical Society held its first meeting.* Rev. Increase Mather, stimulated by a recent comet sighting, and seeking to discuss how God intervenes in the natural order of things, had met earlier in the month with Samuel Willard and a few others to plan the group. Mather's idea was to model their meetings on the Royal Philosophical Society, established in London about 20 years earlier. Each last Monday of most of the following months, the members met and presented papers to emulate the transactions of the London society. However, the few local intellectuals didn't sustain interest in the society beyond about three years. Mather wrote Kometographia, or, A Discourse concerning Comets (1683).*TIS

1695 Bernoulli explains to Leibniz his reasons for the use of the term "integral calculus" for Leibniz's new calculus. Leibniz had used, and tried to get others to use "Sums" but Bernoulli's term had become popular. Bernoulli explained that, "I considered the differential as the infinitesimal part of the whole, or Integral." *VFR

1837 Massachusetts became the first state to establish a board of education. *VFR

1891 Nature magazine publishes Peter Guthrie Tait's "The Role of Quaternions in the Algebra of Vectors."

1895 Georg Cantor, in a letter to Felix Klein, explains the choice of aleph for the cardinality of sets.
In the same letter he comments that, "the usual alphabets seem to me too much used to be fitter for the purpose. On the other hand, I did not want to invent a new symbol, so I chose finally the aleph, which in Hebrew has also the numerical value 1."
*Cantorian Set Theory and Limitation of Size, By Michael Hallett

1897, at the Royal Institution Friday Evening Discourse, Joseph John Thomson (1856-1940) first announced the existence of electrons (as they are now named). Thomson told his audience that earlier in the year, he had made a surprising discovery. He had found a particle of matter a thousand times smaller than the atom. He called it a corpuscle, meaning "small body." Although Thomson was director of the Cavendish Laboratory at the University of Cambridge, and one of the most respected scientists in Great Britain, the scientists present found the news hard to believe. They thought the atom was the smallest and indivisible part of matter that could exist. Nevertheless, the electron was the first elementary particle to be discovered.*TIS

1916 Daylight Saving Time has been used in the U.S. and in many European countries since World War I. At that time, in an effort to conserve fuel needed to produce electric power, Germany and Austria took time by the forelock, and began saving daylight at 11:00 p.m. on April 30, 1916, by advancing the hands of the clock one hour until the following October. *

1982 Science (pp. 505–506) reported that Stanford magician-statistician Perci Diaconis solved the problem of which arrangements of a deck of cards can occur after repeated perfect rifflee shuffles. The answer involves M12, one of the Mathieu simple groups. Mathematics Magazine 55 (1982),
p. 245].*VFR

1984 30 April-4 May 1984. Teacher Appreciation Week. Celebrated the first week of May in Flint, MI. *VFR

1992 The New York Times “in describing the discovery of the new Mersenne prime, felt it necessary to describe the series of primes, which, (according to them) goes: 1, 2, 3, 5, 7, 11, 13, ... . You will notice that they have slipped in what must be another discover (by one of their writers?) of the world’s smallest prime: 1. I’m sure the mathematicians of the world must be tearing their hair out for having missed this one.” [A posting of Ron Rivest to the net.] (In fact it was common prior to the 20th century to consider one as a prime, not that that is an excuse in 1992.)

1993 – CERN announces World Wide Web protocols will be free. *Wik

2011 Walpurgis night or Witches’ Sabbath is celebrated on the eve of May Day, particularly by university students in northern Europe. *VFR According to the ancient legends, this night was the last chance for witches and their nefarious cohorts to stir up trouble before Spring reawakened the land. They were said to congregate on Brocken, the highest peak in the Harz Mountains - a tradition that comes from Goethe's Faust. *Wik

1777 Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.
Sometimes referred to as the Princeps mathematicorum (Latin, "the Prince of Mathematicians" or "the foremost of mathematicians") and "greatest mathematician since antiquity", Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history's most influential mathematicians. He referred to mathematics as "the queen of sciences".. *Wik
His poorly educated mother couldn’t remember his birthdate, but could relate it to a movable religious feast. To confirm the date of his birth Gauss developed a formula for the date of Easter. *VFR
He transformed nearly all areas of mathematics, for which his talent showed from a very early age. For his contributions to theory in magnetism and electricity, a unit of magnetic field has been named the gauss. He devised the method of least squares in statistics, and his Gaussian error curve remains well-known. He anticipated the SI system in his proposal that physical units should be based on a few absolute units such as length, mass and time. In astronomy, he calculated the orbits of the small planets Ceres and Pallas by a new method. He invented the heliotrope for trigonometric determination of the Earth's shape. With Weber, he developed an electromagnetic telegraph and two magnetometers. *TIS He proved that the heptadecagon (17 gon) was constructable (see April 8) with straight-edge and compass. Dave Renfro has a complete and elementary proof.

1904 George Robert Stibitz (30 Apr 1904, 31 Jan 1995) U.S. mathematician who was regarded by many as the "father of the modern digital computer." While serving as a research mathematician at Bell Telephone Laboratories in New York City, Stibitz worked on relay switching equipment used in telephone networks. In 1937, Stibitz, a scientist at Bell Laboratories built a digital machine based on relays, flashlight bulbs, and metal strips cut from tin-cans. He called it the "Model K" because most of it was constructed on his kitchen table. It worked on the principle that if two relays were activated they caused a third relay to become active, where this third relay represented the sum of the operation. Also, in 1940, he gave a demonstration of the first remote operation of a computer.*TIS

1916 Claude Shannon (30 April 1916 in Gaylord, Michigan, USA - 24 Feb 2001 in Medford, Massachusetts, USA) founded the subject of information theory and he proposed a linear schematic model of a communications system. His Master's thesis was on A Symbolic Analysis of Relay and Switching Circuits on the use of Boole's algebra to analyse and optimise relay switching circuits. *SAU While working with John von Neumann on early computer designs, (John) Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948. Among several statues to Shannon, one is erected in his hometown of Gaylord, Michigan. The statue is located in Shannon Park in the center of downtown Gaylord. Shannon Park is the former site of the Shannon Building, built and owned by Claude Shannon's father.
While working with John von Neumann on early computer designs, (John) Tukey introduced the word "bit" as a contraction of "binary digit". The term "bit" was first used in an article by Claude Shannon in 1948.

1865 Robert Fitzroy British naval officer, hydrographer, and meteorologist who commanded the voyage of HMS Beagle, aboard which Charles Darwin sailed around the world as the ship's naturalist. That voyage provided Darwin with much of the material on which he based his theory of evolution. Fitzroy retired from active duty in 1850 and from 1854 devoted himself to meteorology. He devised a storm warning system that was the prototype of the daily weather forecast, invented a barometer, and published The Weather Book (1863). His death was by suicide, during a bout of depression. *TIS
[FitzRoy is buried in the front church yard of All Saints Church in Upper Norwood, London. His memorial was restored by the Meteorological Office in 1981]

1907 Charles Howard Hinton​ (1853, 30 April 1907) was a British mathematician and writer of science fiction works titled Scientific Romances. He was interested in higher dimensions, particularly the fourth dimension, and is known for coining the word tesseract and for his work on methods of visualizing the geometry of higher dimensions. He also had a strong interest in theosophy.
Hinton created several new words to describe elements in the fourth dimension. According to OED, he first used the word tesseract in 1888 in his book A New Era of Thought. He also invented the words "kata" (from the Greek "down from") and "ana" (from the Greek "up toward") to describe the two opposing fourth-dimensional directions—the 4-D equivalents of left and right, forwards and backwards, and up and down.
Hinton was convicted of bigamy for marrying both Mary Ellen (daughter of Mary Everest Boole and George Boole, the founder of mathematical logic) and Maud Wheldon. He served a single day in prison sentence, then moved with Mary Ellen first to Japan (1886) and later to Princeton University in 1893 as an instructor in mathematics.
In 1897, he designed a gunpowder-powered baseball pitching machine for the Princeton baseball team's batting practice. According to one source it caused several injuries, and may have been in part responsible for Hinton's dismissal from Princeton that year. However, the machine was versatile, capable of variable speeds with an adjustable breech size, and firing curve balls by the use of two rubber-coated steel fingers at the muzzle of the pitcher. He successfully introduced the machine to the University of Minnesota, where Hinton worked as an assistant professor until 1900, when he resigned to move to the U.S. Naval Observatory in Washington, D.C.
At the end of his life, Hinton worked as an examiner of chemical patents for the United States Patent Office. He died unexpectedly of a cerebral hemorrhage on April 30, 1907. One source colorfully suggests that his death came he when he died suddenly after being asked to give a toast to "female philosophers" at the Society of Philanthropic Inquiry meeting. *Wik

1957 Konrad Knopp was a German mathematician who worked on generalised limits and complex functions. He was the co-founder of Mathematische Zeitschrift in 1918. *SAU
[His "Theory and application of infinite series" seems to be fully available on Google Books]

1977 Charles Fox (17 March 1897 in London, England - 30 April 1977 in Montreal, Canada) Fox's main contributions were on hypergeometric functions, integral transforms, integral equations, the theory of statistical distributions, and the mathematics of navigation. In the theory of special functions he introduced an H-function with a formal definition. It is a type of generalisation of a hypergeometric function and related ideas can be found in the work of Salvatore Pincherle, Hjalmar Mellin, Bill Ferrar, Salomon Bochner and others. He wrote only one book An introduction to the calculus of variations (1950, 2nd edition 1963, reprinted 1987). *SAU

1989 Gottfried Maria Hugo Köthe (25 December 1905 in Graz; 30 April 1989 in Frankfurt) was an Austrian mathematician working in abstract algebra and functional analysis. Köthe received a fellowship to visit the University of Göttingen, where he attended the lectures of Emmy Noether and Bartel van der Waerden on the emerging subject of abstract algebra. He began working in ring theory and in 1930 published the Köthe conjecture stating that a sum of two left nil ideals in an arbitrary ring is a nil ideal. By a recommendation of Emmy Noether, he was appointed an assistant of Otto Toeplitz in Bonn University in 1929–1930. During this time he began transition to functional analysis. He continued scientific collaboration with Toeplitz for several years afterward. Köthe's best known work has been in the theory of topological vector spaces. In 1960, volume 1 of his seminal monograph Topologische lineare Räume was published (the second edition was translated into English in 1969). It was not until 1979 that volume 2 appeared, this time written in English. He also made contributions to the theory of lattices.*WIK

*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*SAU=St Andrews Univ. Math History
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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