The mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which nature has chosen.
The 293rd day of the year; 293 is a Sophie Germain Prime. (A prime number p such that 2p + 1 is also prime.)
1698 Halley began a scientific voyage on HMS Paramore & set out to measure magnetic variation & search for Terra Incognita. His log entry from the 20th says "Wind WSW a Small Gale I sailed from Deptford about Noon " *Kate Morant@KateMorant (Deptford is a small area near Greenwich, east of London along the Thames)
1735 Benjamin Franklin’s paper “On the Usefulness of Mathematics,” appeared in the Pennsylvania Gazette. [NCTM yearbook # 32(1970), p. 20]*VFR
1744 In Euler's missing letter of October 20, 1744, Euler announced that he had just discovered a simple curve that exhibited something called a cusp of the second kind or a ramphoid from the Greek for a bird’s beak. L'H^opital (1661-1704) is responsible for defining these two types of cusps. In 1740, Jean-Paul de Gua de Malves (1713- 1785) published a proof that no algebraic curve could have a cusp of the second kind in [Gua de Malves 1740]. Euler was familiar with Gua de Malves' work and had initially accepted his result, but in 1744 he discovered that there was a subtle flaw in the supposed proof. In this letter, he wrote to Cramer that even in the fourth order there is a curved line of this kind, whose equation is, y4- 2xy2 + x2 = x3+ 4yx, which simplifies to y = x(1/2) +/- x(3/4)
*Ed Sandifer, How Euler Did It, MAA
1881 In a letter to Newcomb dated Oct. 20, 1881, Sylvester writes, "Who is to be the new superintendent of the Coast Survey?
Why should you not allow it to be known that you would accept the appointment supposing you would be willing to do so!" Sylvester was the eminent British mathematician who served as the first chairman of the Department of Mathematics at the Johns Hopkins University (1876-1883). He returned to England in 1884 to occupy the chair of Savilian Professor of Geometry at Oxford. *THE CHARLES S. PElRCE-SIMON NEWCOMB CORRESPONDENCE
1975 The Public Record office in London released information on the Colossus, one of the ﬁrst programmable electronic digital computers. It was built in 1943 for work on cryptography. The Colossus machines were electronic computing devices used by British codebreakers to help read encrypted German messages during World War II. They used vacuum tubes (thermionic valves) to perform the calculations.
Colossus was designed by engineer Tommy Flowers with input from Harry Fensom, Allen Coombs, Sidney Broadhurst and William Chandler at the Post Office Research Station, Dollis Hill to solve a problem posed by mathematician Max Newman at Bletchley Park. The prototype, Colossus Mark 1, was shown to be working in December 1943 and was operational at Bletchley Park by February 1944. An improved Colossus Mark 2 first worked on 1 June 1944, just in time for the Normandy Landings. Ten Colossi were in use by the end of the war. No information about the computer was released until this date. *Wik
1983, the length of the meter was redefined by the international body Conférence Générale des Poids et Mesures (GCPM) by a method to give greater accuracy. Originally based on one ten-millionth of the distance from the North Pole to the equator, the meter was re-established as the distance that light travels in a vacuum in 1/299,792,458 of a second *TIS
2004 The First Ubuntu Linux Distribution Released. Ubuntu is a free computer operating system based on Debian GNU/Linux. Its name loosely translated from the Zulu means "humanity," or "a person is a person only through other people." Ubuntu is intended to provide an up-to-date, stable operating system for the average user, with a strong focus on usability and ease of installation. Ubuntu has been rated the most popular Linux distribution for the desktop, claiming approximately 30 percent of desktop Linux installations, according to the 2007 Desktop Linux Market survey. Ubuntu is open source and free. It is sponsored by Canonical Ltd, which is owned by South African entrepreneur Mark Shuttleworth.*CHM
1632 Sir Christopher Wren (20 Oct 1632; 25 Feb 1723) Architect, astronomer, and geometrician who was the greatest English architect of his time whose famous masterpiece is St. Paul's Cathedral, among many other buildings after London's Great Fire of 1666. Wren learned scientific skills as an assistant to an eminent anatomist. Through astronomy, he developed skills in working models, diagrams and charting that proved useful when he entered architecture. He inventing a "weather clock" similar to a modern barometer, new engraving methods, and helped develop a blood transfusion technique. He was president of the Royal Society 1680-82. His scientific work was highly regarded by Sir Isaac Newton as stated in the Principia. *TIS (I love the message on his tomb in the Crypt of St. Pauls: Si monumentum requiris circumspice ...."Reader, if you seek his monument, look about you."
1863 William Henry Young (20 Oct 1863 in London, England - 7 July 1942 in Lausanne, Switzerland) discovered Lebesgue integration, independently but 2 years after Lebesgue. He studied Fourier series and orthogonal series in general.
1865 Aleksandr Petrovich Kotelnikov (20 Oct 1865 in Kazan, Russia - 6 March 1944 in Moscow, USSR) In 1927 he published one of his most important works, The Principle of Relativity and Lobachevsky's Geometry. He also worked on quaternions and applied them to mechanics and geometry. Among his other major pieces of work was to edit the Complete Works of two mathematicians, Lobachevsky and Zhukovsky. He received many honours for his work, being named Honoured Scientist in 1934, then one year before he died he was awarded the State Prize of the USSR. *SAU
1891 Sir James Chadwick (20 Oct 1891; 24 Jul 1974) English physicist who received the Nobel Prize for Physics (1935) for his discovery of the neutron. He studied at Cambridge, and in Berlin under Geiger, then worked at the Cavendish Laboratory with Rutherford, where he investigated the structure of the atom. He worked on the scattering of alpha particles and on nuclear disintegration. By bombarding beryllium with alpha particles, Chadwick discovered the neutron - a neutral particle in the atom's nucleus - for which he received the Nobel Prize for Physics in 1935. In 1932, Chadwick coined the name "neutron," which he described in an article in the journal Nature. He led the UK's work on the atomic bomb in WW II, and was knighted in 1945. *TIS
1904 Hans Lewy (October 20, 1904 – August 23, 1988) was an American mathematician, known for his work on partial differential equations and on the theory of functions of several complex variables.*Wik
1914 R. H. Bing (October 20, 1914, Oakwood, Texas – April 28, 1986, Austin, Texas) was an American mathematician who worked mainly in the areas of geometric topology and continuum theory. His first two names were just single letters that do not stand for anything. Bing's mathematical research was almost exclusively in 3-manifold theory and in particular, the geometric topology of R3. The term Bing-type topology was coined to describe the style of methods used by Bing.
Bing established his reputation early on in 1946, soon after completing his Ph.D. dissertation, by solving the Kline sphere characterization problem. In 1948 he proved that the pseudo-arc is homogeneous, contradicting a published but erroneous 'proof' to the contrary. In 1951 he proved results regarding the metrizability of topological spaces, including what would later be called the Bing-Nagata-Smirnov metrization theorem.*Wik
Maestlin studied theology, mathematics, and astronomy/astrology at the Tübinger Stift in Tübingen, a town in Württemberg. He graduated as Magister in 1571 and became in 1576 a Lutheran deacon in Backnang, continuing his studies there.
In 1580 he became a Professor of mathematics, first at the University of Heidelberg, then at the University of Tübingen where he taught for 47 years from 1583. In 1582 Maestlin wrote a popular introduction to astronomy.
Among his students was Johannes Kepler (1571-1630). Although he primarily taught the traditional geocentric Ptolemaic view of the solar system, Maestlin was also one of the first to accept and teach the heliocentric Copernican view. Maestlin corresponded with Kepler frequently and played a sizable part in his adoption of the Copernican system. Galileo Galilei's adoption of heliocentrism was also attributed to Maestlin.
The first known calculation  of the reciprocal of the golden ratio as a decimal of "about 0.6180340" was written in 1597 by Maestlin in a letter to Kepler.
He is also remembered for :
Catalogued the Pleiades cluster on 24 December 1579. Eleven stars in the cluster were recorded by Maestlin, and possibly as many as fourteen were observed.
Occultation of Mars by Venus on 13 October 1590, seen by Maestlin at Heidelberg. *Wik
1896 François-Félix Tisserand (13 Jan 1845, 20 Oct 1896) French astronomer whose 4-volume textbook Traité de mécanique céleste (1889-96; "Treatise on Celestial Mechanics") updated Pierre-Simon Laplace's work. At age 28, he was named Director at Toulouse Observatory (1873-78). He went to Japan to observe the 1874 transit of Venus. The 83-cm telescope he installed at the Toulouse Observatory in 1875 had a wooden base insufficiently stable for photographic work, but he was able to use it for observation of the satellites of Jupiter and of Saturn. From 1892 until his death he was director of the Paris Observatory, where he completed the major work, Catalogue photographique de la carte du ciel, and arranged for its publication.*TIS
1972 Harlow Shapley (2 Nov 1885, 20 Oct 1972) Astronomer, known as "The Modern Copernicus," who discovered the Sun's position in the galaxy. From 1914 to 1921 he was at Mt. Wilson Observatory, where he calibrated Henrietta S. Leavitt's period vs. luminosity relation for Cepheid variable stars and used it to determine the distances of globular clusters. He boldly and correctly proclaimed that the globulars outline the Galaxy, and that the Galaxy is far larger than was generally believed and centered thousands of light years away in the direction of Sagittarius. In the early 1920's, Shapley entered a "Great Debate" with Heber D. Curtis. They truly argued over the "Scale of the Universe."*TIS
1974 Harold Ruse graduated from Oxford and held a position at Edinburgh University. he later became a professor at Southampton and Leeds. He worked on Harmonic Spaces. He became Secretary of the EMS in 1930 and President in 1935. *SAU
1984 Paul A.M. Dirac (8 Aug 1902, 20 Oct 1984) English physicist and mathematician who originated quantum mechanics and the spinning electron theory. In 1933 he shared the Nobel Prize for Physics with the Austrian physicist Erwin Schrödinger.*TIS
1987 Andrey Nikolayevich Kolmogorov (25 Apr 1903, 20 Oct 1987) Russian mathematician whose basic postulates for probability theory that have continued to be an integral part of analysis. This work had diverse applications such as his study of the motion of planets (1954), or the turbulent air flow from a jet engine (1941). In topology, he investigated cohomology groups. He made a major contribution to answering the probability part of Hilbert's Sixth Problem, and completely resolved (1957) Hilbert's Thirteenth Problem. Kolmogorov was active in a project to provide special education for gifted children, not only by writing textbooks and in teaching them, but in expanding their interests to be not necessarily in mathematics, but with literature, music, and healthy activity such as on hikes and expeditions. *TIS
*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