**Suppose a contradiction were to be found in the axioms of set theory.**

**Do you seriously believe that a bridge would fall down?**

The 19th day of the year; 19 is the smallest number n such that n

^{n}contains all 10 digits *Number Gossip

**EVENTS**

**1581**Andreas Dudith (1533–1589), mathematician and opponent of astrology, argued in a letter that observations of the comet of 1577 proved the Aristotelian explanation fallacious (for Aristotle, comets were accidental exhalations of hot air from the earth that rise in the sublunar sphere). Dudith’s use of mathematically precise observations to criticize a general physical theory of Aristotle betokens Galileo’s work ﬁfty years later. *VFR

**1671**Wren and Hooke make a joint presentation on Hooke’s idea of arch design by using gravity and chain links to form an inverted dome. *Lisa Jardine, Ingenious Pursuits, pg 72

**In 1894**, Professor James Dewar exhibited several properties of liquid air, and produced solid air, at the Friday meeting of the Royal Institution. He had previously there exhibited, on 5 Jun 1885, liquid air obtained at the temperature of -192ºC. By Mar 1893 he had produced solid air in the form of ice. *TIS

2012 Mountain View, Ca—January 19, 2012—

The Computer History Museum (CHM), the world’s leading institution exploring the history of computing and its ongoing impact on society, today announced its 2012 Fellow Award honorees: Edward A. Feigenbaum, pioneer of artificial intelligence and expert systems; Steve Furber and Sophie Wilson, chief architects of the ARM processor architecture; and Fernando J. Corbató, pioneer of timesharing and the Multics operating system. The four Fellows will be inducted into the Museum’s Hall of Fellows on Saturday, April 28, 2012, at a formal ceremony where Silicon Valley insiders, technology leaders, and Museum supporters will gather to celebrate the accomplishments of the Fellows and their impact on society. This year’s celebration commemorates the 25th Anniversary of the Fellow Awards and will reunite pioneers from more than two decades.*CHM

**BIRTHS**

**1736 James Watt**(19 Jan 1736; 19 Aug 1819) Scottish instrument maker and inventor whose steam engine contributed substantially to the Industrial Revolution. In 1763 he repaired the model of Newcomen's steam engine belonging to Glasgow University, and began experiments on properties of steam. The Newcomen engine was simple in design: it acted as a pump and a jet of cold water was used to condense the steam. Watt improved on this design by adding a separate condenser and a system of valves to make the piston return to the top of the cylinder after descending. He took out a patent for the separate condenser in 1769. He later adapted the engine to rotary motion, making it suitable for a variety of industrial purposes, and invented the flywheel and the governor. *TIS

**1747 Johann Elert Bode**(19 Jan 1747; 23 Nov 1826) German astronomer best known for his popularization of Bode's law. In 1766, his compatriot Johann Titius had discovered a curious mathematical relationship in the distances of the planets from the sun. If 4 is added to each number in the series 0, 3, 6, 12, 24,... and the answers divided by 10, the resulting sequence gives the distances of the planets in astronomical units (earth = 1). Also known as the Titius-Bode law, the idea fell into disrepute after the discovery of Neptune, which does not conform with the 'law' - nor does Pluto. Bode was director at the Berlin Observatory, where he published Uranographia (1801), one of the first successful attempts at mapping all stars visible to the naked eye without any artistic interpretation of the stellar constellation figures.*TIS

**1833 Rudolf Friedrich Alfred Clebsch**(19 Jan 1833 in Königsberg, Germany (now Kaliningrad, Russia) - 7 Nov 1872 in Göttingen, Germany) Clebsch described the plane representations of various rational surfaces, especially that of the general cubic surface. Clebsch must also be credited with the first birational invariant of an algebraic surface, the geometric genus that he introduced as the maximal number of double integrals of the first kind existing on it.

Clebsch's brilliant career came to a sudden end in 1872 when he died of diphtheria. Max Noether and Brill, who were among his students at Giessen, continued his work on curves. Two volumes of his lectures on geometry were published after his death in 1876 and 1891. A second edition of part of one of these volumes, with Clebsch as joint author, was published in three parts in 1906, 1910 and 1932. *SAU

**1851 Jacobus Cornelius Kapteyn**(19 Jan 1851; 18 Jun 1922) Dutch astronomer who used photography and statistical methods in determining the motions and spatial distribution of stars. Such work was the first major step after the works of William and John Herschel. He tried to solve the questions of space density of stars as a function of distance from the sun, and the distribution of starts according to brightness per unit volume. Some of his results had lasting value, but some were superceded because he had failed to account for the interstellar absorption. In studies using proper motion to determine stellar distances, he discovered stellar motions are not random, as previously thought, but that stars move in two "star streams" (1904). He introduced absolute magnitude and colour index as standard concepts.*TIS

**1879 Guido Fubini**(19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini's theorem and the Fubini–Study metric.

Born in Venice, he was steered towards mathematics at an early age by his teachers and his father, who was himself a teacher of mathematics. He gained some early fame when his 1900 doctoral thesis, entitled Clifford's parallelism in elliptic spaces, was discussed in a widely-read work on differential geometry published by Bianchi in 1902.

During this time his research focused primarily on topics in mathematical analysis, especially differential equations, functional analysis, and complex analysis; but he also studied the calculus of variations, group theory, non-Euclidean geometry, and projective geometry, among other topics. With the outbreak of World War I, he shifted his work towards more applied topics, studying the accuracy of artillery fire; after the war, he continued in an applied direction, applying results from this work to problems in electrical circuits and acoustics. *Wik

**1908 Aleksandr Gennadievich Kurosh**(19 Jan 1908 in Yartsevo (near Smolensk), Russia - 18 May 1971 in Moscow) proved important results in Group Theory and is best-known as the author of one of the standard text-books in the subject.*SAU

**1911 Garrett Birkhoff**(January 19, 1911, Princeton, New Jersey, USA – November 22, 1996, Water Mill, New York, USA) was an American mathematician. He is best known for his work in lattice theory.During the 1930s, Birkhoff, along with his Harvard colleagues Marshall Stone and Saunders Mac Lane, substantially advanced American teaching and research in abstract algebra. During and after World War II, Birkhoff's interests gravitated towards what he called "engineering" mathematics. Birkhoff's research and consulting work (notably for General Motors) developed computational methods besides numerical linear algebra, notably the representation of smooth curves via cubic splines.

The mathematician George Birkhoff (1884–1944) was his father.*Wik

**1912 Leonid Vitalyevich Kantorovich**(19 Jan 1912; 7 Apr 1986) Soviet mathematician and economist who shared the 1975 Nobel Prize for Economics with Tjalling Koopmans for their work on the optimal allocation of scarce resources. Kantorovich's background was entirely in mathematics but he showed a considerable feel for the underlying economics to which he applied the mathematical techniques. He was one of the first to use linear programming as a tool in economics and this appeared in a publication Mathematical methods of organising and planning production which he published in 1939. The mathematical formulation of production problems of optimal planning was presented here for the first time and the effective methods of their solution and economic analysis were proposed. *TIS

**1917 Graham Higman**(19 Jan 1917 in Louth, Lincolnshire, England - 8 April 2008 in Oxford, England) is known for his outstanding work in all aspects of the theory of groups. He published on units in group rings, the subject of his doctoral thesis, in 1940 then there was a break in his publication record during the time he worked in the Meteorological Office. His 1948 papers are on somewhat different topics, being on topological spaces and linkages. They show the influences of Henry Whitehead and, to a lesser extent, Max Newman. *SAU

**DEATHS**

**1878 Henri-Victor Regnault**(21 Jul 1810, 19 Jan 1878) French chemist and physicist noted for his work on the properties of gases. His invaluable work was done as a skilful, thorough, patient experimenter in determining the specific heat of solids, liquids, gases, and the vapour-tensions of water and other volatile liquids, as well as their latent heat at different temperatures. He corrected Mariotte's law of gases concerning the variation of the density with the pressure, determined the coefficients of expansion of air and other gases, devised new methods of investigation and invented accurate instruments. Two laws governing the specific heat of gases are named after him. *TIS

**1913 Robert Gauss**of Denver and his brother

**Charles H. Gauss**of Saint Louis both died on this date. They are grandsons of the mathematician Carl Friedrich Gauss *VFR (Robert died within a few hours of his brother, Charles Henry Gauss. Both died from heart disease.)The names of all the grandchildren of Gauss were listed in a letter from Robert to Felix Klein regarding the biography of Gauss which was being prepared:

P. S. The names and the present places of residence of the grandchildren of Carl Friedrich Gauss, who were born in the United States and are now living, are as follows:

The children of Eugene Gauss: Charles Henry Gauss, St. Charles, Missouri; Robert Gauss, Denver, Colorado; Albert F. Gauss, Los Angeles, California.

The children of William Gauss: Charles Friedrich Gauss, St. Louis, Missouri; Oscar W. Gauss, Greeley, Colorado; Mary Gauss, St. Louis, Missouri; William T. Gauss, Colorado Springs, Colorado; Joseph Gauss, St. Louis, Missouri.

The only one of the great-grandchildren of Carl Friedrich Gauss born in the United States, who has ever visited Germany is Helen W. Gauss, daughter of William T. Gauss of Colorado Springs, Colorado. while in Germany last year she was present at the dedication of the Gauss tower on the Hohenhagen.

**1930 Frank Plumpton Ramsey**(22 Feb 1903, 19 Jan 1930) English mathematician, logician and philosopher who died at age 26, but had already made significant contributions to logic, philosophy of mathematics, philosophy of language and decision theory. He remains noted for his Ramsey Theory, a mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. This theory spans various fields of mathematics, including combinatorics, geometry, and number theory. His papers show he was also a remarkably creative and subtle philosopher. *TIS His father Arthur, also a mathematician, was President of Magdalene College. His brother, Michael Ramsey, later became Archbishop of Canterbury. Suffering from chronic liver problems, Ramsey contracted jaundice after an abdominal operation and died on 19 January 1930 at Guy's Hospital in London at the age of 26. He is buried at the Parish of the Ascension Burial Ground in Cambridge, UK.*Wik

**1954 Theodor Franz Eduard Kaluza**(9 November 1885, Wilhelmsthal, today part of Opole – 19 January 1954, Göttingen) was a German mathematician and physicist known for the Kaluza-Klein theory involving field equations in five-dimensional space. His idea that fundamental forces can be unified by introducing additional dimensions re-emerged much later in string theory. *Wik

**2007 Asger Hartvig Aaboe**(April 26, 1922 – January 19, 2007) was a historian of the exact sciences and mathematician who is known for his contributions to the history of ancient Babylonian astronomy. He studied mathematics and astronomy at the University of Copenhagen, and in 1957 obtained a PhD in the History of Science from Brown University, where he studied under Otto Neugebauer, writing a dissertation "On Babylonian Planetary Theories". In 1961 he joined the Department of the History of Science and Medicine at Yale University, serving as chair from 1968 to 1971, and continuing an active career there until retiring in 1992. In his studies of Babylonian astronomy, he went beyond analyses in terms of modern mathematics to seek to understand how the Babylonians conceived their computational schemes. *Wik

Credits

*VFR = V Frederick Rickey, USMA

*TIS= Today in Science History

*Wik = Wikipedia

*SAU=St Andrews Univ. Math History

*CHM=Computer History Museum

*FFF=Kane, Famous First Facts