**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

19 is also the smallest base ten number that is NOT a palindrome in any base \(2 \leq b \leq 10\) Seems strange that it is the first palindrome (with more than one character) in Roman Numerals XIX.

19⁵ + 19² + 19¹ + 19³ + 19⁵ + 19⁶ + 19⁴ + 19⁰ = 52135640 *Jim Wilder@wilderlab

This 19 digit number is a strobogrammatic palindrome prime (rotate it 180 degrees and it still is a palindrome prime ) and 666 in the middle. 11911961

*666*16911911, with a hat tip to INDER JEET TANEJA@IJTANEJA

Speaking of Prime Speed signs, here's two from Lamplighter way on the approach to Northfield Mount Hermon HS in Massachusetts. (HT to @centerofmath)

**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 Thony Christie points out that " problem is that Hagecius, and through him Dudith, were by no means the only people to accept that parallax measurements showed comets to be supra-lunar thus contradicting the Aristotelian theory of comets, as seems to be implied here. Amongst others, both Tycho and Michael Maestlin, Kepler’s teacher, who were much more influential than Dudith, had also reached this conclusion. In fact much earlier in the sixteenth century, based on their observations of the 1530s comets, Gemma Frisius, Jean Pena, Girolamo Fracastoro and Gerolamo Cardano had already reached the same conclusion" *RMAT You can read his entire post here.

**1669/70**Newton writes to John Collins to provide a solution to a question about evaluating a series of fractions with a common numerator and denominators in an arithmetic sequence. Newton provides an exact solution and then an approximation that converges to the true solution. [a translation is here] *Newton Project

**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

**1784**A huge Montgolfiere hot air balloon carried seven passengers to a height of 3,000 feet over the city of Lyons.

At the time, the Montgolfiers believed they had discovered a new gas (they called Montgolfier gas) that was lighter than air and caused the inflated balloons to rise. In fact, the gas was merely air, which became more buoyant as it was heated. *Mary Bellis, History of Airships and Balloons, About.com

**1882**J J Sylvester writes a letter to support a request of two associates that Christine Ladd's fellowship be continued for another year. She had been allowed to attend the all-male Johns Hopkins in 1878.

*James Joseph Sylvester: Life and Work in Letters By Karen Hunger Parshall

**1887**The Great Southern Comet of 1887 was officially discovered by astronomer John Macon Thome at Córdoba, Argentina, at which point it was located in the constellation Grus. However, correspondence from William Henry Finlay suggests that it may also have been seen from Blauwberg, South Africa, on January 18. At the time of discovery the comet had already passed perihelion a week earlier, and its closest approach to Earth had been a month earlier. A curious feature of the comet was the fact that few, if any observations were made of a cometary head or nucleus. As a result, some older astronomical texts refer to it as the "Headless Wonder". *Wik *David Dickinson @Astroguyz

**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

**1983**The Apple Lisa, the 1st commercial personal computer from Apple to have a graphical user interface & a mouse, is announced. *@LouisTrapani

**1986**First IBM PC computer virus is released. A boot sector virus dubbed (c)Brain, reportedly by Farooq Alvi Brothers in Pakistan. *@LouisTrapani

**2006**The New Horizons probe, launched on Jan. 19, 2006, with Clyde Tombaugh's ashes on board, will arrive at Pluto on July 14, 2015. *The Las Cruces Sun-News

**2016**Great Internet Mersenne Prime Search reported the discovery of the new record largest prime number, 2

^{74,207,281}-1. The huge number has 22,338,618 digits. The record prime was found on a computer loaned by Profesor Curtiss Cooper at the University of Central Missouri. This is the fourth record GIMPS project prime for Dr. Cooper and his university.

In a strange twist, Dr. Cooper's computer reported the prime in GIMPS on September 17, 2015 but it remained unnoticed until routine maintenance data-mined it on January 7th. The official discovery date is January 7th, the day a human took note of the result. The perfect number associated with this new Mersenne prime is over forty-four million digits long. *GIMPS

**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**

**1755 Jean-Pierre Christin**(May 31, 1683 – January 19, 1755) was a French physicist, mathematician, astronomer and musician. His proposal to reverse the Celsius thermometer scale (from water boiling at 0 degrees and ice melting at 100 degrees, to water boiling at 100 degrees and ice melting at 0 degrees) was widely accepted and is still in use today.

Christin was born in Lyon. He was a founding member of the Académie des sciences, belles-lettres et arts de Lyon and served as its Permanent Secretary from 1713 until 1755. His thermometer was known in France before the Revolution as the thermometer of Lyon. *Wik

**1867 Horatio Nelson Robinson,**(Jan 1, 1806; Hartwick, Otsego County, New York - 19 Jan, 1867; Elbridge, New York) received only a common-school education, but early evinced a genius for mathematics, making the calculations for an almanac at the age of sixteen. A wealthy neighbor gave him the means to study at Princeton, and at the age of nineteen he was appointed an instructor of mathematics in the navy, which post he retained for ten years. He then taught an academy at Canandaigua, and afterward one at Genesee, New York, until in 1844 he gave up teaching because his health was impaired, and removed to Cincinnati, Ohio. There he prepared the first of a series of elementary mathematical text-books, which have been adopted in many of the academies and colleges of the United States. In revising and completing the series he had the assistance of other mathematicians and educators. He removed to Syracuse, New York, in 1850, and to Elbridge in 1854. His publications include "University Algebra" (Cincinnati, 1847), with a "Key" (1847) ; "Astronomy, University Edition" (1849) ; " Geometry and Trigonometry" (1850) ; "Treatise on Astronomy" (Albany, 1850) ; "Mathematical Recreations" (Albany, 1851); "Concise Mathematical Operations" (Cincinnati, 1854); "Treatise on Surveying and Navigation" (1857), which, in its revised form, was edited by Oren Root (New York, 1863); "Analytical Geometry and Conic Sections" (New York, 1864) ; "Differential and Integral Calculus" (1861), edited by Isaac F. Quinby (l868). *famousamericans.net

**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 :

*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