Thursday, 19 January 2017

On This Day in Math - January 19

Suppose a contradiction were to be found in the axioms of set theory. 
Do you seriously believe that a bridge would fall down?
~Frank P Ramsey

The 19th day of the year; 19 is the smallest number n such that nn 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. 1191196166616911911, with a hat tip to INDER JEET TANEJA@IJTANEJA


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,

182 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, 274,207,281 -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


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

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). *

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

Wednesday, 18 January 2017

On This Day in Math - January 18

Sooner or later every one of us breathes an atom that has been breathed before by anyone you can think of who has lived before us - Michelangelo or George Washington or Moses.
~Jacob Bronowski

The 18th day of the year; there is only one number (289=172) for which the sum of its proper divisors is 18. (can you figure out which numbers can never appear as the sum of the proper divisors?)

 183=(5+8+3+2)3=5832*jim wilder ‏@wilderlab

And speaking of powers of 18, 18^3 = 5832 and 18^4 = 104976, together they use all ten decimal digits once each. Smallest (only?) such number.*Ben Vitale

Chris Maslanka@ChrisMaslanka pointed out that 18 is involved in another "smallest" number, 
 378 = 2 X 3 X 3 X 3 X 7; sum of these prime factors = 18; sum of the digits of 378 is also 18. The smallest multidigit number for which sum of digits = sum of prime factors.


1663/4 King Charles II’s letter which confirmed the Lucasian statutes forbade the Professor to take any but a Fellow-commoner as his pupil, and Newton was never that. Thus Newton was NEVER Barrow’s pupil. This myth began after Newton’s death with Conduitt’s anecdote of Barrow examining Newton in Euclid as an undergraduate and finding him wanting. Newton did attend Barrow’s lectures in 1665 but would not allow that they were helpful to him; Newton was self-taught in mathematics. [Whiteside, Notes and Records of the Royal Society of London, 19(1964), p. 61; Westfall, p. 99] *VFR

1753 Hans Sloane, whose collection formed the Basis of the British Museum, was buried at Chelsea Old Church with the following memorial:
"In memory of Sir Hans Sloane, Bart, President of the Royal Society and of the College of Physicians, who died in the year of our Lord 1752, the ninety-second year of his age, without least pain of body, and with a conscious serenity of mind ended a virtuous and beneficient life. This monument was erected by his two daughters, Eliza Cadogan and Sarah Stanley".

1800 Thomas Jefferson writes to Joseph Priestley to tell him about the proposed formation of a new college in Virginia, and to seek his input:
" We wish to establish in the upper & healthier country, & more centrally for the state, an University on a plan so broad & liberal & modern, as to be worth patronizing with the public support, and be a temptation to the youth of other states to come and drink of the cup of knowledge & fraternize with us. ...
It has been the subject of consultation among the ablest and highest characters of our State, who only wait for a plan to make a joint & I hope successful effort to get the thing carried into effect. They will receive your ideas with the greatest deference & thankfulness.
*The Letters of Thomas Jefferson,

1802 Gauss read in the newspaper that Olbers had rediscovered Ceres. Gauss wrote to get the observations and a long friendship ensued. Gauss was such an avid newspaper reader that students nicknamed him the “newspaper bear” because of his habits in the library reading room. If someone was reading the paper he wanted he would sit glumly nearby and stare at them until they gave up the paper. *VFR

1844 John Thomas Graves communicated to Sir William Hamilton his theorem respecting sums of eight squares. This is the basis of his work on Octonions. *SAU

1887 The Great Southern Comet of 1887 was officially discovered by astronomer John Macon Thome at Córdoba, Argentina, on Jan 19 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

1895, James Dewar demonstrated the intimate connection between phosphorescence and photographic action of the electric light on bodies cooled to the temperature of boiling liquid air. Presented at the Royal Institution, these experiments were reported as "very remarkable." *TIS

1896, The first x-ray machine is exhibited in the U.S. at Casino Chambers, New York City. For an admission charge of 25 cents, patrons could view the "Parisian sensation" *TIS

1897 The famous Indiana Pi Bill, to change the value of pi to 3 (and several other numbers it seems) was first introduced in the House. See more of this story here.

1916 This 611 gram stone, reported to have struck a house near the town of Baxter, Missouri in 1916.
The meteorite Fell around 9AM, on January 18th, 1916, and was heard and seen by J.W. Jackson, as it hit his house near the town of Baxter. The meteorite broke through the roof, hitting a log beam, and was found in the attic by the homeowners.
The circumstances of the fall were published in a local newspaper, and the Jacksons kept the meteorite until the late 1930s. It was purchased for the Nininger meteorite collection after it came to the attention of H.H. Nininger in 1938. *Center for Meteorite Studies ASU

1938 J.W. Bryce writes a memorandum formalizing IBM's development of a computing machine for Harvard:the Harvard Mark I, completed in 1944. The Harvard Mark I was the first fully automatic machine to be completed and computed three additions or subtractions a second; its memory stored 72 numbers.(I can see my students trying to comprehend this. They laugh out loud when I tell them that my first computer had 4k of memory, embarrassment for me and sure that I MUST have meant 4 meg) Several of J.W. Bryce's major inventions—high-speed multiplying, dividing, cross adding, the read-out, and the emitter—were utilized in the Harvard Mark I. *CHM

1969, pulsars were first identified by University of Arizona astronomers. *TIS

1978 Harvard Sophomore Bill Gates best solution to date of Pancake Sorting Problem is received by Discrete Mathematics Journal, BOUNDS FOR SORTING BY PREFIX REVERSAL William H. GATES , Christos H. PAPADIMITRIOU. The classical solution is two flips per pancake. Gates solution required only 5/3 flips per pancake. *Wik This solution has only recently(2008) been improved. It would be revised in the fall and published in 1979.

1982 Guyana (on the Northeast coast of South America) issued a series of postage stamps celebrating their conversion to the metric system. Can you name two countries that have not yet adopted the metric system? *VFR (The usage of the metric system varies around the world. According to the American Central Intelligence Agency's Factbook, the International System of Units is the official system of measurement for all nations in the world except for Burma, Liberia and the United States... other sources say Liberia has adopted metric system. Russ Rowlett opines that "The U.S. adopted the metric system in 1866. What the U.S. has failed to do is to restrict or prohibit the use of traditional units in areas touching the ordinary citizen: construction, real estate transactions, retail trade, and education." )


1825 Sir Edward Frankland (18 Jan 1825; 9 Aug 1899) English chemist who was one of the first investigators in the field of structural chemistry, invented the chemical bond, and became known as the father of valency. He studied organometallic compounds - hybrid molecules of the familiar organic non-metallic elements (such as carbon, hydrogen, nitrogen, sulphur, phosphorus) with true metals. By 1850, he had prepared small organic molecules containing such metals as zinc. Subsequently, he devised the theory of valence (announced 10 May 1852), that each type of atom has a fixed capacity for combination with other atoms. For his investigations on water purification and for his services to the government as water analyst, Frankland was knighted in 1897.

1856 Luigi Bianchi (18 Jan 1856 in Parma, Italy - 6 June 1928 in Pisa, Italy) made important contributions to differential geometry.*SAU In 1898, Bianchi worked out the Bianchi classification of nine possible isometry classes of three-dimensional Lie groups of isometries of a (sufficiently symmetric) Riemannian manifold. As Bianchi knew, this is essentially the same thing as classifying, up to isomorphism, the three-dimensional real Lie algebras. This complements the earlier work of Lie himself, who had earlier classified the complex Lie algebras.*Wik

1879 Peter Mark Roget (18 Jan 1779; 12 Sep 1869). In 1852, at age 73, he published his famous Thesaurus of English Words and Phrases. He was also one of the founders of the Medical and Chirurgical Society of London. Of more mathematical interest, Roget also invented the log-log scale on slide rules, making exponentiation & roots much easier to calculate. *Wik

1880 Paul Ehrenfest (January 18, 1880 – September 25, 1933) was an Austrian and Dutch physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem. Among his students were Johannes Burgers, Hendrik Kramers, Dirk Coster, George Uhlenbeck and Samuel Goudsmit, who became famous for jointly proposing the concept of electron spin, Jan Tinbergen, Arend Rutgers, Hendrik Casimir, Gerhard Dieke, Dirk Struik, and Gerard Kuiper. His assistants included Yuri Krutkov, Viktor Trkal, Adriaan Fokker, Paul Epstein, and Gregory Breit. Other young foreign scientists who spent an extended period in his laboratory included Gunnar Nordström, Enrico Fermi, Igor Tamm, Oskar Klein, Robert Oppenheimer, Walter Elsasser, Ralph Kronig, Werner Heisenberg, Paul Dirac, and David Dennison.*Wik

1901 Ivan Georgievich Petrovsky (18 Jan 1901 in Sevsk, Orlov guberniya, Russia - 15 Jan 1973 in Moscow, USSR) Petrovsky's main mathematical work was on the theory of partial differential equations, the topology of algebraic curves and surfaces, and probability. Petrovsky also worked on the boundary value problem for the heat equation and this was applied to both probability theory and work of Kolmogorov.*SAU

1908 Jacob Bronowski (18 Jan 1908; 22 Aug 1974) Polish-British mathematician and science writer who eloquently presented the case for the humanistic aspects of science as the writer and presenter of the BBC television series, The Ascent of Man. Bronowski, who had a Ph.D. in algebraic geometry, spent WW II in Operations Research, and was an official observer of the after-effects of the Nagasaki and Hiroshima bombings. After this experience, he turned to biology, to better understand the nature of violence.*TIS

1707 Otto Mencke (22 March (OS) April 2, 1644– 18 Jan (OS) 29 Jan 1707) was a 17th-century German philosopher and scientist. He obtained his doctorate at the University of Leipzig in 1666 with a thesis entitled: Ex Theologia naturali — De Absoluta Dei Simplicitate, Micropolitiam, id est Rempublicam In Microcosmo Conspicuam.
He is notable as being the founder of the very first scientific journal in Germany, established 1682, entitled: Acta Eruditorum. *Wik

1873 Pierre Charles François Dupin (6 Oct 1784 in Varzy, France - 18 Jan 1873 in Paris, France) made contributions to differential geometry and in particular invented the 'Dupin indicatrix' which gives an indication of the local behavior of a surface up to the terms of degree two. His contributions to differential geometry include the introduction of conjugate and asymptotic lines on a surface. *SAU

1963 Edward Charles Titchmarsh (1 Jun 1899, 18 Jan 1963) English mathematician whose contributions to analysis placed him in the forefront of his profession. His contributions helped resolve the differences between the general theory of quantum mechanics and the methods used to solve particular problems in quantum theory. All Titchmarsh's work is in analysis. His early studies were on Fourier series, Fourier integrals, functions of a complex variable, integral equations and the Riemann zeta function. From 1939, Titchmarsh concentrated on the theory of series expansions of eigenfunctions of differential equations, work which helped to resolve problems in quantum mechanics. His work on this topic occupied him for the last 25 years of his life. *TIS

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

Tuesday, 17 January 2017

On This Day in Math - January 17

*New Horizons. August 2001. Artwork commissioned for the New Horizons mission to Pluto. Pluto's horizon spans the foreground, looking past its moon, Charon, toward the distant, star-like Sun. Painting by Dan Durda...who learned some math, but not his art, from me.

Whenever you can, count.
~Sir Francis Galton

The 17th day of the year; there are 17 prime partitions of 17. No other number is equal to its number of prime partitions. (for example, 7 has 3 prime partitions, 7, 3+2+2, and 5+2)

If you write out the numbers from 1 to 5000 in English (e.g., THREE THOUSAND EIGHT HUNDRED SEVENTY-THREE), it turns out that 17 is the only one that has a unique number of characters (nine). (Spaces and hyphens count as characters) .

Also, 17 is the only prime that is equal to the sum of the digits of its cube,173= 4913 *Mario Livio ‏@Mario_Livio

With any number of points less than 17, it is possible to color all the segments between them with two colors without any triangle having all three sides of the same color. With 17 or more, it is not possible.

The sum of the squares of the first seven primes (all primes up to 17) is 666, the "Number of the Beast." \(2^2 + 3^2 + 5^2 + 7^2 + 11^2 + 13^2 + 17^2 = 666 \)

17 mph is an unusual speed limit, but on the campus of Hampshire College in Amherst all the speed limit signs have been changed from 15 to 17 miles per hour to honor retired mathematics professor David Kelly. Kelly spent his career fascinated by the number 17. There is at least two others in the US, at Mountain View, California and Fiesta Mall in Mesa, Az. For those interested, this site lists 17 (of course) interesting facts about 17 from the Professor.
David Kelly at Hampshire College *MSN.COM

photograph from Lowell Observatory
1910 The Great January Comet of 1910, formally designated C/1910 A1 and often referred to as the Daylight Comet appeared in January 1910. It was already visible to the naked eye when it was first noticed, and many people independently "discovered" the comet. At its brightest, it outshone the planet Venus, and was possibly the brightest comet of the 20th century. The first astronomer to properly study the comet was Robert T. A. Innes at the Transvaal Observatory in Johannesburg on January 17, after having been alerted two days earlier by the editor of a Johannesburg newspaper.
The comet reached perihelion on January 17 and was at that time visible in daylight with the unaided eye; following perihelion, it declined in brightness but became a spectacular sight from the northern hemisphere in the evening twilight, its noticeably curved tail reaching up to 50 degrees by early February.
Halley's comet returned on schedule a few months later. *Wik

1929 Edwin Hubble publishes his classic paper,"A relation between distance and radial velocity among extra-galactic nebulae", showing the universe is expanding in The Proceedings of The National Academy of Sciences. *David Dickinson@Astroguyz

In 1949, for the first time, full energy was released by the first synchrotron which was installed at the Radiation Laboratory, University of California, Berkeley. It was invented by Edwin Mattison of the same university, and would accelerate electrons by virtue of their negative charges, using a betatron-type magnet that weighed about 8 tons. The synchrotron was constructed at the General Electric Research Laboratory at Schnectady, N.Y. by Dr. Herbert C. Pollock and Willem F. Westendorp. *TIS

1974 HP introduces the first programmable pocket calculator. The first desktop programmable calculators were produced in the mid-1960s by Mathatronics and Casio (AL-1000). These machines were, however, very heavy and expensive. The first programmable pocket calculator was the HP-65, in 1974; it had a capacity of 100 instructions, and could store and retrieve programs with a built-in magnetic card reader.Bill Hewlett's design requirement was that the calculator should fit in his shirt pocket. That is one reason for the tapered depth of the calculator. The magnetic program cards fed in at the thick end of the calculator under the LED display. The documentation for the programs in the calculator is very complete, including algorithms for hundreds of applications, including the solutions of differential equations, stock price estimation, statistics, and so forth.*Wik

1985 The last day for the card catalog at the New York Public Library. It contained 10 million dog-eared cards in 9,000 oak drawers. It was replaced by 800 bound volumes of photocopies of the cards and a computer catalog. *AP press release, 18 Jan 1985.

1996 Computer is Used in the Discovery of New Planets. Paul Butler and Geoffrey Marcy announced to the American Astronomical Society that they had discovered two new planets using an unconventional computer technique to analyze the movement of stars. Butler and Marcy let computers analyze spectrographic images of stars for eight years, looking for shifts in the light that would imply it is being pulled by the gravity of a planet. The first discovery, a planet orbiting the star 47 Ursae Majoris​, was announced in December 1995 and, since then, this team found 12 planets outside of our solar system.*CHM

1574 Robert Fludd, also known as Robertus de Fluctibus (17 January 1574; Bearsted, Kent, UK – 8 September 1637; London, UK), was a prominent English Paracelsian physician. He is remembered as an astrologer, mathematician, cosmologist, Qabalist and Rosicrucian apologist. He is credited by some with the invention of the thermometer (others credit Cornelis Drebbel, Galileo Galilei or Santorio Santorio).
Fludd is best known for his compilations in occult philosophy. He had a celebrated exchange of views with Johannes Kepler concerning the scientific and hermetic approaches to knowledge.
Between 1598 and 1604, Fludd studied medicine, chemistry and hermeticism on the European mainland. His itinerary is not known in detail. On his own account he spent a winter in the Pyrenees studying theurgy with the Jesuits.
On his return to England, Fludd entered Christ Church, Oxford. In 1605 he graduated M.B. and M.D. He then moved to London, settling in Fenchurch Street, and making repeated attempts to enter the College of Physicians. Fludd encountered problems with the College examiners, both because of his unconcealed contempt for traditional medical authorities, and because of his attitude. After at least six failures, he was admitted in 1609. Subsequently both his career and his standing in the College took a turn very much for the better. He was on good terms with Sir William Paddy. Fludd was one of the first to support in print the theory of the circulation of the blood of the College's William Harvey. To what extent Fludd may have actually influenced Harvey is still debated, in the context that Harvey's discovery is hard to date precisely. The term "circulation" was certainly ambiguous at that time
Fludd's works are mainly controversial. In succession he defended the Rosicrucians against Andreas Libavius, debated with Kepler (claiming the hermetic or "chemical" approach is deeper than the mathematical), argued against French natural philosophers including Gassendi and Mersenne, and engaged in the discussion of the weapon-salve, a form of sympathetic magic, current in the 17th century in Europe, whereby a remedy was applied to the weapon that had caused a wound in the hope of healing the injury it had made. (I suspect much of the success was having the doctors focus on the weapon rather than infecting the wounded body). *Wik

1624 Guarino Guarini (17 Jan 1624; 6 Mar 1683) Italian architect and theologian whose study of
mathematics led him to a career in architecture in which he created the most fantastic geometric elaboration of all baroque churches. In his Santissima Sindone, Guarini created a diaphanous dome - a geometrical optical illusion in the dome made through the use of the actual structure which creates the illusion that the dome recedes farther up into space than it really does. He wrote two architectural treatises and other works that concentrate on his mathematical knowledge. Therein, Guarini discusses Desargue's projective geometry, which reveal a scientific basis for his daring structures. He worked primarily in Turin and Sicily, with his influence stretching into Germany, Austria and Bohemia.*TIS

1647 Elisabeth Catherina Koopmann Hevelius (in Polish also called Elżbieta Heweliusz) (17 Jan 1647 in Danzig, now Gdańsk, Poland - Died: 22 Dec 1693 in Danzig, now Gdańsk, Poland) was the second wife of Johannes Hevelius. Like her husband, she was also an astronomer.
The marriage of the sixteen year old to fifty two year old Hevelius in 1663 allowed her also to pursue her own interest in astronomy by helping him manage his observatory. They had a son, who died soon, and three daughters who survived. Following his death in 1687, she completed and published Prodromus astronomiae (1690), their jointly compiled catalogue of 1,564 stars and their positions.
She is considered one of the first female astronomers, and called "the mother of moon charts". Her life was recently novelized as The Star Huntress (2006).
The minor planet 12625 Koopman is named in her honour, as is the crater Corpman on Venus. *Wik

1706 Benjamin Franklin, (17 Jan 1706; 17 Apr 1790) American scientist. When he observed a balloon launch by the Montgolfier brothers he was asked of what use it was. He replied: Of what use is a new born baby? *VFR
While traveling on a ship, Franklin had observed that the wake of a ship was diminished when the cooks scuttled their greasy water. He studied the effects at Clapham common on a large pond there. "I fetched out a cruet of oil and dropt a little of it on the water...though not more than a teaspoon full, produced an instant calm over a space of several yards square." He later used the trick to "calm the waters" by carrying "a little oil in the hollow joint of my cane." *W. Gratzer, Eurekas and Euphorias, pgs 80,81
American printer and publisher, author, inventor and scientist, and diplomat. He become widely known in European scientific circles for his reports of electrical experiments and theories. He invented a type of stove, still being manufactured, to give more warmth than open fireplaces and the lightning rod, bifocal eyeglasses also were his ideas. Grasping the fact that by united effort a community may have amenities which only the wealthy few can get for themselves, he helped establish institutions people now take for granted: a fire company (1736), a library (1731), an insurance company (1752), an academy (1751), and a hospital (1751). In some cases these foundations were the first of their kind in North America. *TIS

1858 Gabriel Xavier Paul Koenigs (17 January 1858 Toulouse, France – 29 October 1931 Paris, France) was a French mathematician who worked on analysis and geometry. He was elected as Secretary General of the Executive Committee of the International Mathematical Union after the first world war, and used his position to exclude countries with whom France had been at war from the mathematical congresses.*Wik

1868 Louis Couturat (17 Jan 1868 in Ris-Orangis (near Paris), France - 3 Aug 1914 in Between Ris-Orangis and Melun, France), a logician whose historical researches led to the publication of Leibniz’s logical works in 1903.*VFR Couturat was killed in a car accident, his car being hit by the car carrying the orders for mobilization of the French army the day World War I broke out. Ironically he was a noted pacifist. *SAU

1889 Sir Ralph Howard Fowler (17 Jan 1889; 28 Jul 1944) was an English physicist and astronomer whose university education in mathematics led him to working on thermodynamics and statistical mechanics with important applications in physical chemistry. Turning to astronomy, he collaborated with Arthur Milne on the spectra of stars, and their temperatures, and pressures. He also worked on the statistical mechanics of white dwarf stars (1926) with P.A.M. Dirac, whom he had introduced to quantum theory. Fowler proposed that white dwarf stars consist of a degenerate gas of extremely high density. *TIS In 1921 he married Eileen Mary (1901–1930), the only daughter of Ernest Rutherford. They had four children, two sons and two daughters. Eileen died after the birth of their last child. One of his grandchildren is Mary Fowler, a geologist and current Master of Darwin College, Cambridge

1905 Dattaraya Ramchandra Kaprekar (17 Jan 1905 in Dahanu, India - Died: 1986 in Devlali, India) was an Indian mathematician who discovered several results in number theory, including a class of numbers and a constant named after him. Despite having no formal postgraduate training and working as a schoolteacher, he published extensively and became well-known in recreational mathematics circles. A Kaprekar number is a positive integer with the property that if it is squared, then its representation can be partitioned into two positive integer parts whose sum is equal to the original number (e.g. 45, since 452=2025, and 20+25=45, also 9, 55, 99 etc.) However, note the restriction that the two numbers are positive; for example, 100 is not a Kaprekar number even though 1002=10000, and 100+00 = 100. This operation, of taking the rightmost digits of a square, and adding it to the integer formed by the leftmost digits, is known as the Kaprekar operation.*Wik

1913 Shaun Wylie (17 January 1913 – 2 October 2009) was a British mathematician and World War II codebreaker. *Wik

1618 Luca Valerio (1552 in Naples, Italy - 17 Jan 1618 in Rome, Italy) was an Italian mathematician who applied methods of Archimedes to find volumes and centres of gravity of solid bodies. He corresponded with Galileo.*SAU

1670 Jean Leurechon (1591 – 17, Jan 1670) was a French Jesuit priest and mathematician. He often wrote under the pseudonym Hendrik van Etten.He was born in 1591 in Bar le Duc, and died  in Pont-à-Mousson.
At the age of 18, he entered the Jesuit college of Tournai in Belgium.
He joined the priesthood in 1624. In 1629, he became the rector of a college. He was a professor of theology for two years.
His most famous work is the Récréations Mathématiques written under the pseudonym Hendrik van Etten. The book is a collection of recreational mathematical puzzles. The book made him famous all over Europe. Math Historian Albrecht Heeffer has studied the book extensively and believers it was Not Leurechon, but Jean Appier dit Hanelett, a printer who wrote the book. He has also stated that he believes it is the first math book with the word "recreations" in the title.

Much of the mathematical content centers around Claude Bachet's problems and may have been copied from it or some common source. The book also gives the earliest known description of the operation of an ear trumpet and a very early description of the thermometer, which at the time was less than 30 years in existence.
Leurechon may well have created the term "thermometre" which he used in 1626. It made it's way into English through the translations of his work by William Oughtred.
His book led (indirectly) to the common belief that the instrument was "invented by a North Hollander peasant named Drebble. When Caspar Ens copied the problem from Leurechon's book, he inserted the adjective "Drebbvenanum" in front of the word instrument. This was repeated in Journal des sçavans (renamed Journal des savants) and became accepted as a popular truth.

A new edition is available on Amazon

1675 Bernard Frénicle de Bessy (c. 1605 in Paris, France - 17 Jan 1675 in Paris, France), wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for Des quarrez ou tables magiques, a treatise on magic squares published posthumously in 1693, in which he described all 880 essentially different normal magic squares of order 4. The Frénicle standard form, a standard representation of magic squares, is named after him. He solved many problems created by Fermat and also discovered the cube property of the number 1729, later referred to as a taxicab number.(see "Births" 22 Dec,1887 )
Like Fermat, Frénicle was an amateur mathematician, but he still corresponded with the likes of Descartes, Huygens, Mersenne and also Fermat, who was his personal friend. His major contributions were in number theory.

He challenged Christiaan Huygens​ to solve the following system of equations in integers,

x2 + y2 = z2, x2 = u2 + v2, x − y = u − v.

A solution was given by Théophile Pépin in 1880.
In 1973, he was posthumously recognized by the American Mathematical Society for his work in structural combinatorics *Wik

1775 Vincenzo Riccati (Castelfranco Veneto, 11 January 1707 – Treviso, 17 January 1775) was an Italian mathematician and physicist. He was the brother of Giordano Riccati, and the second son of Jacopo Riccati.
Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics. The Riccati equation is named after his father.*Wik

1910 Friedrich Wilhelm Georg Kohlrausch (14 Oct 1840, 17 Jan 1910)German physicist who investigated the properties of electrolytes (substances that conduct electricity in solutions by transfer of ions) and contributed to the understanding of their behaviour. Some of Kohlrausch's pioneering achievements include conductivity measurements on electrolytes, his work on the determination of basic magnetic and electrical quantities, and the enhancement of the associated measuring technologies. It was under his direction that the "Physikalisch-Technische Reichsanstalt" (the then Imperial Physical Technical Institute in Germany) created numerous standards and calibration standards which were also used internationally outside Germany.*TIS

1911 Sir Francis Galton (16 Feb 1822, 17 Jan 1911) English scientist, founder of eugenics, statistician and investigator of intellectual ability. He explored in south-western Africa. In meteorology, he was first to recognise and name the anticyclone. He interpreted the theory of evolution of (his cousin) Charles Darwin to imply inheritance of talent could be manipulated. Galton had a long-term interest in eugenics - a word he coined for scientifically selected parenthood to enable inheritance of beneficial characteristics. He coined the phrase "nature versus nurture." Galton experimentally verified the uniqueness of fingerprints, and suggested the first classification based on grouping the patterns into arches, loops, and whorls. On 1 Apr 1875, he published the first newspaper weather map - in The Times *TIS

1954 Leonard Eugene Dickson (22 Jan 1874,Independence, Iowa, 17 Jan 1954, Harlingen, Texas)American mathematician who made important contributions to the theory of numbers and the theory of groups. He published 18 books including Linear groups with an exposition of the Galois field theory. The 3-volume History of the Theory of Numbers (1919-23) is another famous work still much consulted today. *TIS

1997 Clyde William Tombaugh (4 Feb 1906 on Ranch near Streator, Illinois, 17 Jan 1997) was an American astronomer who discovered what was then recognized as the planet Pluto, which he photographed on 23 Jan 1930, the only planet discovered in the twentieth century, after a systematic search instigated by the predictions of other astronomers. Tombaugh was 24 years of age when he made this discovery at Lowell Observatory in Flagstaff, Ariz. He also discovered several clusters of stars and galaxies, studied the apparent distribution of extragalactic nebulae, and made observations of the surfaces of Mars, Venus, Jupiter, Saturn, and the Moon.Born of poor farmers, his first telescope was made of parts from worn-out farming equipment. *TIS
From my personal blog after a visit to Mars Hill, Flagstaff, Az. (much material from Wikipedia)
In the late 19th and early 20th century, observers of Mars drew long straight lines that appeared on the surface between 60 degrees north and south of the martian equator. Italian astronomer Giovanni Schiaparelli called these lines canali, which became canals in English. Lowell extended this observation to a theory that Mars had polar ice caps that would melt in the martian spring and fill the canals. He even extended the theory to include intelligent life on Mars that had designed the canals.
Eventually it became clear that there were no martian canals, but Mars hill went on to be the sight where a self educated Kansas schoolboy found his dream of working in astronomy in 1929, when the observatory director, V M Slipher, "handed the job of locating Planet X to Clyde Tombaugh, a 23-year-old Kansas man who had just arrived at the Lowell Observatory after Slipher had been impressed by a sample of his astronomical drawings."
On the nights of Jan 23 and 30th of January, 1930, he found a planet in the images that he thought was the Planet X. "The discovery made front page news around the world. The Lowell Observatory, who had the right to name the new object, received over 1000 suggestions, from "Atlas" to "Zymal". Tombaugh urged Slipher to suggest a name for the new object quickly before someone else did. Name suggestions poured in from all over the world. Constance Lowell proposed Zeus, then Lowell, and finally her own first name. These suggestions were disregarded.
The name "Pluto" was proposed by Venetia Burney (later Venetia Phair), an eleven-year-old schoolgirl in Oxford, England. Venetia was interested in classical mythology as well as astronomy, and considered the name, one of the alternate names of Hades, the Greek god of the Underworld, appropriate for such a presumably dark and cold world. She suggested it in a conversation with her grandfather Falconer Madan, a former librarian of Oxford University's Bodleian Library. Madan passed the name to Professor Herbert Hall Turner, who then cabled it to colleagues in America. The object was officially named on March 24, 1930."
Among the many awards Tombaugh received was a scholarship to the Univ of Kansas, where he would eventually earn a Bachelors and Masters Degree. It is said that the Astronomy Dept head refused to allow him to take the introductory astronomy class because it would be undignified for the discoverer of a planet.

When New Horizons rocketed away from Cape Canaveral on Jan. 19, 2006, Pluto was the ninth planet in our solar system. It was demoted to dwarf planet a scant seven months later.
Tombaugh's widow and two children offered up an ounce of his ashes for the journey to Pluto. The ashes of the farm boy-turned-astronomer are in a 2-inch aluminum capsule inscribed with these words:

"Interned herein are remains of American Clyde W. Tombaugh, discoverer of Pluto and the solar system's 'third zone.' Adelle and Muron's boy, Patricia's husband, Annette and Alden's father, astronomer, teacher, punster, and friend: Clyde Tombaugh (1906-1997)"

2000 Eugène Ehrhart (29 April 1906 Guebwiller – 17 January 2000 Strasbourg) was a French mathematician who introduced Ehrhart polynomials in the 1960s. Ehrhart received his high school diploma at the age of 22. He was a mathematics teacher in several high schools, and did mathematics research on his own time. He started publishing in mathematics in his 40s, and finished his PhD thesis at the age of 60. The theory of Ehrhart polynomials can be seen as a higher-dimensional generalization of Pick's theorem. *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

Monday, 16 January 2017

On This Day in Math - January 16


“It has nothing to do with defending our country, except to make it worth defending.”
~Robert R Wilson, 1969 (at Senate Hearing to justify Fermilab funding)

The 16th day of the year; 16 is the only number that can be written as ab = ba when a and b are not equal.

16 and its next smaller square, 9,  form a square when added or multiplied: 16+9=25, 16x9=144

16 is the smallest number which is the sum of two distinct primes in two ways,  16 = 3 + 13 = 5 + 11

Jim Wilder pointed out that 1616 ends in 1616 , 18446744073709551616

1741 John Harrison receives a 500 Pound grant from the Board of Longitude, "on account of his making a Machine with Improvements upon two Others before contrived by him." *Derek Howse, Britain's Board of Longitude:the Finances, 1714-1828

1777 Euler last attended a meeting of the St. Petersburg Academy on this date, after which he sent his papers in to the Academy with his assistants. *Ed Sandifer

1826 Neils Henrik Abel wrote his teacher and friend Holmboe: “The divergent series are the invention of the devil.” *VFR

1831 In an audience with the King of Sardinia, Cauchy answered five questions with “I expected Your Majesty would ask me this, so I have prepared to answer it.” Then he took a memoir from his pocket and read it. *VFR

1832 János Bolyai's pioneering work, The Absolutely True Science of Space, was published in 1832. This important work was published as an appendix to the first volume of his father,Farkas Bolyai's Tentamen , but its off-print had already been ready the previous year, in April 1831. The latter was the version which, together with a letter, was sent to Gauss by Farkas Bolyai on the 20th of June 1831. Gauss got the letter but János's work was lost on the way. On the 16th of January 1832 Farkas sent the Appendix to his friend again with another letter in which he wrote: ``My son appreciates Your critique more than that of whole Europe and it is the only thing he is waiting for''.
After twenty-three years of silence, Gauss replied to his ``old, unforgettable friend'' on the 6th of March 1832. One of his well-known sentences was: ``if I praised your son's work I would praise myself''. The letter deeply afflicted and upset János Bolyai, although it reflects appreciation, too: ``... I am very glad that it is my old friend's son who so splendidly preceded me'' *Komal Journal

1865 Founding of the London Mathematical Society. Despite its name, the London Mathematical Society (LMS) has, almost since its foundation, served as the national society for the British mathematical community. Its establishment in 1865 made Britain one of the first countries in the world to have such an organisation. What was to become the London Mathematical Society arose from a chance remark in a conversation between two former students of University College London in the summer of 1864. The two young men were Arthur Cowper Ranyard and George Campbell De Morgan, the son of one of the most influential British mathematicians of the day. Augustus De Morgan was the founding professor of mathematics at University College, which he had single-handedly established as the home of advanced mathematical education in London. Conscious of the key role the Professor's reputation could play in attracting members to the Society, it was agreed that George should ask his father to take the chair at the first meeting.
Agreeing to this, the senior De Morgan apparently insisted that their tentative title of The London University Mathematics Society, be changed, first to the University College Mathematical Society, and then, in order to widen the scope of the society's membership, to the London Mathematical Society. The newly-retitled society held its inaugural meeting at University College London on Monday, January 16th 1865, with De Morgan as its first president giving the opening address. Within months, it had attracted over 60 new members from around the country, including many of the leading British mathematicians of the 19th century, such as Arthur Cayley, James Joseph Sylvester, Henry John Stephen Smith, George Salmon, William Kingdon Clifford and James Clerk Maxwell. *A Brief History of the London Mathematical Society

1910 At six o’clock in the evening, Richard Courant was scheduled to be examined for his Ph.D. by Hilbert in mathematics, Voight in physics, and Husserl in philosophy. Hilbert arrived early and was anxious to get on with it so he could go home, but the others did not appear. Since Courant had written his dissertation under Hilbert, he had no need to probe Courant’s mathematical knowledge, so they talked about non-mathematical things. After forty minutes, Husserl appeared. Hilbert excused himself and went home. After Husserl asked one question, Courant asked him to explain a delicate point in phenomenology. This took the remainder of the alloted time. Voight never appeared. Later several friends rented a horse-drawn carriage and hauled Courant around the quiet town of Gottingen while they blared over megaphones: “Dr. Richard Courant summa cum laude!” [Constance Reid, Courant in Gottingen and New York. The Story of an Improbable Mathematician (Springer 1976), pp. 33-34] *VFR

1913 Srinivasa Ramanujan, a 23 year old clerk in Madras, India, wrote G. H. Hardy, Professor at Cambridge, sending “a few examples of my theorems,” and asking for advice. Although he was inclined to dismiss it as a letter from a crank, Hardy and his colleague J. E. Littlewood puzzled out some of the 120 formulas in the letter after dinner and concluded that Ramanujan was a mathematical genius. Hardy immediately invited Ramanujan to England, where they collaborated on a number of important papers in number theory. *VFR ( Hardy figured that Ramanujan's theorems "must be true, because, if they were not true, no one would have the imagination to invent them".)

1956 The U.S. government's Semi-Automatic Ground Environment (SAGE) is disclosed to the public. SAGE, an air defense system, linked hundreds of radar stations in the United States and Canada in the first large-scale computer communications network. With the increasing possibility of a large-scale bomber attack on the United States in the mid-1950s, it became evident that further improvements in the nation's defense capability were needed. MIT's Lincoln Laboratory was commissioned to develop an automated nationwide computer-based air defense system. SAGE was completed in the early 1960s, revolutionizing air defense and civilian air traffic control. In 1979 SAGE was replaced by Regional Operations Control Centers (ROCC).*CHM

2015 The London Mathematical Society begins its 150th Anniversary Celebrations. The Launch event tok place at the prestigious Goldsmiths’ Hall, London. *London Mathematical Society


1477 Johannes Schöner (16 Jan 1477; 16 Jan 1547) German geographer who is noted for making and printing geographical globes. A notable work from 1515 is one of the earliest surviving globes produced following the discovery of new lands by Christopher Columbus. It was the first to show the name America that had been suggested by Waldseemüller. Tantalizingly, it also depicts a passage around South America before it was recorded as having been discovered by Magellan. Schöner was a professor mathematics at the University of Nuremberg and was the author of numerous mathematical, astronomical and geographical works. In his first career, he was an ordained Roman Catholic priest, which he gave up on becoming a university professor and converted to a Lutheran. *TIS
 Only one specimen of the famous Waldseemüller map survives. It once was owned by Schöner and was rediscovered in 1901 at Schloss Wolfegg in Upper Swabia. Since 2003 it is in possession of the Library of Congress.
It is best to refer to him using the usual 16th-century Latin term "mathematicus", as the areas of study to which he devoted his life were very different from those now considered to be the domain of the mathematician. He was a priest, astronomer, astrologer, geographer, cosmographer, cartographer, mathematician, globe and scientific instrument maker and editor and publisher of scientific tests. In his own time he enjoyed a European wide reputation as an innovative and influential globe maker and cosmographer and as one of the continents leading and most authoritative astrologers. Today he is remembered as an influential pioneer in the history of globe making and as a man who played a significant role in the events that led up to the publishing of Copernicus' "De revolutionibus" in Nürnberg in 1543. In 1538, Georg Joachim Rheticus, a young professor of mathematics at Wittenberg, stayed for some time with Schöner who convinced him to visit Nicolaus Copernicus in Frauenburg. In 1540, Rheticus dedicated the first published report of Copernicus work, the Narratio prima, to Schöner. As this was well received, Copernicus finally agreed to publish his main work, and Rheticus prepared Copernicus' manuscript for printing. *Wik
A recent book about this little-known polymath was written by John W. Hessler

1730 Jean-Baptiste-Gaspard Bochart de Saron (16 Jan 1730; 20 Apr 1794) French lawyer and natural scientist who pursued his interest in astronomy both as a productive amatuer and a patron. He assembled a significant collection of astronomical instruments made by renowned craftsmen. He both utilized then himself and gave access to his academic colleagues. In collaboration with Charles Messier, who provided the data, he calculated orbits of comets, helping his friend find them again after they had disappeared behind the sun. He funded the publication of Laplace's Theory of the Movement and Elliptic Figure of the Planets (1784). Bochart made calculations for what was at first called Herschel's comet, supposing a circular orbit at twelve time the Sun-Saturn distance. This was refined by Laplace, and contributed to the discovery of Uranus. Bochart died as a politician guillotined during the French Revolution.*TIS

1801 Thomas Clausen. (16 Jan 1801 in Snogbaek, Denmark - 23 May 1885 in Dorpat, Russia (now Tartu, Estonia)) In 1854 he factored the Fermat number F (6) = 226 +1 as 274177 times 67280421310721, thus providing another counterexample to a conjecture of Fermat. (Euler factored F(5) in 1732.)*VFR Clausen wrote over 150 papers on pure mathematics, applied mathematics, astronomy and geophysics and worked with some of the best mathematicians of his day. *SAU

1807 Charles Henry Davis (16 Jan 1807; 18 Feb 1877) U.S. naval officer and scientist who published several hydrographic studies, was a superintendent of the Naval Observatory (1865–67, 1874–77) and worked to further scientific progress. Between his naval duties at sea, he studied mathematics at Harvard. He made the first comprehensive survey of the coasts of Massachusetts, Rhode Island, and Maine, including the intricate Nantucket shoals area. He helped establish and then supervised the preparation of the American Nautical Almanac (1849) for several years. Davis was a co-founder of the National Academy of Sciences (1863), and wrote several scientific books.*TIS

1906 Erich Kähler (16 January 1906, Leipzig – 31 May 2000, Wedel) was a German mathematician with wide-ranging geometrical interests.
As a mathematician he is known for a number of contributions: the Cartan–Kähler theorem on singular solutions of non-linear analytic differential systems; the idea of a Kähler metric on complex manifolds; and the Kähler differentials, which provide a purely algebraic theory and have generally been adopted in algebraic geometry. In all of these the theory of differential forms plays a part, and Kähler counts as a major developer of the theory from its formal genesis with Élie Cartan.
Kähler manifolds — complex manifolds endowed with a Riemannian metric and a symplectic form so that the three structures are mutually compatible — are named after him.
The K3 surface is named after Kummer, Kähler, and Kodaira.
His earlier work was on celestial mechanics; and he was one of the forerunners of scheme theory, though his ideas on that were never widely adopted.*Wik

1925 Germund Dahlquist (January 16, 1925 – February 8, 2005) was a Swedish mathematician known primarily for his early contributions to the theory of numerical analysis as applied to differential equations.*Wik


1547 Johannes Schöner (16 Jan 1477; 16 Jan 1547) See births above, born and died on the same calendar day.

1834 Jean Nicolas Pierre Hachette was a French mathematician who worked on descriptive geometry. When the Ecole Polytechnique was established, he was appointed along with Monge over the department of descriptive geometry. There he instructed some of the ablest Frenchmen of the day, among them SD Poisson, François Arago and A Fresnel. *Wik

1887 Edward Olney (ALL-nee*) (July 24, 1827 - January 16, 1887) was born in Moreau, Saratoga County, New York. His ancestry can be traced back to Thomas Olney who accompanied Roger Williams in founding the city of Providence and colony of Rhode Island. Benjamin Olney's family moved to Oakland County, Michigan, in 1833 and, a few months later, settled on a farm in Weston, Wood County, Ohio.
Olney was largely self-taught. Calloway tells about Edward hiring a neighbor boy to drive the team of oxen on the Olney farm so that he could attend school for six weeks in order to master Day's Algebra. During this time he also ran an arithmetic school at home in the evenings in order to earn the money to pay for his substitute driver.
At age 19, Olney began his career as a teacher in the local elementary schools, while studying mathematics, natural science, and languages on his own. Cajori reports that "though he had never studied Latin, he began teaching it and kept ahead of the class because he 'had more application'." In 1848 Olney was hired as a teacher in the district school at Perrysburg, Ohio. The following year he was named principal of the grammar department in the new Union School. Over the next five years he would become the school's superintendent, marry Miss Sarah Huntington (a teacher at the school), and receive an honorary A. M. degree from Madison University (now Colgate University) in Hamilton, New York. Today there is an Olney School in Lake Township, Wood County, named after him.
In 1853 Olney was appointed Professor of Mathematics at Kalamazoo College, Michigan, where he remained for ten years and established the first mathematics curriculum at that institution. He inspired his colleagues and students alike with "his high Christian aims; his generous, self-sacrificing spirit; his thoroughness in government and discipline; and the inspiration which attended him." Although he insisted that his students recite using exact and correct language, he always tried to simplify the explanations of concepts and processes and make them more understandable. Kalamazoo college later conferred the honorary degree, LL. D. upon him.
In 1863 Olney was named Professor of Mathematics at the University of Michigan, succeeding George P. Williams, whose title was then changed to Professor of Physics. In those days the freshmen at Michigan were taught by inexperienced instructors, but once a week they had to recite for Professor Olney. His reputation for being a stern disciplinarian and a stickler for correct details earned him the nickname "Old Toughy." Nevertheless, he took great pains to see that the poorer students obtained help in making up their deficiencies. According to a former student, G. C. Comstock, "He was not a harsh man, and although the students stood in awe of him, I think that he was generally liked by them."
While he was at Michigan, Professor Olney began writing a series of successful mathematics textbooks for use in both grammar schools and colleges. In many places these displaced the works of such highly regarded authors as Charles Davies and Elias Loomis. Among the titles are: Elements of Arithmetic for Intermediate, Grammar, and Common Schools (1877), A University Algebra (1873), Elementary Geometry (1883), Elements of Trigonometry (1870), and A General Geometry and Calculus (1871) (online). Olney's treatment of calculus was criticized for using infinitesimal methods, but praised for giving "the elegant method, discovered by Prof. James C. Watson [Professor of Astronomy at Michigan], of demonstrating the rule for differentiating a logarithm without the use of series." It is said that Olney preferred geometry to analysis, and when teaching calculus, he would attempt to translate analytical expressions into their geometrical equivalents. This, along with his own struggles in self-education, contributed to his great success as a teacher and textbook author. Edward Olney died on January 16, 1887, after suffering for three years from the effects of a stroke. *David E. Kullman

1922 Pierre René Jean Baptiste Henri Brocard (12 May 1845 in Vignot (part of Commercy), France - 16 Jan 1922 in Bar-le-Duc, France) mathematician best known for his discovery of the so-called Brocard points of a triangle. His two major publications were the two volumes of Notes de bibliographie des corbes géométriques (1897, 1899) and the two volumes of Courbes géométriques remarkables the first of which was published in 1920, the second in 1967 long after his death. This last work was written in collaboration with T Lemoyne. The Notes may be regarded as a source book of geometric curves, with a painstakingly prepared index containing more than a thousand named curves. The text consists of brief descriptive paragraphs, with diagrams and equations of these curves. *SAU

1938 William Henry Pickering (15 Feb 1858, 16 Jan 1938) American astronomer who discovered Phoebe, the ninth moon of Saturn (1899). This was the first planetary satellite with retrograde motion to be detected, i.e., with orbital motion directed in an opposite sense to that of the planets. He set up a number of observing stations for Harvard. He made extensive observations of Mars and claimed, like Lowell, that he saw signs of life on the planet by observing what he took to be oases in 1892. He went further than Lowell however when in 1903 he claimed to observe signs of life on the Moon. By comparing descriptions of the Moon from Giovanni Riccioli's 1651 chart onward, he thought he had detected changes that could have been due to the growth and decay of vegetation.*TIS

1941 Charles Thurstan Holland (Mar 1863, 16 Jan 1941) English radiologist who pioneered the clinical use of X-rays in the UK, beginning shortly after Roentgen announced their discovery. He was present at the first clinical use of X-rays in England, (7 Feb 1896) in the laboratory of Oliver Lodge, head of the physics department at Liverpool University. The wrist of a 12-year-old boy who had shot himself the previous month was examined. The boy had been brought there by surgeon Sir Robert Jones who with Lodge reported the case in the 22 Feb 1896 of The Lancet. Jones subsequently financed an X-ray apparatus for Holland to pioneer radiology at Royal Southern Hospital, Liverpool. During WWI, he perfected methods of detecting bullets and shell fragments in patients' bodies. *TIS

1967 Robert Jemison Van de Graaff (20 Dec 1901; 16 Jan 1967) American physicist and inventor of the Van de Graaff generator, a type of high-voltage electrostatic generator that can be used as a particle accelerator in atomic research. The potential differences achieved in modern Van de Graaff generators can be up to 5 MV. It is a principle of electric fields that charges on a surface can leap off at points where the curvature is great, that is, where the radius is small. Thus, a dome of great radius will inhibit the electric discharge and added charge can reach a high voltage. This generator has been used in medical (such as high-energy X-ray production) and industrial applications (sterilization of food). In the 1950s, Van de Graaff invented the insulating core transformer able to produce high voltage direct current.*TIS

2000 Robert Rathbun Wilson (4 Mar 1914, 16 Jan 2000) was an American physicist who was the first director of Fermilab. From 1967, he led the design and construction of Fermilab (the Fermi National Accelerator Laboratory) near Chicago, Illinois. He also improved the environment by restoring prairie at the site. It began operating in 1972 with the world's most powerful particle accelerator. With later improvements, it retained that status for well over three decades until it was superceded by the LHC (Large Hadron Collider) at the CERN laboratory in Geneva, Switzerland. Wilson is remembered for his justification of the needed financing at a Senate hearing in 1969, where he said “It has nothing to do with defending our country, except to make it worth defending.” He resigned in 1978 because he did not believe the government was giving it sufficient funding for its research mission.*TIS

2002 Robert Hanbury Brown (31 Aug 1916, 16 Jan 2002) English astronomer who was a pioneer in radar and observational astronomy. During and after WW II he worked with R.A. Watson-Watt and then E.G. Bowen to develop radar for uses in aerial combat. In the 1950s he applied this experience to radio astronomy, developing radio-telescope technology at Jodrell Bank Observatory and mapping stellar radio sources. He designed a radio interferometer capable of resolving radio stars while eliminating atmospheric distortion from the image (1952). With R.Q. Twiss, Brown applied this method to measuring the angular size of bright visible stars, thus developing the technique of intensity interferometry. They set up an intensity interferometer at Narrabri in New South Wales, Australia, for measurements of hot stars.*TIS

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