## Sunday, 14 January 2018

### On This Day in Math - January 14

 Halley Plaque in Westminster Abbey, *Wik

"One accurate measurement is worth a thousand expert opinions."
~Grace Hopper

The 14th day of the year; there are exactly the same number of composite and prime numbers less than fourteen. There is no larger number for which that is true.

By selecting one of + or - between each number, there are 14 solutions to $\pm 1 \pm 2 \pm 3 \pm 4 \pm 5 \pm 6 \pm 7 \pm 8 = 0$ *Derek Orr

EVENTS

1667/8 In his diary Samuel Pepys mentions a “very pretty, but not very useful” arithmetical machine devised by Sir Samuel Morland (1625–1695 or 6). After a successful diplomatic career under Cromwell, Morland was appointed salaried “Master of Mechanics” to the King and devoted the rest of his life to instrument making. *Oldenburg Correspondence, 9, 432,
Perhaps the multiplying calculator below? Looks impressive to me for the time.

1858 Arthur Cayley's A Memoir on the Theory of Matrices (received Dec 10, 1857) is read at the the Royal Society. Cayley establishes rules of notation and operations for these newly emerging ideas in mathematics. This paper also contained the first formal statement of what we now call the Cayley-Hamilton Theorem. *Jacqueline Stedall, Mathematics Emerging

1909 Hermann Minkowski is buried. He died at noon on Tuesday, January 12th following an attack of appendicitis, and an operation on Sunday evening. On Wednesday morning the announcement was made to the students. One student recalled the shock of seeing Hilbert crying was almost greater than hearing of Minkowski's death.
It was his regular practice to walk and talk with Hilbert, Klein, Runge, and other mathematics professors who chose to accompany them. They would walk together to the Kehrhotel on the Hainberg and return each Thursday at 3pm. And so, on Thursday January 14th, Klein, Hilbert, Runge and the other mathematics professors walked together to carry Hermann Minkowski to his grave, at exactly 3pm. *Constance Reid, Hilbert; pg 11 He was buried in Berlin at the Waldfriedhof Heerstrasse

1916 Four women were elected to Fellowship of the Royal Astronomical Society – the first women to be accepted alongside
men as ordinary members of the Society (A few women had been accepted in 1835 by introducing Honorary Membership for
women, conferring this honor on both Caroline Herschel and Mary Somerville) . The four new female members were Miss Mary Adela Blagg, Miss Ella K Church, Miss A Grace Cook and Mrs Fiammetta Wilson. *Royal Astronomical Soc.

1980 Robert J. Griess, Jr. announced that he had constructed the conjectured sporadic simple group F1 known as the “monster.” This group consists 808,017,424,794,512,875,886,459,904, 961,710,757,005,754,368,000,000 square matrices each of size 196,883 by 196,883. This led to the completion of the classiﬁcation of the ﬁnite simple groups. [Mathematics Magazine 53(1980),
p. 253 and 54(1981), p. 41]. *VFR

2008  the memorial plaque of Mark Krein was unveiled on the main administration building of I.I. Mechnikov Odessa National University. *Wik

BIRTHS

1806 Matthew Fontaine Maury (14 Jan 1806; 1 Feb 1873) As a U.S. naval officer, Maury was a pioneer hydrographer. He was the first person to undertake a systematic and comprehensive study of the ocean. His work on oceanography and navigation led to an international conference (Brussels, 1853) the first ever of its kind in the world. In 1855, during the Western gold rush, Maury’s updated information helped sea captains cut a ship’s average travel time from New York to San Francisco from 180 to 133 days. That same year, Maury prepared a report that proved the practicality — and assured the success — of the first trans-Atlantic cable between the United States and Europe. Maury was director of the U.S. Naval Observatory from 1844 to 1861. *TIS

1819 James Cockle (14 Jan 1819 in Great Oakley, Essex, England - 27 Jan 1895 in Bayswater, London, England) Cockle was remarkably productive as a mathematician publishing over 100 papers. He wrote papers on both pure and applied mathematics, as well as on the history of science. On the former topic he wrote on fluid dynamics and magnetism. Most of his work, however, was in pure mathematics where he studied algebra, the theory of equations, and differential equations. He had a collaborator on mathematical work, a Congregationalist minister named Robert Harley. *SAU

1887 Władysław Hugo Dionizy Steinhaus (January 14, 1887 – February 25, 1972) was a Polish mathematician and educator. Steinhaus obtained his PhD under David Hilbert at Göttingen University in 1911 and later became a professor at the University of Lwów, where he helped establish what later became known as the Lwów School of Mathematics. He is credited with "discovering" mathematician Stefan Banach, with whom he gave a notable contribution to functional analysis through the Banach-Steinhaus theorem. After World War II Steinhaus played an important part in the establishment of the mathematics department at Wrocław University and in the revival of Polish mathematics from the destruction of the war.
Author of around 170 scientific articles and books, Steinhaus has left its legacy and contribution on many branches of mathematics, such as functional analysis, geometry, mathematical logic, and trigonometry. Notably he is regarded as one of the early founders of the game theory and the probability theory preceding in his studies, later, more comprehensive approaches, by other scholars. *Wik
His Mathematical Snapshots is a delight to read, but get the ﬁrst English edition if you can—there are lots of surprises there. *VFR

1902 Alfred Tarski, (14 Jan 1902 (some sources list 1901); 26 Oct 1983) Polish-born American mathematician and logician who made important studies of general algebra, measure theory, mathematical logic, set theory, and metamathematics. Formal scientific languages can be subjected to more thorough study by the semantic method that he developed. He worked on model theory, mathematical decision problems and with universal algebra. He produced axioms for "logical consequence", worked on deductive systems, the algebra of logic and the theory of definability. Group theorists study 'Tarski monsters', infinite groups whose existence seems intuitively impossible. *TIS

1919 Nathaniel Rochester, The chief architect of IBM's first scientific computer, the 701, is born. Rochester also developed the prototype for the IBM 702, the growing company's first commercial computer. Both machines signaled IBM’s slow transition from its lucrative punch card accounting business to markets based on developments in electronics resulting from WW II research and development. *CHM

1924 Linards Eduardovich Reizins (14 Jan 1924 in Riga, Latvia - 1991 in Latvia) Of the many other important contributions made by Reizins we should mention in particular his work on Pfaff's equations and his contributions to the history of mathematics. In particular he edited the Complete Works of Piers Bohl which was published in 1974. Other important historical papers include Mathematics in University of Latvia 1919-1969 (1975, joint with E Riekstins) and From the History of the General Theory of Ordinary Differential Equations (1977). *SAU

DEATHS

1679 Jacques de Billy (18 March 1602 in Compiègne, France - 14 Jan 1679 in Dijon, France) was a French Jesuit. Billy corresponded with Fermat and produced a number of results in number theory which have been named after him. Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum (New discovery in the art of analysis) as an annex to his edition of the Arithmetica of Diophantus (1670). *SAU

1687 Nicholas (Nikolaus) Mercator (c. 1620, Holstein – 1687, Versailles), also known by his Germanic name Kauffmann, was a 17th-century mathematician. He lived in the Netherlands from 1642 to 1648. He lectured at the University of Copenhagen during 1648–1654 and lived in Paris from 1655 to 1657. He was mathematics tutor to Joscelyne Percy, son of the 10th Earl of Northumberland, at Petworth, Sussex (1657). He taught mathematics in London (1658–1682). In 1666 he became a member of the Royal Society. He designed a marine chronometer for Charles II, and designed and constructed the fountains at the Palace of Versailles (1682–1687).
Mathematically, he is most well known for his treatise Logarithmo-technica on logarithms, published in 1668. In this treatise he described the Mercator series, also independently discovered by Gregory Saint-Vincent:
$\ln(1 + x) = x - \frac{1}{2}x^2 + \frac{1}{3}x^3 - \frac{1}{4}x^4 + \cdots.$
It was also in this treatise that the first known use of the term natural logarithm appears, in the Latin form log naturalis. His use of this term is somewhat surprising, since it predates the development of infinitesimal calculus, in which the most natural properties of this logarithm appear.
To the field of music he contributed the first precise account of 53 equal temperament, which was of theoretical importance, but not widely practiced. *Wik
In 1683 he accepted Colbert’s commission to plan the waterworks at Versailles. Payment was contingent upon turning Catholic. This he refused to do and soon died of frustration and poverty. * VFR He gave the first accepted derivation of Kepler's 2nd Law. *@Rmathematicus, Twitter

1742 Edmond (Edmund) Halley (8 Nov 1656, 14 Jan 1742) He is best known for his accurate prediction that the comet of 1682 would return in 1758. The BAYEUX TAPESTRY (Tapisserie de la Reine Mathilde) includes a clear picture of Halley's Comet.*VFR
He became professor of geometry at Oxford and was later appointed the second Astronomer Royal. After originating the question that prodded Newton to write the Principia, Halley edited and arranged the publication of this seminal work. Halley identified the proper motion of stars, studied the moon's motion and tides, realized that nebulae were clouds of luminous gas among the stars, and that the aurora was associated with the earth's magnetism. His prediction of the transit of Venus led to Cook's voyage to Tahiti.*TIS
Halley was buried in the graveyard of the old church of St. Margaret, Lee. In the same vault is Astronomer Royal John Pond; the unmarked grave of Astronomer Royal Nathaniel Bliss is nearby. *Wik (Halley's gravesite is in a cemetery at the junction of Lee Terrace and Brandram Road, across from the Victorian Parish Church of St. Margaret. The cemetery is a 30-minute walk from the Greenwich Observatory.)

1753 Bishop George Berkeley (12 March 1685 in Kilkenny, County Kilkenny, Ireland
- 14 Jan 1753 in Oxford, England). In 1734 he published The Analyst, Or a Discourse Addressed to an Inﬁdel Mathematician (namely, Edmund Halley). This work was a strong and reasonably justiﬁed attack on the foundation of the differential calculus. He called differentials “the ghosts of departed quantities.” *VFR

1814 Charles Bossut (11 Aug 1730 in Tartaras (near Rive de Gier), Rhône-et-Loire, France - 14 Jan 1814 in Paris, France) Bossut is famed for his textbooks which were widely used throughout France. He wrote his first textbook Traité élémentaire de méchanique et de dinamique appliqué principalement aux mouvements des machines (1763) while at the École du Génie. He also published the more famous Cours complet de mathematiques in 1765. The economist Turgot, Baron De L'Aulne, was appointed 'comptroller general' of France by Louis XVI on 24 August 1774. Among his first actions was the creation of a chair of hydrodynamics at the Louvre, where he himself had studied. Turgot's friend the Marquis de Condorcet, who he had appointed as Inspector General of the Mint, may well have influenced him to create the chair. Since Condorcet and Bossut were close collaborators it may have essentially been created for Bossut who certainly was appointed and filled it until 1780. In 1775 Bossut participated with d'Alembert and Condorcet in experiments on fluid resistance. Also during this period he was editing an edition of the works of Pascal which was published in five volumes in 1779.
He was later to collaborate with d'Alembert on the mathematical part of Diderot's Encyclopédie méthodique. Also later in his career he wrote Méchanique en général (1792) and his treatise on the history of mathematics in two volumes Essai sur l'histoire générale des mathématique (1802). *SAU

1898 Charles Lutwidge Dodgson, pen-name Lewis Carroll (27 Jan 1832, 14 Jan 1898), was an English logician, mathematician, photographer, and novelist, remembered for Alice's Adventures in Wonderland (1865) and its sequel. After graduating from Christ Church College, Oxford in 1854, Dodgson remained there, lecturing on mathematics and writing treatises until 1881. As a mathematician, Dodgson was conservative. He was the author of a fair number of mathematics books, for instance A syllabus of plane algebraical geometry (1860). His mathematics books have not proved of enduring importance except Euclid and his modern rivals (1879) which is of historical interest. As a logician, he was more interested in logic as a game than as an instrument for testing reason.*TIS (I once read that if Dodgson had not written "Alice", he would be remembered today for his photography, and if he had not done either of those, then, if he was remembered at all, it would be for his logic book. One of my favorite Lewis Carroll stories is about his gift of a book to Queen Victoria. Here is the version as it is told on the Mathworld page):
Several accounts state that Lewis Carroll (Charles Dodgson ) sent Queen Victoria a copy of one of his mathematical works, in one account, An Elementary Treatise on Determinants. Heath (1974) states, "A well-known story tells how Queen Victoria, charmed by Alice in Wonderland, expressed a desire to receive the author's next work, and was presented, in due course, with a loyally inscribed copy of An Elementary Treatise on Determinants," while Gattegno (1974) asserts "Queen Victoria, having enjoyed Alice so much, made known her wish to receive the author's other books, and was sent one of Dodgson's mathematical works." However, in Symbolic Logic (1896), Carroll stated, "I take this opportunity of giving what publicity I can to my contradiction of a silly story, which has been going the round of the papers, about my having presented certain books to Her Majesty the Queen. It is so constantly repeated, and is such absolute fiction, that I think it worth while to state, once for all, that it is utterly false in every particular: nothing even resembling it has occurred" (Mikkelson and Mikkelson)
.

1901 Charles Hermite (24 Dec 1822, 14 Jan 1901) French mathematician whose work in the theory of functions includes the application of elliptic functions to provide the first solution to the general equation of the fifth degree, the quintic equation. In 1873 he published the first proof that e is a transcendental number. Hermite is known also for a number of mathematical entities that bear his name, Hermite polynomials, Hermite's differential equation, Hermite's formula of interpolation and Hermitian matrices. Poincaré is the best known of Hermite's students.*TIS

1905 Ernst Abbe (23 Jan 1840, 14 Jan 1905) German physicist who made theoretical and technical innovations in optical theory. He improved microscope design, such as the use of a condenser lens to provide strong, even illumination (1870). His optical formula, now called the Abbe sine condition, applies to a lens to form a sharp, distortion-free image He invented the Abbe refractometer for determining the refractive index of substances. In 1866, he joined Carl Zeiss' optical works, later became his partner in the company, and in 1888 became the owner of the company upon Zeiss' death. Concurrently, he was appointed professor at the Univ. of Jena in 1870 and director of its astronomical and meteorological observatories in 1878.*TIS  His monument at Jenna has the formula for the diffraction limit which he found. (image http://www.w-volk.de/museum)

1912 Arnold Droz-Farny (12 Feb 1856 in La Chaux-de-Fonds, Switzerland - 14 Jan 1912 in Porrentruy, Switzerland) Droz-Farny is best known for results published in the publications of 1899 and 1901 mentioned in this quote. The first of these was Question 14111 in The Educational Times 71 (1899), 89-90. In this he stated the following remarkable theorem without giving a proof:
If two perpendicular straight lines are drawn through the orthocentre of a triangle, they intercept a segment on each of the sidelines. The midpoints of these three segments are collinear.
This is known as the Droz-Farny line theorem, but it is not known whether Droz-Farny had a proof of the theorem. Looking at other work by Droz-Farny, one is led to conjecture that indeed he would have constructed a proof of the theorem. The 1901 paper we mentioned above is, for example, one in which he gives a proof of a theorem stated by Steiner without proof. Droz-Farny's proof appears in the paper Notes sur un théorème de Steiner in Mathesis 21 (1901), 268-271. The theorem is as follows:
If equal circles are drawn on the vertices of a triangle they cut the lines joining the midpoints of the triangle in six points. These six points lie on a circle whose centre is the orthocentre of the triangle.
Droz-Farny died "a long and painful disease".

1914 Benjamin Osgood Peirce (11 February 1854 Beverly, Massachusetts, USA — 14 January 1914 Cambridge, Massachusetts, USA) was an American mathematician and a holder of the Hollis Chair of Mathematics and Natural Philosophy at Harvard from 1888 until his death in 1914.*Wik

1931 William Ernest Johnson (June 23, 1858 – January 14, 1931) was a British logician mainly remembered for his Logic (1921–1924), in 3 volumes.
He taught at King's College, Cambridge for nearly thirty years. He wrote a bit on economics, and John Maynard Keynes was one of his students. Johnson was a colleague of Keynes's father, John Neville Keynes.
Logic was dated at the time of its publication, and Johnson can be seen as a member of the British logic "old guard" pushed aside by the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. But an article entitled "The Logical Calculus" (Johnson 1892) reveals that he had nontrivial technical capabilities in his youth, and that he was significantly influenced by the formal logical work of Charles Sanders Peirce. *Wik

1970 William (Vilim) Feller born Vilibald Srećko Feller (July 7, 1906 – January 14, 1970), was a Croatian-American mathematician specializing in probability theory. Feller was one of the greatest probabilists of the twentieth century, who is remembered for his championing of probability theory as a branch of mathematical analysis in Sweden and the United States. In the middle of the 20th century, probability theory was popular in France and Russia, while mathematical statistics was more popular in the United Kingdom and the United States, according to the Swedish statistician, Harald Cramér. His two-volume textbook on probability theory and its applications was called "the most successful treatise on probability ever written" by Gian-Carlo Rota. By stimulating his colleagues and students in Sweden and then in the United States, Feller helped establish research groups studying the analytic theory of probability. In his research, Feller contributed to the study of the relationship between Markov chains and differential equations, where his theory of generators of one-parameter semigroups of stochastic processes gave rise to the theory of "Feller operators". *Wik

1978 Kurt Gödel (28 Apr 1906, 14 Jan 1978)Austrian-born U.S. mathematician, logician, and author of Gödel's proof. He is best known for his proof of Gödel's Incompleteness Theorems (1931) He proved fundamental results about axiomatic systems showing in any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved. This ended a hundred years of attempts to establish axioms to put the whole of mathematics on an axiomatic basis. *TIS
In later life, Gödel suffered periods of mental instability and illness. He had an obsessive fear of being poisoned; he would only eat food his wife, Adele, prepared for him. Late in 1977, Adele was hospitalized for six months and could no longer prepare Gödel's food. In her absence, he refused to eat, eventually starving to death. He weighed 65 pounds (approximately 30 kg) when he died. His death certificate reported that he died of "malnutrition and inanition caused by personality disturbance" in Princeton Hospital on January 14, 1978 *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