Wednesday, 18 October 2017

On This Day in Math - October 18

All models are wrong, some models are useful.

~George Box

The 291st day of the year; 291 is the largest number that is not the sum of distinct non-trivial powers.

\( \phi(291) = 192 \)  The number of integers less than, and relatively prime to 291 is equal to it's reversal, 192.

291 is also equal to the nth prime + n.... but for which n, children?

1092 Walcher, the Prior of the monastery in Great Malvern, U.K., carried out the first known Western Experiment to improve astronomical predictions when he pointed an astrolabe toward a lunar eclipse. At this time his astrolabe was one of only a few in Europe. *Jonathan Lyons, The House of Wisdom: How the Arabs Transformed Western Civilization.

1640 Pierre de Fermat (1601–1665) explains his ‘little theorem’ to Bernard Frenicle de Bessey in a follow up to two previous letters. ("On the subject of progressions, I have sent to you in advance the propositions that serve to determine the properties of powers minus one"). The theorem, which states that np−1 ≡ 1 (mod p) if p is prime and relatively prime to n, was proved by Euler in 1736 by induction on n.[Scientific American, December 1982]
Fermat actually made three statements:
1) When the exponent, n, is composite, 2n-1 is also composite,
2) When the exponent, n, is prime, 2n -2 is divisible by 2*n,
3) When the exponent, n, is prime, the number 2n -1 can not be divided by any number less than 2n+1

*Jacqueline Stedall, Mathematics Emerging

1740  In a letter to Johann Bernoulli, Euler uses imaginary in the exponent. exi + e-xi = 2 cos(x) {note Euler used squareroot of -1 rather than i. Euler would be the first to use i for the imaginary constant, but not until a paper he presents in St. Petersburg in 1777.} Cajori seems to imply, but does not state explicitly, that this is the first time an imaginary has been used as an exponent.

1954, Texas Instruments & Industrial Development Engineering Assoc launch the first transistor radio, Regency TR-1,

1955, a new atomic subparticle called a negative proton (antiproton) was discovered at U.C. Berkeley. The hunt for antimatter began in earnest in 1932, with the discovery of the positron, a particle with the mass of an electron and a positive charge. However, creating an antiproton would be far more difficult since it needs nearly 2,000 times the energy. In 1955, the most powerful "atom smasher" in the world, the Bevatron built at Berkeley could provide the required energy. Detection was accomplished with a maze of magnets and electronic counters through which only antiprotons could pass. After several hours of bombarding copper with protons accelerated to 6.2 billion electron volts of energy, the scientists counted a total of 60 antiprotons.*TIS

1962, Dr. James D. Watson of the U.S., Dr. Francis Crick and Dr. Maurice Wilkins of Britain won the Nobel Prize for Medicine and Physiology for their work in determining the double-helix molecular structure of DNA (deoxyribonucleic acid).*TIS


1863 Alan Archibald Campbell-Swinton, FRS (October 18, 1863, Scotland - February 19, 1930, London) was a Scottish consulting electrical engineer. He was an earlier experimenter in cathode rays and after 1896 he was frequently called upon by the medical professesion to take "Roentgen Pictures" of bones.
He described an electronic method of producing television in a June 18,1908 letter to Nature.
He gave a speech in London in 1911 where he described in great detail how distant electric vision could be achieved. This was to be done by using cathode ray tubes (CRTs) at both the transmitting and receiving ends.[4] This was the first iteration of the electronic television which is still in use today. When Swinton gave his speech others had already been experimenting with the use of cathode ray tubes as a receiver, but the use of the technology as a transmitter was unheard of. *Wik

1902 (Ernst) Pascual Jordan (18 October 1902 in Hanover, German Empire; d. 31 July 1980 in Hamburg, Federal Republic of Germany) German physicist who in the late 1920s founded (with Max Born and later Werner Heisenberg) quantum mechanics using matrix methods, showing how light could be interpreted as composed of discrete quanta of energy. Later, (with Wolfgang Pauli and Eugene Wigner), while it was still in its early stages of development, he contributed to the quantum mechancs of electron-photon interactions, now called quantum electrodynamics. He also originated (concurrently with Robert Dicke) a theory of cosmology that proposed to make the universal constants of nature, (such as the universal gravitational constant G), variable over time. *TIS

1919 George Edward Pelham Box (born 18 October 1919) is a statistician, who has made important contributions in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference.
Box has written research papers and published books. These include Statistics for experimenters (1978), Time series analysis: Forecasting and control (1979, with Gwilym Jenkins) and Bayesian inference in statistical analysis. (1973, with George C. Tiao). Today, his name is associated with important results in statistics such as Box–Jenkins models, Box–Cox transformations, Box–Behnken designs, and others. Box married Joan Fisher, the second of Ronald Fisher's five daughters. In 1978, Joan Fisher Box published a biography of Ronald Fisher, with substantial collaboration of Box. *Wik

1938 Phillip Griffiths (October 18, 1938, Raleigh, North Carolina -  ) is an American mathematician, known for his work in the field of geometry, and in particular for the complex manifold approach to algebraic geometry. He was a major developer in particular of the theory of variation of Hodge structure in Hodge theory and moduli theory.*Wik

1786 Alexander Wilson FRSE (1714 – 16 October 1786) was a Scottish surgeon, type-founder, astronomer, mathematician and meteorologist. He was the first scientist to record the use of kites in meteorological investigations. Wilson noted that sunspots viewed near the edge of the Sun's visible disk appear depressed below the solar surface, a phenomenon referred to as the Wilson effect. When the Royal Danish Academy of Sciences and Letters announced a prize to be awarded for the best essay on the nature of solar spots, Wilson submitted an entry. On 18 February 1772 the Academy presented Wilson with a gold medal for his work on sunspots.*Wik

1793 John Wilson (6 Aug 1741 in Applethwaite, Westmoreland, England - 18 Oct 1793 in Kendal, Westmoreland, England) In 1764 Wilson was elected a Fellow of Peterhouse and he taught mathematics at Cambridge with great skill, quickly gaining an outstanding reputation for himself. However, he was not to continue in the world of university teaching, for in 1766 he was called to the bar having begun a legal career on 22 January 1763 when he was admitted to the Middle Temple. It was a highly successful career, too.
He is best known among mathematicians for Wilson's theorem which states that
... if p is prime then 1 + (p - 1)! is divisible by p
This result was first published by Waring, without proof, and attributed to Wilson. Leibniz appears to have known the result. It was first proved by Lagrange in 1773 who showed that the converse is true, namely
... if n divides 1 + (n - 1)! then n is prime.
Almost certainly Wilson's theorem was a guess made by him, based on the evidence of a number of special cases, which neither he nor Waring knew how to prove. *SAU

1845 Jean-Dominique Comte de Cassini (30 June 1748 in Paris, France - 18 Oct 1845 in Thury, France)  French mathematician and surveyor who worked on his father's map of France.  He was the son of César-François Cassini de Thury and was born at the Paris Observatory. In 1784 he succeeded his father as director of the observatory; but his plans for its restoration and re-equipment were wrecked in 1793 by the animosity of the National Assembly. His position having become intolerable, he resigned on September 6, and was thrown into prison in 1794, but released after seven months. He then withdrew to Thury, where he died fifty-one years later.
He published in 1770 an account of a voyage to America in 1768, undertaken as the commissary of the French Academy of Sciences with a view to testing Pierre Le Roy’s watches at sea. A memoir in which he described the operations superintended by him in 1787 for connecting the observatories of Paris and Greenwich by longitude-determinations appeared in 1791. He visited England for the purposes of the work, and saw William Herschel at Slough. He completed his father’s map of France, which was published by the Academy of Sciences in 1793. It served as the basis for the Atlas National (1791), showing France in departments.
Cassini’s Mémoires pour servir à l’histoire de l’observatoire de Paris (1810) embodied portions of an extensive work, the prospectus of which he had submitted to the Academy of Sciences in 1774. The volume included his Eloges of several academicians, and the autobiography of his great-grandfather, Giovanni Cassini.*Wik

1871 Charles Babbage,(26 Dec 1792-18 Oct 1871) computer pioneer. His obsession for mechanizing computation made him into an embittered and crotchety old man. He especially hated street musicians, whose activities, he figured, ruined a quarter of his working potential. *VFR   English mathematician and pioneer of mechanical computation, which he pursued to eliminate inaccuracies in mathematical tables. By 1822, he had a small calculating machine able to compute squares. He produced prototypes of portions of a larger Difference Engine. (Georg and Edvard Schuetz later constructed the first working devices to the same design which were successful in limited applications.) In 1833 he began his programmable Analytical Machine, a forerunner of modern computers. His other inventions include the cowcatcher, dynamometer, standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, heliograph opthalmoscope. He also had an interest in cyphers and lock-picking. *TIS

1931 Thomas Alva Edison (11 Feb 1847-18 Oct 1931) Inventor, died in West Orange, NJ. He invented the first phonograph (1877) and the prototype of the practical incandescent electric light bulb (1879). His many inventions led to his being internationally known as "the wizard of Menlo Park", from the name of his first laboratory. By the late 1880s he was contributing to the development of motion pictures. By 1912 he was experimenting with talking pictures. His many inventions include a storage battery, a dictaphone, and a mimeograph. Meanwhile, he had become interested in the development of a system for widespread distribution of electric power from central generating stations. He held over 1,000 patents.In 1962 his second laboratory and home in West Orange, NJ, would be designated a National Historic Site.*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 October 2017

On This Day in Math - October 17

To parents who despair because their children are unable to master the first problems in arithmetic I can dedicate my examples. For, in arithmetic, until the seventh grade I was last or nearly last.
~Jacques Hadamard

The 290th day of the year, 290 is a sphenic (wedge) number, the product of three distinct primes (290 = 2*5*29).

It is also the sum of four consecutive primes (67 + 71 + 73 + 79) [Students might try to construct and examine a list of numbers that can be written as the sum of two or more consecutive primes]

290 is conjectured to be the smallest number such that the Reverse and Add! algorithm in base 4 does not lead to a palindrome.

290 is the tenth prime(29) times ten


1604 In Prague, Kepler first observes the supernova now known as supernova 1604 and Kepler's Star. The first recorded observation of this supernova was in northern Italy on October 9, 1604. It was named after Kepler because his observations tracked the object for an entire year and because of his book on the subject, entitled De Stella nova in pede Serpentarii ("On the new star in Ophiuchus's foot", Prague 1606). Here is an image of Kepler's De Stella Nova, open to the foldout star map placing the supernova of 1604, from the twitter feed of @Libroantiguo . It was the second supernova to be observed in a generation (after SN 1572 seen by Tycho Brahe in Cassiopeia). No further supernovae have since been observed with certainty in the Milky Way, though many others outside our galaxy have been seen since S Andromedae. *Wik

1776 Euler read a paper to the St. Petersburg Academy of Science entitled “De quadratis magicis,” in which he gave a method of constructing magic squares by means of two orthogonal Latin squares. *Peter Ullrich, “An Eulerian square before Euler and an experimental design before R. A. Fisher: On the early history of Latin squares,” Chance, vol. 12, no. 1, Winter 1999, pp. 22–26.

1831 After discovering induced current on October 1st using two electrified coils,  on the 17th of October Michael Faraday  observers the same effect on the galvanometer when he inserts a permanent steel magnet into the electrified coil. *A history of physics in its elementary branches By Florian Cajori

1843 Hamilton Writes to his friend, John Graves, with a description of Quaternions. By December, Graves will have extended the idea to an eight dimensional algebra which will become "octonians". 

Observatory, October 17, 1843
My dear Graves,|A very curious train of mathematical speculation occurred to me
yesterday, which I cannot but hope will prove of interest to you. You know that I have long
wished, and I believe that you have felt the same desire, to possess a Theory of Triplets,
analogous to my published Theory of Couplets, and also to Mr. Warren's geometrical representation
of imaginary quantities. Now I think that I discovered1 yesterday a theory of
quaternions which includes such a theory of triplets.

The complete letter is available at this site. *David R. Wilkins, *John Derbyshire, Unkown Quantity
In his preface to the ‘Lectures on Quaternions’ and in a prefatory letter to a communication to the Philosophical Magazine for December 1844 are acknowledgments of his indebtedness to Graves for stimulus and suggestion. *Wik

1858 DeMorgan writes a letter about Euler’s  prodigious output. *W W Rouse Ball, from The genius of Euler: reflections on his life and work, By William Dunham, pg 89

1933 Albert Einstein seeks asylum in the US, one of many Jewish/left-wing intellectuals fleeing the Nazi govt in Germany and Europe. The Nazi government put a bounty now worth £50,000 on his head while a German magazine included him in a list of the Nazis’ enemies who were 'not yet hanged'.

1952 D. H. Lehmer, University of California, announced that 2n − 1 for n = 2203 and 2281 are Mersenne primes. He was aided by a SWAC computing machine, the first result taking 59 minutes. *VFR This may have been predated by Raphael Mitchel Robinson (November 2, 1911 – January 27, 1995) at Berkeley may have beaten him by a week or so on October 7th of the same year.
D. H. Lehmer continued his fathers interest in combinatorial computing and in fact wrote the article "Machine tools of Computation," which is chapter one in the book "Applied Combinatorial Mathematics," by Edwin Beckenbach, 1964. It describes methods for producing permutations, combinations etc. This was a uniquely valuable resource and has only been rivaled recently by Volume 4 of Donald Knuth's series. In 1950, Lehmer was one of 31 University of California faculty fired after refusing to sign a loyalty oath, a policy initiated by the Board of Regents of the State of California in 1950 during the Communist scare personified by Senator Joseph McCarthy. (see below)*Wik

1952 The California Supreme Court declared the state loyalty oath unconstitutional and declared that the eighteen faculty members who had refused to sign the oath be reinstated.*VFR

1978 James Burke's history of science series Connections first airs, on BBC Television in the United Kingdom (with accompanying book). *Wik

1983 Gerard Debreu, who holds a joint appointment in Mathematics and Economics at Berkeley, won a Nobel Prize for his work in mathematical economics. For a non-technical description of his work see The Mathematical Intelligencer, 6(1984), no. 2, pp. 61–62. *VFR

2012 Car size pieces of Halley's Comet lit up the skies over the Bay Area in California. Hundreds of residents from Oakland, San Francisco and Santa Cruz called ABC News station KGO-TV, reporting a loud boom, explosions and streaks of light around 7:45 p.m. local time. The Orionids are one of two annual meteor showers produced by icy pieces of Halley's Comet. The other shower, called the Eta Aquarids, peaks each year in early May, according to NASA. Video *ABC News


1759 Jakob II Bernoulli (17 October 1759, Basel – 3 July 1789, Saint Petersburg), younger brother of Johann III Bernoulli. Having finished his literary studies, he was, according to custom, sent to Neuchâtel to learn French. On his return he graduated in law. This study, however, did not check his hereditary taste for geometry. The early lessons which he had received from his father were continued by his uncle Daniel, and such was his progress that at the age of twenty-one he was called to undertake the duties of the chair of experimental physics, which his uncle’s advanced years rendered him unable to discharge. He afterwards accepted the situation of secretary to count de Brenner, which afforded him an opportunity of seeing Germany and Italy. In Italy he formed a friendship with Lorgna, professor of mathematics at Verona, and one of the founders of the Società Italiana for the encouragement of the sciences. He was also made corresponding member of the royal society of Turin; and, while residing at Venice, he was, through the friendly representation of Nicolaus von Fuss, admitted into the academy of St Petersburg. In 1788 he was named one of its mathematical professors. *Wik
He drowned while bathing in the Neva in July 1789, a few months after his marriage with a granddaughter of Leonhard Euler.  (Can't tell your Bernoulli's without a scorecard?  Check out "A Confusion of Bernoulli's" by the Renaissance Mathematicus.)

1788 Paul Isaak Bernays (17 Oct 1888; 18 Sep 1977) Swiss mathematician and logician who is known for his attempts to develop a unified theory of mathematics. Bernays, influenced by Hilbert's thinking, believed that the whole structure of mathematics could be unified as a single coherent entity. In order to start this process it was necessary to devise a set of axioms on which such a complete theory could be based. He therefore attempted to put set theory on an axiomatic basis to avoid the paradoxes. Between 1937 and 1954 Bernays wrote a whole series of articles in the Journal of Symbolic Logic which attempted to achieve this goal. In 1958 Bernays published Axiomatic Set Theory in which he combined together his work on the axiomatisation of set theory. *TIS

1927 Friedrich Ernst Peter Hirzebruch (17 October 1927 – 27 May 2012) was a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation. He has been described as "the most important mathematician in the Germany of the postwar period.
Amongst many other honours, Hirzebruch was awarded a Wolf Prize in Mathematics in 1988 and a Lobachevsky Medal in 1989. The government of Japan awarded him the Order of the Sacred Treasure in 1996. He also won an Einstein Medal in 1999, and received the Cantor medal in 2004.*Wik


1817 John West (10 April 1756 in Logie (near St Andrews), Scotland - 17 Oct 1817 in Morant Bay, Jamaica) The achievements of the little-known Scottish mathematician, John West (1756–1817), deserve recognition: hisElements of Mathematics(1784) shows him to be a skilled expositor and innovative geometer while his manuscript,Mathematical Treatises,unpublished until 1838, reveal him also to be an accomplished exponent of “continental” analysis, familiar with works of Lagrange, Laplace, and Arbogast then little studied in Britain.
First an assistant at St. Andrews University in Scotland, West then worked in isolation in Jamaica, combining mathematics with the duties of an Anglican rector. His life and his pastoral and mathematical works are here described. *abstract for Geometry, Analysis, and the Baptism of Slaves: John West in Scotland and Jamaica, Alex D.D. Craik

1877 Gustav Robert Kirchhoff (12 Mar 1824, 17 Oct 1887) German physicist who, with Robert Bunsen, established the theory of spectrum analysis (a technique for chemical analysis by analyzing the light emitted by a heated material), which Kirchhoff applied to determine the composition of the Sun. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated, which explained the numerous dark lines (Fraunhofer lines) in the Sun's spectrum. In his Kirchhoff's laws (1845) he generalized the equations describing current flow to the case of electrical conductors in three dimensions, extending Ohm's law to calculation of the currents, voltages, and resistances of electrical networks. He demonstrated that current flows in a zero-resistance conductor at the speed of light. *TIS

1923 August Adler (24 Jan 1863 in Opava, Austrian Silesia (now Czech Republic)-17 Oct 1923 in Vienna, Austria) In 1906 Adler applied the theory of inversion to solve Mascheroni construction problems in his book Theorie der geometrischen Konstruktionen published in Leipzig. In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.
Since he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses. However Adler did not simplify Mascheroni proof. On the contrary, his new methods were not as elegant, either in simplicity or length, as the original proof by Mascheroni.
This 1906 publication was not the first by Adler studying this problem. He had published a paper on the theory of Mascheroni's constructions in 1890, another on the theory of geometrical constructions in 1895, and one on the theory of drawing instruments in 1902. As well as his interest in descriptive geometry, Adler was also interested in mathematical education, particularly in teaching mathematics in secondary schools. His publications on this topic began around 1901 and by the end of his career he was publishing more on mathematical education than on geometry. Most of his papers on mathematical education were directed towards teaching geometry in schools, but in 1907 he wrote on modern methods in mathematical instruction in Austrian middle schools. He produced various teaching materials for teaching geometry in the sixth-form in Austrian schools such as an exercise book which he published in 1908. *SAU

1937 Frank Morley (9 Sept 1860 in Woodbridge, Suffolk, England-17 Oct 1937 in Baltimore, Maryland, USA) wrote mainly on geometry but also on algebra.*SAU Morley is remembered most today for a singular theorem which bears his name in recreational literature.  Simply stated, Morley's Theorem says that if the angles at the vertices of any triangle (A, B, and C in the figure) are trisected, then the points where the trisectors from adjacent vertices intersect (D, E, and F) will form an equilateral triangle. In 1899 he observed the relationship described above, but could find  no  proof. It spread from discussions with his friends to become an item  of  mathematical gossip. Finally in 1909 a trigonometric solution was   discovered by M. Satyanarayana. Later an elementary proof was developed.   Today the preferred proof is to begin with the result and work   backward. Start with an equilateral triangle and show that the vertices   are the intersection of the trisectors of a triangle with any given set   of angles. For those interested in seeing the proof, check Coxeter's Introduction to Geometry, Vol 2, pages 24-25. Find more about this unusual man here.  *PB

1941 John Stanley Plaskett (17 Nov 1865, 17 Oct 1941) Canadian astronomer known for his expert design of instruments and his extensive spectroscopic observations. He designed an exceptionally efficient spectrograph for the 15-inch refractor and measured radial velocities and found orbits of spectroscopic binary stars. He designed and supervised construction of the 72-inch reflector built for the new Dominion Astrophysical Observatory in Victoria and was appointed its first director in 1917. There he extended the work on radial velocities and spectroscopic binaries and studied spectra of O and B-type stars. In the 1930s he published the first detailed analysis of the rotation of the Milky Way, demonstrating that the sun is two-thirds out from the center of our galaxy about which it revolves once in 220 million years.*TIS

1952 Ernest Vessiot (8 March 1865 in Marseilles, France-17 Oct 1952 in La Bauche, Savoie, France) applied continuous groups to the study of differential equations. He extended results of Drach (1902) and Cartan (1907) and also extended Fredholm integrals to partial differential equations.  Vessiot was assigned to ballistics during World War I and made important discoveries in this area. He was honoured by election to the Académie des Sciences in 1943. *SAU

1963 Jacques-Salomon Hadamard (8 Dec 1865, 17 Oct 1963) French mathematician who proved the prime-number theorem (as n approaches infinity, the limit of the ratio of (n) and n/ln(n) is 1, where (n) is the number of positive prime numbers not greater than n). Conjectured in the 18th century, this theorem was not proved until 1896, when Hadamard and also Charles de la Vallée Poussin, used complex analysis. Hadamard's work includes the theory of integral functions and singularities of functions represented by Taylor series. His work on the partial differential equations of mathematical physics is important. He introduced the concept of a well-posed initial value and boundary value problem. In considering boundary value problems he introduced a generalization of Green's functions (1932). *TIS

1978 Gertrude Mary Cox (January 13, 1900 – October 17, 1978) was an influential American statistician and founder of the department of Experimental Statistics at North Carolina State University. She was later appointed director of both the Institute of Statistics of the Consolidated University of North Carolina and the Statistics Research Division of North Carolina State University. Her most important and influential research dealt with experimental design; she wrote an important book on the subject with W. G. Cochran. In 1949 Cox became the first female elected into the International Statistical Institute and in 1956 she was president of the American Statistical Association.*Wik

2008 Andrew Mattei Gleason (November 4, 1921 – October 17, 2008) was an American mathematician and the eponym of Gleason's theorem and the Greenwood–Gleason graph. After briefly attending Berkeley High School (Berkeley, California) he graduated from Roosevelt High School in Yonkers, then Yale University in 1942, where he became a Putnam Fellow. He subsequently joined the United States Navy, where he was part of a team responsible for breaking Japanese codes during World War II. He was appointed a Junior Fellow at Harvard in 1946, and later joined the faculty there where he was the Hollis Professor of Mathematicks and Natural Philosophy. He had the rare distinction among Harvard professors of having never obtained a doctorate. (In graph theory, the Greenwood–Gleason graph (Image at top of page) is also known as the Clebsch graph. It is an undirected graph with 16 vertices and 40 edges. It is named after Alfred Clebsch, a German mathematician who discovered it in 1868. It is also known as the Greenwood–Gleason graph after the work of Robert M. Greenwood and Andrew M. Gleason (1955), who used it to evaluate the Ramsey number R(3,3,3) = 17 *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 October 2017

On This Day in Math - Oct 16

I have often pondered over the roles of knowledge or experience, on the one hand, and imagination or intuition, on the other, in the process of discovery. I believe that there is a certain fundamental conflict between the two, and knowledge, by advocating caution, tends to inhibit the flight of imagination. Therefore, a certain naivete, unburdened by conventional wisdom, can sometimes be a positive asset.

The 289th day of the year; 289 is a Friedman number since (8 + 9)2 = 289 (A Friedman number is an integer which, in a given base, is the result of an expression using all its own digits in combination with any of the four basic arithmetic operators (+, −, ×, ÷) and sometimes exponentiation.)Students might try to find the first few multi-digit Friedman numbers.

289 is the square of the sum of the first four primes, 289 = (2 + 3 + 5 + 7)2

289 is the largest 3-digit square with increasing digits.

289 is the hypotenuse of a primitive Pythagorean triple. Find the legs students!


1707 Roger Cotes elected first Plumian Professor of Astronomy and Experimental Philosophy at Cambridge at age 26. He is best known for his meticulous and creative editing of the second edition (1713) of Newton’s Principia. He was also an important developer of the integral calculus. *Ronald Gowing, Roger Cotes, Natural Philosopher, p. 14

1797 Gauss records in his diary that he has discovered a new proof of the Pythagorean Theorem. See Gray, Expositiones Mathematicae, 2(1984), 97–130. *VFR

1819  Thomas Young writes to Fresnel to thank him for a copy of his memoirs (sent to Young by Arago). "I return a thousand thanks, Monsieur, for the gift of your admirable memoir, which surely merits a very high rank amongst the papers which have contributed most to the progress of optics." *A history of physics in its elementary branches By Florian Cajori

1843 Hamilton discovered quaternions while walking along the Royal Canal in Dublin and immediately scratches the multiplication formulas on a bridge. Today a plaque on the bridge reads, "Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplication i2 = j2 = k2 = ijk = −1 & cut it in a stone on this bridge." Since 1989, the Department of Mathematics of the National University of Ireland, Maynooth has organized a pilgrimage, where scientists (including the physicists Murray Gell-Mann in 2002, Steven Weinberg in 2005, and the mathematician Andrew Wiles in 2003) take a walk from Dunsink Observatory to the Royal Canal bridge where no trace of Hamilton's carving remains, unfortunately.
Here is how Hamilton described his memory of the discovery of the Quaternions to his son, "Every morning in the early part of the above-cited month, on my coming down to breakfast, your (then) little brother, William Edwin, and yourself, used to ask me, `Well, papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: `No, I can only add and subtract them. But on the 16th day of the same month (Oct) - which happened to be Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula which contains the Solution of the Problem, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on `Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following.'' *from Hamilton By Sir Robert Stawell Ball.

The plaque says:
Here as he walked by
on the 16th of October 1843
Sir William Rowan Hamilton
in a flash of genius discovered
the fundamental formula for
quaternion multiplication
i2 = j2 = k2 = i j k = −1
& cut it on a stone of this bridge

(Quatenion was a Latin term before Hamilton used it.  Milton uses it in Paradise Lost to refer to the four elements of antiquity: air, earth, water, and fire. The last three are “the eldest birth of nature’s womb” because they are mentioned in Genesis before air is mentioned. *John Cook )

In 1982, Halley's Comet was observed on its 30th recorded visit to Earth, first detected using the 5-m (200-in) Hale Telescope at the Mount Palomar Observatory by a team of astronomers led by David Jewett and G. Edward Danielson. They found the comet, beyond the orbit of Saturn, about 11 AU (1.6 billion km) from the Sun. While 50 million times fainter than the faintest objects our eyes can see, they needed to use not only the largest American telescope but also special electronic equipment developed for the Space Telescope. In 1705, Halley used Newton's theories to compute the orbit and correctly predicted the return of this comet about every 76 years. After his death, for correctly predicting its reappearance, it was named after Halley. *TIS (The next predicted perihelion of Halley's Comet is 28 July 2061)
In 1982 the first image of the returning Halley's Comet was recorded with the 200-inch Hale telescope at Palomar Mountain. Caltech astronomers David Jewitt and G. Edward Danielson found the comet when it was still beyond the orbit of Saturn, more than 1.6 billion kilometers (960 million miles) from the Sun. *National Air and Space Museum

1988 Connect Four Solved first by James D. Allen (Oct 1, 1988), and independently by Victor Allis (Oct 16, 1988). First player can force a win. Strongly solved by John Tromp's 8-ply database (Feb 4, 1995). Weakly solved for all boardsizes where width+height is at most 15 (Feb 18, 2006). *Wik

2016 The 27th Hamilton walk takes place on this day. Students, professors, and math lovers in general will gather at the Dunsink Observatory around 3:30 pm and proceed to Broombridge in Cabra where he had his Eureka moment about Quaternions. (see 1843 in Events above) The annual event is part of Irish Math week.

1689 Robert Smith (16 October,1689 – 2 February, 1768) was an English mathematician and Master of Trinity College.
Smith was probably born at Lea near Gainsborough, the son of the rector of Gate Burton, Lincolnshire. He entered Trinity College, Cambridge, in 1708, and becoming minor fellow in 1714, major fellow in 1715 and senior fellow in 1739. From 1716 to 1760 he was Plumian Professor of Astronomy,and was chosen Master in 1742, in succession to Richard Bentley.
Besides editing two works by his cousin, Roger Cotes, who was his predecessor in the Plumian chair, he published A Compleat System of Opticks in 1738, (which was the principal textbook on Optics in the 18th Century) , and Harmonics, or the Philosophy of Musical Sounds in 1749.
Smith never married but lived with his unmarried sister Elzimar (1683–1758) in the lodge at Trinity College. Although he is often portrayed as a rather reclusive character, John Byrom's journal shows that in the 1720s and 1730s Smith could be quite sociable. Yet ill health, particularly gout, took its toll and severely inhibited his academic work and social activities. He died at the lodge on 2 February 1768, and on 8 February he was buried in Trinity College Chapel.
In his will Smith left £3500 South Sea stock to the University of Cambridge. The net income on the fund is annually divided equally between the Smith's Prize and the stipend of the Plumian Professor. *Wik

1879 Philip Edward Bertrand Jourdain (16 October 1879 – 1 October 1919) was a British logician and follower of Bertrand Russell. He corresponded with Georg Cantor and Gottlob Frege, and took a close interest in the paradoxes related to Russell's paradox, formulating the card paradox version of the liar paradox. He also worked on algebraic logic, and the history of science with Isaac Newton as a particular study. He was London editor for The Monist. *Wik

1882 Ernst Erich Jacobsthal (16 October 1882, Berlin – 6 February 1965, Überlingen) was a German mathematician, and brother to the archaeologist Paul Jacobsthal.
In 1906, he earned his PhD at the University of Berlin, where he was a student of Georg Frobenius, Hermann Schwarz and Issai Schur; his dissertation, Anwendung einer Formel aus der Theorie der quadratischen Reste (Application of a Formula from the Theory of Quadratic Remainders), provided a proof that prime numbers of the form 4n + 1 are the sum of two square numbers. *Wik

1930 John Charlton Polkinghorne KBE FRS (born 16 October 1930) is an English theoretical physicist, theologian, writer, and Anglican priest. He was professor of Mathematical physics at the University of Cambridge from 1968 to 1979, when he resigned his chair to study for the priesthood, becoming an ordained Anglican priest in 1982. He served as the president of Queens' College, Cambridge from 1988 until 1996.*Wik


1937 William Sealy Gosset (13 June 1876 in Canterbury, England - 16 October 1937 in Beaconsfield, England) Gosset was the eldest son of Agnes Sealy Vidal and Colonel Frederic Gosset who came from Watlington in Oxfordshire. William was educated at Winchester, where his favourite hobby was shooting, then entered New College Oxford where he studied chemistry and mathematics. While there he studied under Airy. He obtained a First Class degree in both subjects, being awarded his mathematics degree in 1897 and his chemistry degree two years later.

Gosset obtained a post as a chemist with Arthur Guinness Son and Company in 1899. Working in the Guinness brewery in Dublin he did important work on statistics. In 1905 he contacted Karl Pearson and arranged to go to London to study at Pearson's laboratory, the Galton Eugenics Laboratory, at University College in session 1906-07. At this time he worked on the Poisson limit to the binomial and the sampling distribution of the mean, standard deviation, and correlation coefficient. He later published three important papers on the work he had undertaken during this year working in Pearson's laboratory.
Many people are familiar with the name "Student" but not with the name Gosset. In fact Gosset wrote under the name "Student" which explains why his name may be less well known than his important results in statistics. He invented the t-test to handle small samples for quality control in brewing. Gosset discovered the form of the t distribution by a combination of mathematical and empirical work with random numbers, an early application of the Monte-Carlo method.

McMullen says:-

To many in the statistical world "Student" was regarded as a statistical advisor to Guinness's brewery, to others he appeared to be a brewer devoting his spare time to statistics. ... though there is some truth in both these ideas they miss the central point, which was the intimate connection between his statistical research and the practical problems on which he was engaged. ... "Student" did a very large quantity of ordinary routine as well as his statistical work in the brewery, and all that in addition to consultative statistical work and to preparing his various published papers.

From 1922 he acquired a statistical assistant at the brewery, and he slowly built up a small statistics department which he ran until 1934.
Gosset certainly did not work in isolation. He corresponded with a large number of statisticians and he often visited his father in Watlington in England and on these occasions he would visit University College, London, and the Rothamsted Agricultural Experiment Station. He would discuss statistical problems with Fisher, Neyman and Pearson. *SAU

1983 Harish-Chandra (11 October 1923 – 16 October 1983) was an Indian mathematician, who did fundamental work in representation theory, especially Harmonic analysis on semisimple Lie groups.*Wik

1998 Jonathan Bruce Postel (6 Aug 1943, 16 Oct 1998) American computer scientist who played a pivotal role in creating and administering the Internet. In the late 1960s, Postel was a graduate student developing the ARPANET, a forerunner of the Internet for use by the U.S. Dept. of Defense. As director of the Internet Assigned Numbers Authority (IANA), which he formed, Postel was a creator of the Internet's address system. The Internet grew rapidly in the 1990s, and there was concern about its lack of regulation. Shortly before his death, Postel submitted a proposal to the U.S. government for an international nonprofit organization that would oversee the Internet and its assigned names and numbers. He died at age 55, from complications after heart surgery.*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

Sunday, 15 October 2017

On This Day in Math - October 15

Many have argued that a vacuum does not exist, others claim it exists only with difficulty in spite of the repugnance of nature; I know of no one who claims it easily exists without any resistance from nature.
— Evangelista Torricelli in a Letter to Michelangelo Ricci

The 288th day of the year; 288 is the super-factorial of four. 1! x 2! x 3! x 4! =288. It is important that math students learn not to say this number in public as it is two gross. (I apologize for the really bad pun)

288 is also the sum of the first four integers raised to their own power \(1^1 + 2^2 + 3^3 + 4^4 = 288 \)

288 is the smallest non-palindrome, non-square, that when multiplied by its reverse is a square: 288 x 882 = 254,016 = 5042.


1582 St Theresa of Avila died overnight on the night between the 4th and the 15th of October. On that day the Gregorian calendar went into effect in Spain and the day after the 4th, was the 15th in order to catch up for the misalignment of the Julian Calendar. *VFR

1698 King William III commissioned Edmund Halley as Royal Naval Captain of the HMS
Paramore and provided him with a complete set of instructions. The Admiralty’s instructions to Halley dated 15 October 1698 were :
Whereas his Maty. has been pleased to lend his Pink the Paramour for your proceeding with her on an Expedition, to improve the knowledge of the Longitude and variations of the Compasse, which Shipp is now compleatly Man’d, Stored and Victualled at his Mats. Charge for the said Expedition ... *Lori L. Murray, The Construction of Edmond Halley’s 1701 Map of Magnetic Declination

1783 The first manned ascension in a balloon. After the flight of September 19, 1783, Louis XVI forbade men to go aloft, making the adventurers furious. Later he extended the privilege to convicts, figuring they were expendable. de Rozier’s loud fulmigations against such glory for “vile criminals” soon changed the king’s mind. The hydrogen balloon, Aerostat Reveillon, carrying Pilâtre, first man to leave the earth, rose to the end of its 250- ft tether. It stayed aloft for 15 minutes, then landed safely nearby.
 On 21 Nov 1783, untethered, Pilâtre and Marquis d'Arlande made the first manned free flight, across Paris. On 15 Jun 1785, Pilâtre attempt the first east-to-west crossing of the English Channel with a hybrid balloon combining lift from both hydrogen and hot air. Within minutes of launch, the craft exploded, and plunged to the rocks on the coast of Wimereux. Neither Pilâtre nor his co-pilot, Romain, survived the crash. *TIS (American Scientist and U S emissary to the court of Louis XVI, Ben Franklin, was present for some of the Balloon ascensions in 1783. When asked what was the use of Ballooning, he replied, “Of what use is a newborn baby?”)

In 1827, Charles Darwin was accepted into Christ's College at Cambridge, but did not start until winter term because he needed to catch up on some of his studies. A grandson of Erasmus Darwin of Lichfield, and of Josiah Wedgwood, he had entered the University of Edinburgh in 1825 to study medicine, intending to follow his father Robert's career as a doctor. However, Darwin found himself unenthusiastic about his studies, including that of geology. Disappointing his family that he gave up on a medical career, he left Edinburgh without graduating in April 1827. His scholastic achievements at Cambridge were unremarkable, but after graduation, Darwin was recommended by his botany professor to be a naturalist to sail on HM Sloop Beagle. *TIS

1956 The first FORTRAN reference manual is released on October 15, 1956, six months before the first compiler's release. Only 60 pages long, with large print and wide margins, that first programming language was miniscule by today's standard. The original FORTRAN development team comprised John Backus, Sheldon Best, Richard Goldberg, Lois Mitchell Haibt, Harlan Herrick, Grace Mitchell, Robert Nelson, Roy Nutt, David Sayre, Peter Sheridan, and Irving Ziller.*CHM

In 2003, China became the third nation to send a man into space. Lieutenant Colonel Yang Liwei, 38, was launched on a Long March CZ-2F rocket in the Shenzhou-5 spacecraft at 9 am local time (1 am GMT). He completed 14 Earth orbits during a 21-hour flight which ended with a parachute-assisted landing in the on the grasslands of Inner Mongolia in northern China. The Shenzhou spacecraft was based on the three-seat Russian Soyuz capsule, but with extensive modifications. The country began planning manned spaceflight in 1992. Russia began providing advice on technology and astronaut training in 1995. The first of four unmanned test flights of a Shenzhou craft (took place in Nov 1999. The name Shenzhou translates as "divine vessel." *TIS


1608 Evangelista Torricelli (15 Oct 1608; 25 Oct 1647) Born in Faenza, Italy, Torricelli was an Italian physicist and mathematician who invented the barometer and whose work in geometry aided in the eventual development of integral calculus. Inspired by Galileo's writings, he wrote a treatise on mechanics, De Motu ("Concerning Movement"), which impressed Galileo. He also developed techniques for producing telescope lenses. The barometer experiment using "quicksilver" filling a tube then inverted into a dish of mercury, carried out in Spring 1644, made Torricelli's name famous. The Italian scientists merit was, above all, to admit that the effective cause of the resistance presented by nature to the creation of a vacuum (in the inverted tube above the mercury) was probably due to the weight of air. *TIS He succeeded his teacher, Galileo as professor of mathematics at Florence. One of his most amazing discoveries was a solid which had infinite length but finite volume. He also invented the mercury barometer.*VFR

1735 Jesse Ramsden FRSE (15 October 1735 – 5 November 1800) was an English astronomical and scientific instrument maker.
Ramsden created one of the first high-quality dividing engines. This machine permitted the automatic and highly accurate division of a circle into degrees and fractions of degrees of arc.The machine  led to mass production of precision octants and sextants and gave British manufacturers dominance in the field of marine instruments for decades.  His invention was so valuable to the nation’s maritime interests that he received a share of the Longitude Prize.
  His most celebrated work was a 5-feet vertical circle, which was finished in 1789 and was used by Giuseppe Piazzi at Palermo in constructing his catalog of stars. He was the first to carry out in practice a method of reading off angles (first suggested in 1768 by the Duke of Chaulnes) by measuring the distance of the index from the nearest division line by means of a micrometer screw which moves one or two fine threads placed in the focus of a microscope.
Ramsden's transit instruments were the first which were illuminated through the hollow axis; the idea was suggested to him by Prof. Henry Ussher in Dublin. He published a Description of an Engine for dividing Mathematical Instruments in 1777.
Ramsden is also responsible for the achromatic eyepiece named after him, and also worked on new designs of electrostatic generators. He was elected to the Royal Society in 1786. The exit pupil of an eyepiece was once called the Ramsden disc in his honour. In 1791 he completed the Shuckburgh telescope, an equatorial mounted refractor telescope.
In about 1785, Ramsden provided a new large theodolite for General William Roy of the Royal Engineers, which was used for a new survey of the distance between Greenwich, London and Paris. This work provided the basis for the subsequent Ordnance Survey of the counties of Britain. For his part with Roy in this work he received the Copley Medal in 1795. He died five years later at Brighton, England.*Wik

1745 George Atwood (Baptized October 15, 1745, Westminster,London – 11 July 1807, London) was an English mathematician who invented a machine for illustrating the effects of Newton's first law of motion. He was the first winner of the Smith's Prize in 1769. He was also a renowned chess player whose skill for recording many games of his own and of other players, including François-André Danican Philidor, the leading master of his time, left a valuable historical record for future generations.
He attended Westminster School and in 1765 was admitted to Trinity College, Cambridge. He graduated in 1769 with the rank of third wrangler and was awarded the inaugural first Smith's Prize. Subsequently he became a fellow and a tutor of the college and in 1776 was elected a fellow of the Royal Society of London.
In 1784 he left Cambridge and soon afterwards received from William Pitt the Younger the office of patent searcher of the customs, which required but little attendance, enabling him to devote a considerable portion of his time to mathematics and physics.
He died unmarried in Westminster at the age of 61, and was buried there at St. Margaret's Church. Over a century later, a lunar crater was renamed Atwood in his honour. *Wik

1776 Peter Barlow (15 Oct 1776, 1 March 1862) Peter Barlow was self-educated but this education was sufficiently good that he was able to compete successfully to became an assistant mathematics master at the Royal Military Academy at Woolwich. He was appointed to the post in 1801 and he began publishing mathematical articles in the Ladies Diary and he became sufficiently well established as a leading authority on mathematics that after a while he was asked to contribute various articles on mathematics for encyclopedias.
In addition to these articles, Barlow also published several important books, for example in 1811 he published An elementary investigation of the theory of numbers and three years later he published A new mathematical and philosophical dictionary.
He is remembered most for two important contributions. In 1814 he produced a second book, in addition to the one described above, entitled New mathematical tables. These soon became known as Barlow's Tables and this work gives factors, squares, cubes, square roots, reciprocals and hyperbolic logarithms of all numbers from 1 to 10 000. The book "...was considered so accurate and so useful that it has been regularly reprinted ever since. "
In the mathematical library at the University of St Andrews we have several well worn copies of these tables which must have been used intensely for many years. Today, however, they are only of historical interest since they were made completely obsolete by calculators and computers.
Barlow's second major contribution makes his name still well known by amateur astronomers today. He invented the Barlow lens, a telescope lens consisting of a colorless liquid between two pieces of glass, the "Barlow lens", a modification of this telescope lens, is a negative achromatic combination of flint glass and crown glass.
In 1819 Barlow began work on the problem of deviation in ship compasses caused by the presence of iron in the hull. For his method of correcting the deviation by juxtaposing the compass with a suitably shaped piece of iron, he was awarded the Copley Medal ... *SAU
Barlow is quoted on SAU as saying, "230(231-1) is the greatest perfect number that will ever be discovered, for, as they are merely curious without being useful, it is not likely that any person will attempt to find a number beyond it."

1829 Asaph Hall (15 Oct 1829; 22 Nov 1907) American astronomer, discovered and named the two moons of Mars, Phobos and Deimos, and calculated their orbits.Born in Goshen, Conn. and apprenticed as a carpenter at age 16, he had a passion for geometry and algebra. Hall obtained a position at the Harvard Observatory in Cambridge, Mass. in 1857 and became an expert computer of orbits. In August 1862, he joined the staff of the Naval Observatory in Washington, D.C. where he made his discoveries, in mid- Aug 1877, using the Observatory's 26-inch "Great Equatorial" refracting telescope, then the largest of its kind in the world. He stayed there 30 years until 1891. His son, Asaph Hall, Jr., followed him and worked at the Observatory at various times between 1882-1929.*TIS

1837 Leo Königsberger (15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject. The biography of Helmholtz was published in 1902 and 1903. He also wrote a biography of C. G. J. Jacobi.
Königsberger's own research was primarily on elliptic functions and differential equations. He worked closely with Lazarus Fuchs, a childhood friend.*Wik

1867 Jacques Inaudi (October 15, 1867 – November 10, 1950) Born to a poor family in the Italian Piedmont, Jacques Inaudi began life as a shepherd but soon discovered a prodigious talent for calculation, and soon he was giving exhibitions in large cities.
Camille Flammarion wrote, “He was asked, for example, how many minutes have elapsed since the birth of Jesus Christ, or what the population would be if the dead from the past ten centuries were resurrected, or the square root of a number of twelve digits, and he gave the response accurately and in two or three minutes — while amusing himself with another activity.”
“The subtraction of numbers consisting of twenty-four figures is an easy matter for him,” reported Scientific American. “Problems for which logarithm tables are generally used he solves mentally with wonderful precision.”
Unlike other prodigies, Inaudi did not visualize his work. “I hear the figures,” he told Alfred Binet, “and it is my ear which retains them; I hear them resounding after I have repeated them, and this interior sensation remains for a long time.”
Inaudi’s father had approached Flammarion hoping that his son could be educated toward a career in astronomy. “It had been an error, whichever way one looked at it,” Flammarion wrote 10 years later. “In science, one cannot make use of his methods, of his adapted formulae, which are tailored to mental calculation.” It was just as well: “Regarding his financial position, he now has, as a result of the curiosity his ability has aroused, a salary, which is over three times that of the Director of the Paris Observatory.” *Greg Ross, Futility Closet

1905 Baron C(harles) P(ercy) Snow (15 Oct 1905; 1 Jul 1980) British former physicist, turned novelist and government administrator. In 1959, C.P. Snow gave a controversial lecture called The Two Cultures and the Scientific Revolution claiming there were two cultures - the literary intellectuals and the scientists, who didn't understand each other and didn't trust each other. The split was not new; Snow noted that in the 1930s, literary theorists had begun to use the word "intellectual" to refer only to themselves. He illustrated this gap by asking a group of literary intellectuals to tell him about the Second Law of Thermodynamics, which he called the scientific equivalent of `Have you read a work of Shakespeare?'" Since then, debate about this polarization has continued.*TIS

1875 André-Louis Cholesky (October 15, 1875 – August 31, 1918,) a French military officer and mathematician. He worked in geodesy and map-making, was involved in surveying in Crete and North Africa before World War I. But he is primarily remembered for the development of a matrix decomposition known as the Cholesky decomposition which he used in his surveying work. He served the French military as engineer officer and was killed in battle a few months before the end of World War I; his discovery was published posthumously by his fellow officer in the "Bulletin Géodésique".*Wik

Bernhard Hermann Neumann (15 Oct 1909, 21 Oct 2002) Neumann is one of the leading figures in group theory who has influenced the direction of the subject in many different ways. While still in Berlin he published his first group theory paper on the automorphism group of a free group. However his doctoral thesis at Cambridge introduced a new major area into group theory research. In his thesis he initiated the study of varieties of groups, that is classes of groups defined which are by a collection of laws which must hold when any group elements are substituted into them. *SAU
(check the dates of birth and death between this entry and the next... I checked, it seems to be correct, PB)

1909 Jesse L. Greenstein (15 Oct 1909; 21 Oct 2002) American astronomer who was a co-discoverer of quasars. His interest in astronomy began at age 8 when his grandfather gave him a brass telescope. By age 16, he was a student at Harvard University, and later earned his Ph.D.(1937), then joined the Yerkes Observatory under Otto Struve. Thereafter, he spent most of his career at the California Institute of Technology.. He measured the composition of stars, through which he found less heavy elements in the stars of globular clusters, thus proving they are younger than our Sun. In 1963, he and Maarten Schmidt were the first to correctly describe the nature of quasars, by interpreting their red shift as compact, very distant and thus very old objects. With Louis Henyey he designed and constructed a new spectrograph and wide-view camera to improve astronomical observations. *TIS


1959 Lipót Fejér (9 Feb 1880, 15 Oct 1959) Fejér's main work was in harmonic analysis working on Fourier series and their singularities. Fejér collaborated to produce important papers with Carathéodory on entire functions and with Riesz on conformal mappings. *SAU

1965 Abraham Halevi (Adolf) Fraenkel (February 17, 1891, Munich, Germany – October 15, 1965, Jerusalem, Israel) known as Abraham Fraenkel, was an Israeli mathematician born in Germany. He was an early Zionist and the first Dean of Mathematics at the Hebrew University of Jerusalem. He is known for his contributions to axiomatic set theory, especially his addition to Ernst Zermelo's axioms which resulted in Zermelo–Fraenkel axioms.*Wik

1980 Mikhail Alekseevich Lavrentev(19 Nov 1900 in Kazan, Russia, 15 Oct 1980 in Moscow) is remembered for an outstanding book on conformal mappings and he made many important contributions to that topic.*SAU

1990 Wilhelm Magnus (February 5, 1907, Berlin, Germany – October 15, 1990, New York City) made important contributions in combinatorial group theory, Lie algebras, mathematical physics, elliptic functions, and the study of tessellations.*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