Friday 15 May 2020

On This Day in Math - May 14

“I have found a very great number of exceedingly beautiful theorems.”
Pierre de Fermat

The 135th day of the year; 135 = 11 + 32 + 53. *What's So Special About This Number 

135 is also equal to (1 x 3 x 5)( 1 + 3 +5) (can you find another number which is either the product or sum of the two factors formed by the product of its digits, and the sum of its digits?)

Both 1!+3!+5!= 127 is prime; and 1!!+3!!+5!! is prime if the double factorial n!! means n (n-2)(n-4).... (the same symbol is sometimes used for the factorial of n! ).

135 is the "partition number", or the number of ways to partition 14. We still do not know if there are an infinite number of "partition numbers" which are divisible by 3, although we do know there are an infinite number divisible by 2


May 14, 1230 "On the 14th May, which was the Tuesday in Rogation Week, the unusual eclipse of the Sun took place very early in the morning, immediately after sunrise; and it became so dark that the labourers, who had commenced their morning's work, were obliged to leave it, and returned again to their beds to sleep; but in about an hour's time, to the astonishment of many, the Sun regained its usual brightness." Refers to the total solar eclipse of 14 May 1230. From: Rogerus de Wendover, Flores Historiarum, vol.
ii. p.235 *NASA with HT to David Dickinson ‏ @Astroguyz

1539 Georg Joachim Rheticus writes from Posen to his teacher/friend Johannes Schoener in Nuremberg to tell him he is on the way to visit Copernicus. It may well have been Schoener that urged him to visit Copernicus. No record of the letter itself exists, but it was mentioned in the dedication of the Narratio prima by Rheticus sent to Schoener in 1540 while Rheticus was still studying with Copernicus. *John W. Hessler, A Renaissance Globemaker's Toolbox

1607 The first permanent English settlement in American was founded at Jamestown, VA. *VFR

1631 Pierre de Fermat installed at Toulouse, at age 31, as commissioner of requests. *VFR He would retain the position until his death.

1743 In a letter to Nikolaus Bernoulli in 1743, Euler writes 1 + x + x2 + ... +  xn. One of the first uses of ellipses for series.  Cajori states earlier use was most commonly "etc." or "&c." 

1755 Joseph Louis Vincens de Mauleon, governor of the principality of Orange, published his “proof” that the circle could be squared. He claimed this proof enabled him to explain the mysteries of original sin and of the Holy Trinity.Although he offered a prize of 300,000 franks to anyone who could show his proof fallacious, it is pure nonsense. *VFR

1791, the twenty-one year old Alexander von Humboldt wrote a to the Prussian minister and director of the Mining and Smelting Department (Bergwerks- und Hüttendepartment) in Berlin. In the letter he described his ‘plan’ (Entwurf) for his ‘future public life.’ Young Humboldt had manifold interests, but in spring 1791 he had made up his mind. He wanted to serve his Fatherland, not as a member of the military, but as a scientifically trained, practical mining official.
‘I am of the age,’ he stated, ‘in which I must desire to enter a certain sphere of activity, and to become useful to my Fatherland through the minor forces I sense within me.’ His wish to join von Heynitz's mining department and to ‘undergo comprehensive training’ in his department, he further explained, was motivated by ‘the decisive inclination for mineralogy [and] for the science of salt works and mining (Salz- und Bergwerkskunde)’ along with ‘the hope, one day perhaps to contribute to the large and beneficial plans’ through which von Heynitz, based on the ‘principles of state economy,’ had ‘opened new sources of national wealth. *Ursula Klein,The Prussian Mining Official Alexander von Humboldt, Annals of Science, 2012

1832 "In March 1832 a cholera epidemic swept Paris and prisoners, including Galois, were transferred to the Pension Sieur Faultrier. There he apparently fell in love with Stephanie-Felice du Motel, the daughter of the resident physician. After he was released on 29 April Galois exchanged letters with Stephanie, and it is clear that she tried to distance herself from the affair. The name Stephanie appears several times as a marginal note in one of Galois' manuscripts." *SAU On May 14, Galois received a rejection letter from Stephanie. (Am I the only one who finds it funny that he met a woman named Motel in a Pension.)

1910 Halley's comet was big news during its visible period in New York City. Beginning with the Saturday edition of May 14 and continuing on through the Sunday edition of May 22, the comet was given top billing in the New York Times. This was the period when the comet was at the height of its brilliance and activity and the coverage clearly reflected this. "May 14: NYC hotel roofs being used for comet parties; Professor S. A. Mitchell tells of superstitions surrounding comets through the ages in NYC speech." *Joseph M. Laufer, Halley's Comet Society - USA

1953 Results of the third annual MAA Mathematics Contest for high school students were announced. Tied for fourth place was Geraldine Anne Ferraro who later became the first woman vice-presidential nominee of a major political party. *VFR


1679 Peder [Nielsen] Horrebow (Horrebov) (14 May 1679; Løgstør, Jutland – 15 April 1764; Copenhagen) From 1703 to 1707, he served as an assistant to Ole Rømer and lived in Rømer's home. He worked as a household tutor from 1707 to 1711 to a Danish baron, and entered the governmental bureaucracy as an excise writer in 1711.
After repeatedly petitioning King Frederick IV, Horrebow became professor of mathematics at the University of Copenhagen in 1714. He also became director of the university's observatory (called the Rundetårn, "the Round Tower"). His son Christian succeeded him in this position. Horrebow and his wife, Anne Margrethe Rossing, had a total of 20 children.
In 1728, the great fire of Copenhagen destroyed all of the papers and observations made by Rømer, who had died in 1710. Horrebow wrote the Basis Astronomiae (1734–35), which describes the scientific achievements made by Rømer. Horrebow's own papers and instruments were destroyed in the same fire. Horrebow was given a special grant from the government to repair the observatory and instruments. Horrebow received further support from a wealthy patron.
Horrebow invented a way to determine a place's latitude from the stars. The method fixed latitude by observing differences of zenith distances of stars culminating within a short time of each other, and at nearly the same altitude, on opposite sides of the zenith. The method was soon forgotten despite its value until it was rediscovered by the American Andrew Talcott in 1833. It is now called the Horrebow-Talcott Method.
He wrote on navigation and determined the sun parallax, 9", an approximative solution to the Kepler equation. Horrebow also learned how to correct inherent flaws in instruments. This preceded Tobias Mayer's theory of correction of 1756.
Horrebow was a member of a number of scientific societies, including the Académie des Sciences (from 1746). He also worked as a medical doctor and as an academic notary (from 1720). *Wik

1701 William Emerson (14 May 1701 – 20 May 1782), English mathematician, was born at Hurworth, near Darlington, where his father, Dudley Emerson, also a mathematician, taught a school. William himself had a small estate in Weardale called Castle Gate situated not far from Eastgate where he would repair to work throughout the Summer on projects as disparate as stonemasonry and watchmaking. Unsuccessful as a teacher, he devoted himself entirely to studious retirement. Possessed of remarkable energy and forthrightness of speech, Emerson published many works which are singularly free from errata.

In The Principles of Mechanics (1754) he shows a wind-powered vehicle in which the vertically mounted propeller gives direct power to the front wheels via a system of cogs. In mechanics he never advanced a proposition which he had not previously tested in practice, nor published an invention without first proving its effects by a model. He was skilled in the science of music, the theory of sounds, and the ancient and modern scales; but he never attained any excellence as a performer. He died on 20 May 1782 at his native village, where his gravestone bears epitaphs in Latin and Hebrew.

Emerson dressed in old clothes and his manners were uncouth. He wore his shirt back to front and his legs wrapped in sacking so as not to scorch them as he sat over the fire. He declined an offer to become FRS because it would cost too much after all the expense of farthing candles he had been put to in the course of his life of study. Emerson rode regularly into Darlington on a horse like Don Quixote's, led by a hired small boy. In old age, plagued by the stone, he would alternately pray and curse, wishing his soul 'could shake off the rags of mortality without such a clitter-me-clatter.' *Wik

1832 Rudolf Otto Sigismund Lipschitz (14 May 1832 – 7 October 1903)  is remembered for the "Lipschitz condition", an inequality that guarantees a unique solution to the differential equation y' = f (x, y). *SAU
Lipschitz discovered Clifford algebras in 1880, two years after William K. Clifford (1845–1879) and independently of him, and he was the first to use them in the study of orthogonal transformations. Up to 1950 people mentioned “Clifford-Lipschitz numbers” when they referred to this discovery of Lipschitz. Yet Lipschitz’s name suddenly disappeared from the publications involving Clifford algebras; for instance Claude Chevalley (1909–1984) gave the name “Clifford group” to an object that is never mentioned in Clifford’s works, but stems from Lipschitz’s. Pertti Lounesto (1945–2002) contributed greatly to recalling the importance of Lipschitz’s role. *Wik

1863 John Charles Fields (May 14, 1863 - August 9, 1932) born in Toronto, Canada. After earning his Ph.D. at Johns Hopkins in 1887, he taught at Allegheny College (1889-1892) before going to Europe for a decade to study in Paris and Berlin. In 1902 he joined the faculty at the University of Toronto, where he remained until his death on 9 August 1932. *VFR
He originated the idea, posthumously given his name - for the Fields Medal. It became the most prestigious award for mathematicians, often referred to as the equivalent of a Nobel Prize for mathematicians. As a professor at the University of Toronto, he had worked to bring the International Congress of Mathematicians to Toronto (1924). The Congress was so successful that afterward there was a surplus of about \($2,500\) which Fields, as chairman of the organizing committee, proposed be used to fund two medals to be awarded at each of future Congresses. This was approved on 24 Feb 1931. He died the following year, leaving \($47,000\) as additional funding for the medals, which have been awarded since 1936. *TIS

1917 William Thomas Tutte FRS (May 14, 1917 – May 2, 2002) was a British, later Canadian codebreaker and mathematician. During World War II he broke a major German code system, which had a significant impact on the Allied invasion of Europe. He also had a number of significant mathematical accomplishments, including foundation work in the fields of combinatorics and graph theory. *Wik;


1669 Denis de Sallo, Sieur de la Coudraye (1626 - May 14, 1669) was a French writer and lawyer from Paris, known as the founder of the first French literary and scientific journal - the Journal des sçavans.
De Sallo obtained classical education and was admitted to the Paris bar in 1652, although he later devoted himself to scholarly aspects of the law rather than active practice, serving also as a counsel in the French government. He belonged to the clique of Jean-Baptiste Colbert, minister of finance under Louis XIV, and had active contacts with other prominent European scholars.
In 1665 he published the first issue of the Journal des sçavans under the pseudonym Sieur d'Hédouville. The idea for the journal was similar in scope to an outline written by the historian François Eudes de Mézeray who also belonged to the Colbert's clique and briefly lived in the same household as de Sallo. It included recording news and inventions in the various arts and sciences, decisions of secular and ecclesiastical courts, reviews of new scholarly books and other items of broader interest to a modern scholar.
De Sallo's health deteriorated in his final years so that he was unable to walk; his condition has been attributed to diabetes. *Wik

1761 Thomas Simpson (20 August 1710 – 14 May 1761) is best remembered for his work on interpolation and numerical methods of integration. However the numerical method known today as "Simpson's rule", although it did appear in his work, was something he learned from Newton as Simpson himself acknowledged. By way of compensation, however, the Newton-Raphson method for solving the equation f (x) = 0 is, in its present form, due to Simpson. Newton described an algebraic process for solving polynomial equations which Raphson later improved. The method of approximating the roots did not use the differential calculus. The modern iterative form xn+1 = xn - f (xn) / f '(xn) is due to Simpson, who published it in 1740. *SAU

1797 Giovanni Francesco Fagnano dei Toschi (31 Jan 1715 in Sinigaglia, Italy - 14 May 1797 in Sinigaglia, Italy) He proved that the triangle which has as its vertices the bases of the altitudes of any triangle has those altitudes as its bisectors. *VFR Of all the triangles that could be inscribed in a given triangle, the one with the smallest perimeter is the orthic triangle. This has sometimes been called Fagnano's Problem since it was first posed and answered by Giovanni Francesco Fagnano dei Toschi. Fagnano also was the first to show that the altitudes of the original triangle are the angle bisectors of the orhtic triangle, so the incenter of the orthic triangle is the orthocenter of the original triangle.*pb

1893 Ernst Eduard Kummer (29 January 1810 – 14 May 1893)  He was professor at the University of BRESLAU (now WROCLAW, Poland) in 1842-1855 and developed his theory of ideals here. KRONECKER studied with him. Later he replaced Dirichlet at The University of Berlin. He died at age 83, after a short attack of influenza. German mathematician whose introduction of ideal numbers, which are defined as a special subgroup of a ring, extended the fundamental theorem of arithmetic to complex number fields. He worked on Function theory, and  extended Gauss's work on hypergeometric series, giving developments that are useful in the theory of differential equations. He was the first to compute the monodromy groups of these series. Later. Kummer
devoted himself to the study of the ray systems, but treated these geometrical problems algebraically. He also discovered the fourth order surface based on the singular surface of the quadratic line complex. This Kummer surface has 16 isolated conical double points and 16 singular tangent planes.  *TIS and others   An oft told, and almost certianly untrue anecdote is told about Kummer: Kummer was so inept at simple arithmetic that he often asked students to help him in class. On one occasion, Kummer sought the result of a simple multiplication. "Seven times nine," he began. "Seven times nine is er - ah - ah - seven times nine is..." "Sixty-one," a mischievous student suggested and Kummer wrote the "answer" on the blackboard. "Sir," another one interjected, "it should be sixty-seven." "Come,  gentlemen, it can't be both," Kummer exclaimed. "It must be one or the other!" According to Erdos, Kumer reasoned out the answer as follows, -It can't be 61 as that is prime, as is 67, and 65 is a multiple of five, and 69 is too big, so it must be 63.

1924 Enrico Barone (December 22, 1859, Naples – May 14, 1924, Rome) Italian mathematical economist who built on the general equilibrium theory of Léon Walras and was instrumental in convincing Walras to incorporate variable production techniques - and, by extension, marginal productivity theory - into the Walras theory. Barone's greatest contribution was in getting the "Socialist Calculation" debate started with his famous 1908 article. His position was that it was indeed possible in a collectivist state for a planning agency to calculate prices for maximum efficiency. He was the first to apply indifference curve analysis to compare the relative burdens of income taxes and excise taxes (1912). He opposed "progressive" taxation schemes as based on dubious utilitarian calculations. *TIS

1985 Charles Leonard Hamblin (1922 – 14 May 1985) was an Australian philosopher, logician, and computer pioneer, as well as a professor of philosophy at the New South Wales University of Technology (now the University of New South Wales) in Sydney.
Among his most well-known achievements in the area of computer science was the introduction of Reverse Polish Notation and the use in 1957 of a push-down pop-up stack.[1] This preceded the work of Friedrich Ludwig Bauer and Klaus Samelson on use of a push-pop stack.[2] The stack had been invented by Alan Turing in 1946 when he introduced such a stack in his design of the ACE computer. Hamblin's most well-known contribution to philosophy is his book Fallacies, a standard work in the area of the false conclusions in logic. *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

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