## Thursday, 7 April 2016

### On This Day in Math - April 7

The 98th day of the year, 98 is the smallest number that starts a sequence of three consecutive numbers with at least 3 prime divisors. (What would be the smallest number to start a sequence of four numbers with at least four prime divisors?)

I am creating the term ambinumerals (from ambigram) to describe pairs of numbers like 98 and 86 which are the rotation of the other as opposed to strobogrammatic numbers (like 808)

98 is the sum of three consecutive fourth powers, $= 1^4 + 2^4 + 3^4$
and eight consecutive primes, = 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23

EVENTS
1646  Torricelli sends "The geometry of indivisibles" To Michelangelo Ricci.  He communicated the “universal theorem,” still considered the most general possible even today, which allows determination of the center of gravity of any figure through the relation between two integrals. *Encylopedia.com (Torricelli would use this method to find the volume of Torricelli's Trumpet (today often called Gabriel's Horn).  A finite solid volume with an infinite surface area.

*Weisstein, Eric W. "Gabriel's Horn." From MathWorld

1666 Perhaps the kindest rejection letter ever, John Pell to Samuel Morland. British Polymath Morland had considered writing a book on the "quadrature of curvlinear spaces" and sent a sample to Pell, who responded:
*A brief account of the life, writings, and inventions of Sir. S. Morland

1794 Joseph Priestley  forever left England and traveled to the United States. Only a few years before, on 14 Jul 1791, his laboratory, home and library were burned to destruction by a mob of people angry at his support of the French Revolution. His French colleague, Lavoisier, was executed a week  after Priestley left England. Priestley's discovery of oxygen was 20 years earlier, on 1 Aug 1774. During the last years of his life in America he spent his time quietly writing, and furthering the cause of Unitarianism in the new nation.

1795, France adopted by law, the metre as the unit of length and the base of the metric system. Since there had been no uniformity of French weights and measures prior to the Revolution, the Academy of Sciences had been charged on 8 May 1790 to organise a better system. Delambre and Méchain measured an arc of the meridian from Dunkirk to Barcelona, so that the metre could be defined as one ten-millionth part of the distance between the poles and the equator. *TIS

1880 Charles Darwin sent a letter to Francis Galton to call his attention to a letter and circular on “a queer subject” (fingerprinting) from Henry Faulds. Darwin suggests that Galton might want to present it at the Anthropological Institute, which he did. In his response the next day Galton says that he had taken several thumb prints several years before after “having heard of the Chinese plan with criminals.”. *Karl Pearson, The Life, Letters and Labours of Francis Galton

1953 IBM 701 formally dedicated at a luncheon at which Oppenheimer was the principal speaker. It used electrostatic storage tubes, a magnetic drum, and magnetic tapes. In all, 19 of these ma­chines were built, and IBM was launched into the new world of electronic computers. [Goldstein, The Computer from Pascal to von Neumann, p. 328]*VFR

1964 IBM Announces "System 360" Computer Family:
IBM announces the release of its "System 360" mainframe computer architecture--embodied in five new models--launching its most successful computer system of all time. Called the "360" because it was meant to address all possible sizes and types of customer with one unified software-compatible architecture, the 360 family of machines generated in excess of \$100 billion in revenue for IBM.*CHM

1970 The Netherlands issued a set of ﬁve stamps designed with the aid of a computer.Journal of Recreational Mathematics, 4(1971), 20–23, . *VFR

1978 An editorial in the Pensacola Journal on minimum competency in English and mathematics stated, “After all, if you give the test to four students and four ﬂunk, that’s a 50 percent failure rate.” [The AMATYC Journal, 13(1979), 59]

1981 The fastest computation of the 13th root of a 100-digit number is in 1 minute and 28.8 seconds by Willem Klein. [Guinness]

1989 To start his after-dinner remarks at a meeting of the Ohio Section of the MAA, Gerald Alexanderson told the following story that he had heard from Polya, who heard it from Lebesgue: At the coliseum in Rome the emperor ordered a lion to be brought into the arena with a christian. The christian whispered something in the lion’s ear and the lion became meek and whimpered away. This scene was repeated with increasingly ferocious lions. Finally the emperor told the christian that he could go free if he would tell him what he was saying to the lion. The response was truly frightening: “After dinner you have to give a speech.”

BIRTHS

1768 François Joseph Français (7 April 1768 in Saverne, Bas-Rhin, France - 30 Oct 1810 in Mainz, Germany)  Much of François Français's work was published after his death by his brother who added to it in a way to make the contribution of each hard to distinguish. François worked on partial differential equations and his memoir of 1795 on this topic was developed further and presented to the Académie des Sciences in 1797. Lacroix praised Français' work and described it as making a major contribution to the study of partial differential equations; however, it was not published.*SAU

1823 Guillaume-Jules Hoüel (April 7, 1823 in Thaon; June 14, 1886 in Périers) was a French mathematician. He entered the École Normale Supérieure in 1843. He originally did research on celestial mechanics, but later became interested in Non-Euclidean geometry and corresponded with Joseph Tilly.*Wik
Hoüel became interested in non-euclidean geometry once he had been made aware of the work of Bolyai and Lobachevsky. He published translations of many important works by Bolyai, Beltrami, Helmholtz and Riemann. He corresponded with Tilly on non-euclidean geometry. *SAU

1866 Erik Ivar Fredholm (April 7, 1866 – August 17, 1927)  Swedish mathematician who is remembered for Fredholm integral equations with applications in mathematical physics and actuarial science. His first paper (1890) was on a special class of functions inspired by the heat equation. His 1898 doctoral dissertation involved a study of partial differential equations motivated by an equilibrium problem in elasticity. Fredhlom also had a career in actuarial science and from 1902 onwards he studyied various questions in this area, including an elegant formula he proposed to determine the surrender value of a life insurance policy. He built a machine to solve differential equations. David Hilbert extended one of Fredholm's integral equations discoving Hilbert spaces on which would be built the quantum theory.*TIS

1923 Peter John Hilton (7 April 1923 – 6 November 2010) was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during the Second World War. Hilton's principal research interests were in algebraic topology, homological algebra, categorical algebra, and mathematics education. He published 15 books and over 600 articles in these areas, some jointly with colleagues.*Wik

DEATHS

1823 Jacques-Alexandre-César Charles (12 Nov 1746, 7 Apr 1823 at age 76) French mathematician, physicist, and inventor. When Benjamin Franklin visited France in 1779, Charles was inspired to study physics. He soon became an eloquent speaker to non-scientific audiences. His lectures and demonstrations attracted notable patrons and helped popularize Franklin's theory of electricity and other new scientific concepts. With Nicolas and Anne-Jean Robert, he made several balloon ascents, and was the first to use hydrogen for balloon inflation (1783). Charles invented most of the equipment that is still used in today's balloons. About 1787 he developed Charles's law concerning the thermal expansion of gases that for a gas at constant pressure, its volume is directly proportional to its absolute temperature. *TIS

1889 Paul David Gustav du Bois-Reymond (2 December 1831 – 7 April 1889) was a German mathematician who was born in Berlin and died in Freiburg. He was the brother of Emil du Bois-Reymond.
His thesis was concerned with the mechanical equilibrium of fluids. He worked on the theory of functions and in mathematical physics. His interests included Sturm–Liouville theory, integral equations, variational calculus, and Fourier series. In this latter field, he was able in 1873 to construct a continuous function whose Fourier series is not convergent (more specifically, that diverges at every point). His lemma defines a sufficient condition to guarantee that a function vanishes almost everywhere.
Du Bois-Reymond also established that a trigonometric series that converges to a continuous function at every point is the Fourier series of this function.
He developed a theory of infinitesimals in Über die Paradoxen des Infinitär-Calcüls ("On the paradoxes of the infinitary calculus") in 1877. He wrote,
The infinitely small is a mathematical quantity and has all its properties in common with the finite ... A belief in the infinitely small does not triumph easily. Yet when one thinks boldly and freely, the initial distrust will soon mellow into a pleasant certainty ... A majority of educated people will admit an infinite in space and time, and not just an "unboundedly large". But they will only with difficulty believe in the infinitely small, despite the fact that the infinitely small has the same right to existence as the infinitely large ...
*Wik

1933 Raymond Edward Alan Christopher Paley,(7 January 1907 – 7 April 1933)  was killed at age 26 in an avalanche while skiing near Banﬀ, Alberta, Canada. G. H. Hardy wrote of this young analyst: “There is something very intimidating to an older man in such youthful quickness and power, and of all the people who frightened me when I came back to Cambridge, Paley was the man who frightened me the most.” [Collected Papers of G. H. Hardy, vol. 7, p. 745.]*VFR (He was buried in Banff)
His contributions include the Paley construction for Hadamard matrices (closely related to the Paley graphs in graph theory) and his collaboration with Norbert Wiener in the Paley–Wiener theorem (harmonic analysis). He collaborated with A. Zygmund on Fourier series (see also Paley–Zygmund inequality) and worked with J. E. Littlewood on what became known as Littlewood–Paley theory, an application of real-variable techniques in complex analysis. *Wik

1934 Ernst Paul Heinz Prüfer (10 Nov 1896 in Wilhelmshaven, Germany - 7 April 1934 in Münster, Germany)proved important results about abelian groups.*SAU
He worked on abelian groups, algebraic numbers, knot theory and Sturm-Liouville theory. His advisor was Issai Schur.*Wik

1986 : Leonid Vitalyevich Kantorovich (19 Jan 1912, 7 Apr 1986 at age 74)  Soviet mathematician and economist who shared the 1975 Nobel Prize for Economics with Tjalling Koopmans for their work on the optimal allocation of scarce resources. Kantorovich's background was entirely in mathematics but he showed a considerable feel for the underlying economics to which he applied the mathematical techniques. He was one of the first to use linear programming as a tool in economics and this appeared in a publication Mathematical methods of organising and planning production which he published in 1939. The mathematical formulation of production problems of optimal planning was presented here for the first time and the effective methods of their solution and economic analysis were proposed *TIS

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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