Tuesday 3 April 2012

On This Day in Math - April 3

Alberti's Statue in the courtyard of the Uffizi Gallery, Florence; *Wik

Knowing what is big and what is small is more important than being able to solve partial differential equations.
~Stan Ulam

The 94th day of the year; 94!-1 is prime. The number 94!-1 ends in 21 consecutive nines. Students might inquire how they could have known this without being told.

1769 A letter from Mr. Richard Price, F. R. S. to Benjamin Franklin, Esq; LL.D. discusses De Moivre's work on Population and survival rates. The paper runs to 38 pages. "Observations on the Expectations of Lives, the Increase of Mankind, the Influence of Great Towns on Population, and Particularly the State of London with Respect to Healthfulness and Number of Inhabitants." *Phil. Trans. January 1, 1769 59:89-125;

In 1934, a British patent application for the first catseye road marker was recorded for inventor Percy Shaw (1889-1975), described as "Improvements relating to Blocks for Road Surface." These are the familiar reflectors which mark the lines that are lit up at night by the lights of passing vehicles. The raised surface in which the reflectors are mounted have a construction that "will yield when traveled over by a vehicle wheel and sink to the level of the road surface" such as a resilient white rubber cushion mounted in a metal holder sunk below the road surface. The patent No. 436,290 was accepted 3 Oct 1935. A revised design was patented the following year as No. 457,536. Shaw started Reflecting Roadstuds Ltd. to manufacture them. *TIS (While this is of little mathematical interest, before I learned what the term meant, I regularly wondered about a sign I passed on the way from Stoke Ferry to King's Lynn in Norfolk Shire which said, "Cat's Eyes Removed Ahead."

1964 It is reported in the New York Times that the casinos in Las Vegas have changed their rules in blackjack so as to defeat the winning strategy devised by Edward O. Thorp. See 27 March 1964. *VFR
Thorp is described as an American mathematics professor, author, hedge fund manager, and blackjack player. He was a pioneer in modern applications of probability theory, including the harnessing of very small correlations for reliable financial gain.*Wik

1983 The Republic of China (Taiwan) marks the 400th anniversary of the arrival of Father Matteo Ricci (1552–1610) in China with a pair of stamps. [Scott #2359–2360] *VFR

1529 – Michael Neander (April 3, 1529 – October 23, 1581) German mathematician and astronomer was born in Joachimsthal, Bohemia, and was educated at the University of Wittenberg, receiving his B.A. in 1549 and M.A. in 1550.
From 1551 until 1561 he taught mathematics and astronomy in Jena, Germany. He became a professor in 1558 when the school where he taught became a university. From 1560 until his death he was a professor of medicine at the University of Jena. He died in Jena, Germany. The crater Neander on the Moon is named after him. *Wik

1835 John Howard Van Amringe (3 April 1835 in Philadelphia, Pennsylvania, USA - 10 Sept 1915 in Morristown, New Jersey, USA) was a U.S. educator and mathematician. He was born in Philadelphia, and graduated from Columbia in 1860. Thereafter, he taught mathematics at Columbia, holding a professorship from 1865 to 1910 when he retired. Van Amringe was also the first Dean of Columbia College, the university's undergraduate school of arts and sciences, which he defended from dismemberment and incorporation into the larger university. During his long presence at the school, he made many addresses and enjoyed unrivaled popularity. He is memorialized with a bust enshrined in a column-supported cupola on "Van Am Quad" in the southeastern portion of the campus, surrounded by three College dormitories (John Jay Hall, Hartley Hall, and Wallach Hall) and by the main College academic building, Hamilton Hall. He is buried in Greenwood Cemetery in Brooklyn.
Van Amringe served as the first president of the American Mathematical Society between 1888 and 1890.
In honor of Van Amringe, Columbia University's Department of Mathematics has presented a "Van Amringe Mathematical Prize" each year (since 1911) to the best freshman or sophomore mathematics student, based on a very challenging examination. *Wik

1842 Hermann Karl Vogel (3 Apr 1842; died 13 Aug 1907 at age 65) German astronomer who discovered spectroscopic binaries (double-star systems that are too close for the individual stars to be discerned by any telescope but, through the analysis of their light, have been found to be two individual stars rapidly revolving around one another). He pioneered the study of light from distant stars, and introduced the use of photography in this field.*TIS

1859 Karl Heun (3 April 1859 in Wiesbaden, Germany - 10 Jan 1929 in Karlsruhe, Germany) was a German mathematician best known for the Heun differential equation which generalizes the hypergeometric differential equation. *SAU

1892 Hans Rademacher (3 April 1892 in Wandsbeck (part of Hamburg), Schleswig-Holstein, Germany - 7 Feb 1969 in Haverford, Pennsylvania, USA) It was philosophy that he intended to take as his main university subject when he entered the university of Göttingen in 1911, but he was persuaded to study mathematics by Courant after having enjoyed the excellent mathematics teaching of Hecke and Weyl. He is remembered for the system of orthogonal functions (now known as Rademacher functions) which he introduced in a paper published in 1922. Berndt writes "Since its discovery, Rademacher's orthonormal system has been utilised in many instances in several areas of analysis." Rademacher's early arithmetical work dealt with applications of Brun's sieve method and with the Goldbach problem in algebraic number fields. About 1928 he began research on the topics for which he is best known among mathematicians today, namely his work in connection with questions concerning modular forms and analytic number theory. Perhaps his most famous result, obtained in 1936 when he was in the United States, is his proof of the asymptotic formula for the growth of the partition function (the number of representations of a number as a sum of natural numbers). This answered questions of Leibniz and Euler and followed results obtained by Hardy and Ramanujan. Rademacher also wrote important papers on Dedekind sums and investigated many problems relating to algebraic number fields. *SAU

1900 Albert Edward Ingham (3 April 1900–6 September 1967) was an English mathematician. His book On the distribution of prime numbers published in 1932 was his only book and it is a classic. Many of the ideas here, as in other work of Ingham's, came from the joint work undertaken by Harald Bohr and Littlewood.

1907 Mark Grigorievich Krein (3 April 1907 – 17 October 1989) was a Soviet Jewish mathematician, one of the major figures of the Soviet school of functional analysis. He is known for works in operator theory (in close connection with concrete problems coming from mathematical physics), the problem of moments, classical analysis and representation theory.
He was born in Kiev, leaving home at age 17 to go to Odessa. He had a difficult academic career, not completing his first degree and constantly being troubled by anti-Semitic discrimination. His supervisor was Nikolai Chebotaryov.
He was awarded the Wolf Prize in Mathematics in 1982 (jointly with Hassler Whitney), but was not allowed to attend the ceremony.
He died in Odessa.
On 14 January 2008, the memorial plaque of Mark Krein was unveiled on the main administration building of I.I. Mechnikov Odessa National University. *Wik

1909 Stan Ulam (13 April 1909 – 13 May 1984) Polish-American mathematician who played a major role in the development of the hydrogen bomb at Los Alamos. He solved the problem of how to initiate fusion in the hydrogen bomb by suggesting that compression was essential to explosion and that shock waves from a fission bomb could produce the compression needed. He further suggested that careful design could focus mechanical shock waves in such a way that they would promote rapid burning of the fusion fuel. Ulam, with J.C. Everett, also proposed the "Orion" plan for nuclear propulsion of space vehicles. While Ulam was at Los Alamos, he developed "Monte-Carlo method" which searched for solutions to mathematical problems using a statistical sampling method with random numbers. *TIS He is buried in Santa Fe National Cemetery in Santa Fe, New Mexico.

1472 Leone Battista Alberti (18 Feb 1404 in Genoa, French Empire (now Italy)- 3 April 1472 in Rome, Papal States (now Italy) The date of his death is given by Wikipedia as April 20, 1472) Italian mathematician who wrote the first general treatise on the laws of perspective and also wrote a book on cryptography containing the first example of a frequency table. Alberti died in Rome, but his ashes were brought from Rome and put in the family vault in the Santa Croce Cathedral (where Galileo is buried).

1717 Jacques Ozanam (16 June 1640, Sainte-Olive, Ain - 3 April 1718, Paris)In 1670, he published trigonometric and logarithmic tables more accurate than the then existing ones of Ulacq, Pitiscus, and Briggs. An act of kindness in lending money to two strangers secured for him the notice of M. d'Aguesseau, father of the chancellor, and an invitation to settle in Paris. There he enjoyed prosperity and contentment for many years. He married, had a large family, and derived an ample income from teaching mathematics to private pupils, chiefly foreigners. *Wik
He is remembered for his book on mathematical recreations. “He was wont to say that it was the business of the Sorbonne doctors to discuss, of the pope to decide, and of a mathematician to go straight to heaven in a perpendicular line.” [DSB 10, 264]. *VFR
On the flyleaf of J. E. Hofmann's copy of the 1696 edition of Ozanam's Recreations is a pencil portrait labelled Ozanam -- the only one I know of. This copy is at the Institut für Geschichte der Naturwissenschaft in Munich. *David Singmaster

1817 Friedrich Ludwig Wachter (1792–1817), a student of Gauss, called the geometry obtained by denying Euclid’s parallel postulate “anti-Euclidean geometry”. Had he returned from his cus­tomary evening walk on this date he might now be known as one of the founders of non-Euclidean geometry. [G. E. Martin, Foundations of Geometry and the Non-Euclidean Plane, p. 306] *VFR
(… In a letter to Gauss in 1816 he states that as a circle’s radius increases toward infinity as being identical to a plane, “even in the case of the fifth postulate being false, there would be geometry on this surface identical with that of the ordinary plane.)

 Chladni pattern on plate

1827 Ernst Florenz Friedrich Chladni, physicist and amateur musician, died. He is best remembered for the spectacular symmetrical patterns formed when a sand covered plate is vibrated with a violin bow. He was a Professor of Physics in Breslau when he developed Chladni figures c1800. He came to Paris in 1808 to present his work at the Institut and Laplace had him give a two hour demonstration to Napoleon, who gave him 6000 francs.
German physicist who is known as the “father of acoustics” for his mathematical investigations of sound waves. Chladni figures, seen when thin plates covered in sand at set in vibration, are complex patterns of vibration with nodal lines that remain stationary and retain sand. He demonstrated these to an audience of scientists in Paris in 1809. He measured the speed of sound in various gases by determining the pitch of the note of an organ pipe filled with different gases. To determine the speed of sound in solids, Chladni used analysis of the nodal pattern in standing-wave vibrations in long rods. He performed on the euphonium, an instrument he invented, made of glass and steel bars vibrated by rubbing with a moistened finger. He also investigated meteorites. *TIS

1900 Joseph-Louis-François Bertrand (11 Mar 1822; 5 Apr 1900 at age 78) was a French mathematician and educator and educator remembered for his elegant applications of differential equations to analytical mechanics, particularly in thermodynamics, and for his work on statistical probability and the theory of curves and surfaces. In 1845 Bertrand conjectured that there is at least one prime between n and (2n-2) for every n greater than 3, as proved five years later by Chebyshev. In 1855 he translated Gauss's work on the theory of errors and the method of least squares into French. He wrote a number of notes on the reduction of data from observations. *TIS At age 11 he started to attend classes at the Ecole Polytechnique, where his Uncle Duhamel was a well-known professor of mathematics. At 17 he received his doctor of science degree. *VFR
1998 – Mary Cartwright, English mathematician (b. 1900) G.H. Hardy was her Doctorial advisor, She did early investigations with Littlewood of fine structure of solutions to some types of differential equations, today seen to be a typical instance of the butterfly effect. She was the first woman:

to receive the Sylvester Medal
to serve on the Council of the Royal Society
to be President of the London Mathematical Society (in 1961–62)

She also received the De Morgan Medal of the Society in 1968. In 1969 she received the distinction of being honoured by the Queen, becoming Dame Mary Cartwright, Dame Commander of the Order of the British Empire.

*WM = Women of Mathematics, Grinstein & Campbell
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

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