Friday 2 September 2022

On This Day in Math - September 2

The importance of the "New Mathematics" lies mainly in the fact that it has taught us the difference between the disc and the circle.

D MacHale, Comic Sections (Dublin 1993)
(I realize that a whole generation has grown up who have no idea what "New Mathematics" means, my apologies to them for a dated quote)

The 245th day of the year; 245 is the fifth StellaOctangula number. The sum of the 5th octahedral number (85) and eight of the fourth tetrahedral numbers (20). 245 =85 + 8 (20)

245 is also the sum of three consecutive squares, 245=82+92+102

There are 245 odd entries in the first 33 rows of the Arithmetic Triangle.

245 is also the 46th prime plus 46, 199+46=245

See Math Facts for every Year Day here.


1666 Five days previously Wren had visited Old St. Paul's Cathedral to determine the reconstruction needs for the decaying old building.    During the night of Sep 2, and for the next five days, the Great Fire of London will burn out about 7/8 of the city of London and greatly alter Wren's work at St Paul's.  [The Great Fire of is supposed to have started in the house of King Charles II's baker on Pudding Lane near London Bridge.*@History Magazine]

 Image from Wikipedia,

In 1752, today was the last day of the Julian calendar in Great Britain and the British colonies; the Gregorian Calendar designed to correct the extra leap year day problem went into effect the next day with tomorrow being September 14, hence 11 days were dropped. Most other countries made the adjustment in 1582. *TIS

1808 Gauss writes Wolfgang Bolyai: “It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.” * Mathematical Circles Squared,Howard Eves, pg 113

1905 While a student at Kumbakonam, Ramanujan was so obsessed with his math studies that he failed all his other classes. It seems after a conflict at home, he ran away, causing his mother to send a missing-person letter to the newspaper:

1958 The National Defense Education act was passed in response to Sputnik (4 October 1957). $840 million was appropriated to improve the teaching of mathematics, science, and foreign languages. *VFR

1997 After its Deep Blue chess-playing computer defeated human world chess champion Gary Kasparov​ in a closely watched match in May, the pioneering computer company decided to make the machine even faster and stronger. On September 2, IBM announced that its RS/6000 SP model, a parallel supercomputer, was now 58 percent faster thanks to a new microprocessor and some software refinements. Kasparov was not available for comment.*CHM


1841 Paul Matthieu Hermann Laurent born (2 September 1841 Luxembourg City – 19 February 1908 Paris, France). He developed statistical formulas for the calculation of actuarial tables and studied heat conduction. *VFR (Laurent series expansions for complex functions were not named after him)

1850 Alfred Pringsheim born (2 September 1850 – 25 June 1941), a German mathematician who worked on real and complex functions. *SAU Pringsheim's theorem concerns the convergence of a power series with non-negative real coefficients. Pringsheim and Ivan Śleszyński, working separately, proved what is now called the Śleszyński–Pringsheim theorem on convergence of certain continued fractions.*Wik

1856 Wilhelm Franz Meyer born (2 September 1856 in Magdeburg; 11 April 1934 in Königsberg . Meyer studied algebraic geometry, algebraic curves and invariant theory.*SAU He was a Founding member of the German Mathematical Society. *Wik

1877 Frederick Soddy (2 September 1877 – 22 September 1956) was an English radiochemist and monetary economist who explained, with Ernest Rutherford, that radioactivity is due to the transmutation of elements, now known to involve nuclear reactions. He also proved the existence of isotopes of certain radioactive elements. He received the Nobel Prize for Chemistry in 1921, and named after him is small crater on the far side of the Moon and the radioactive Uranium mineral, Soddyite. He rediscovered the Descartes' theorem in 1936 and published it as a poem. The kissing circles in this problem are sometimes known as Soddy circles.
The Poem begins,

For pairs of lips to kiss maybe
Involves no trigonometry.
'Tis not so when four circles kiss
Each one the other three.

The entire poem is found here, along with a story about how, In a strange "chain reaction" of ideas, Soddy played a part in the US developing an atomic bomb. *(Assorted notes)

1878 (René-)Maurice Fréchet (2 Sep 1878; 4 June 1973) was a French mathematician known chiefly for his contribution to real analysis. He is credited with being the founder of the theory of abstract spaces, which generalized the traditional mathematical definition of space as a locus for the comparison of figures; in Fréchet's terms, space is defined as a set of points and the set of relations. In his dissertation of 1906, he investigated functionals on a metric space and formulated the abstract notion of compactness. In 1907, he discovered an integral representation theorem for functionals on the space of quadratic Lebesgue integrable functions. He also made important contributions to statistics, probability and calculus. *TIS

1891 Ivan Matveyevich Vinogradov (2 Sep 1891[OS? SAU gives 14 Sep], 20 Mar 1983)Soviet mathematician known for his contributions to the analytical theory of numbers, including a partial solution of the Goldbach conjecture proving that every sufficiently large odd integer can be expressed as the sum of three odd primes. He described his methods in his most celebrated piece of work Some Theorems Concerning the Theory of Prime Numbers (1937)*TIS

1892 Frank Wilcoxon, (2 September 1892 - 18 November 1965) whose name should be familiar to anyone who has used classic nonparametric (distribution-free) tests, was born in County Cork, Ireland, to American parents. He spent much of his early life in the Hudson River Valley region of New York, and in 1924 received a doctorate in inorganic chemistry from Cornell. Thus, much of his early work was in research related to chemistry, with his interest in statistics resulting from reading Fisher's well-known book Statistical Methods for Research Workers (which I
recall reading somewhere was for some time the most cited book in all of science). During the 1940s Dr. Wilcoxon was perhaps most instrumental in the growth of the fledgling field of nonparametric or distribution-free statistics, introducing his signed-rank test for paired samples and his famous two-sample rank-sum test as an alternative to Student's unpaired two-sample t-test, each of which carry Wilcoxon's name in its appellation. (Wilcoxon's 1945 paper introducing these two tests
was titled "Individual Comparisons by Ranking Methods".)
For a good description of how outliers led the chemist Wilcoxon to develop these tests, read Chapter 16, "Doing Away With Parameters", in David Salsburg's book The Lady Tasting Tea, in which Salsburg writes in a footnote that "the nonparametric approach was not fully understood to be such a drastic revolution until Wilcoxon's work in this field" *David Bee

1909 Deane Montgomery (2 Sept 1909 - 15 March 1992 in Chapel Hill, North Carolina, USA) was a mathematician specializing in topology who was one of the contributors to the final resolution of Hilbert's fifth problem in the 1950s. He served as President of the American Mathematical Society from 1961 to 1962.
Born in the small town of Weaver, Minnesota, he received his B.S. from Hamline University in St. Paul, MN and his Masters and Ph.D. from the University of Iowa in 1933; his dissertation advisor was Edward Chittenden.
In 1941 Montgomery was awarded a Guggenheim Fellowship. In 1988, he was awarded the American Mathematical Society Leroy P. Steele Prize for Lifetime Achievement.*Wik

1923 René Thom (September 2, 1923 – October 25, 2002) is known for his development of catastrophe theory, a mathematical treatment of continuous action producing a discontinuous result. *SAU
Born in Montbeliard, France. In 1958 he received a Fields Medal for his 1954 creation of cobordism in algebraic topology. His classification of manifolds used homotopy theory in a fundamental way and this work became an important example of general cohomology theory. *VFR Thom is also known for his later work developing the catastrophe theory (1972), a mathematical treatment of continuous action producing a discontinuous result. Thom's theory is an attempt to describe, in a way that is impossible using differential calculus, those situations in which gradually changing forces lead to so-called catastrophes, or abrupt changes. The theory has widespread application in the physical and biological sciences and in the social sciences, but eventually fell from favour.*TIS

1925 Roy Jay Glauber (born September 1, 1925) is an American theoretical physicist. He is the Mallinckrodt Professor of Physics at Harvard University and Adjunct Professor of Optical Sciences at the University of Arizona. Born in New York City, he was awarded one half of the 2005 Nobel Prize in Physics "for his contribution to the quantum theory of optical coherence", with the other half shared by John L. Hall and Theodor W. Hänsch.
In this work, published in 1963, he created a model for photodetection and explained the fundamental characteristics of different types of light, such as laser light (see coherent state) and light from light bulbs (see blackbody). His theories are widely used in the field of quantum optics. *Wik

1948 Christa McAuliffe (2 Sep 1948; died 28 Jan 1986) Astronaut, first teacher in space, who died on

the Challenger Space Shuttle when 73 seconds into its 10th launch, Challenger (STS-51L) exploded in midair, killing its crew of seven. Space shuttle flights were suspended until 1988. An independent U.S. commission blamed the disaster on unusually cold temperatures that morning and the failure of the O-rings, a set of gaskets in the rocket boosters. *TIS


1764 Nathaniel Bliss (28 November 1700 – 2 September 1764) was an English mathematician and astronomer who went on to become Astronomer Royal. He succeeded Edmond Halley as professor of geometry at Oxford University in 1742 and was elected a Fellow of the Royal Society the same year. He succeeded James Bradley to become the fourth Astronomer Royal in 1762, but held the post for too short a period to make a significant impact (1762-1764).*Wik

1768 Antoine Deparcieux (October 28, 1703 – September 2, 1768) was a French mathematician who is best known for an early work on annuities and mortality.*SAU In 1746, he published Essai sur les probabilités de la durée de la vie humaine (An Essay on the Probabilities of the Duration of Human Life). Deparcieux analyzed in detail empirical observations. As a mathematician and physicist, he can be considered, after Halley and Struyck, one of the founders of the estimation of longevity and all the issues surrounding that concept. *Wik

1832 Franz Xaver von Zach (4 June 1754, 2 Sep 1832) German-Hungarian astronomer patronized by Duke Ernst of Saxe-Gotha-Altenburg. Director of observatory near Gotha (1787-1806). There he organized in 1798 the first congress of astronomers with Josef Lalande (1732-1807) as celebrated guest. In last years of the 18th century he formed a group of 24 astronomers chosen from throughout Europe to track down a "missing" planet between the orbits of Mars and Jupiter, where they instead discovered the asteroids. His greatest contribution was in the organizational area, for he maintained an enormous correspondence with all the astronomers of his time, and edited 28 volumes of Monatliche Korrespondenz zur Beforderung der Erd- und Himmelskunde (1800-13).*TIS

1865 Sir William Rowan Hamilton (4 Aug 1805, 2 Sep 1865) Irish mathematician in the fields of optics, geometrics, and classical mechanics. By age 12, Hamilton had already learned fourteen languages when he met the American, Zerah Colburn, who could perform amazing mental arithmetical feats, and they joined in competitions. It appears that losing to Colburn sparked Hamilton's interest in mathematics. At 15, he began studied the works of LaPlace and Newton so by age 17 had become the greatest living mathematician. He contributed to the development of optics, dynamics, and algebra. His invention of the calculus of quaternions enabled a three-dimensional algebra or geometry which provided a basis for the later development of quantum mechanics. *TIS

2002 Sheila Edmonds was one of the last of the old-style Cambridge dons who devoted their lives to teaching and to their colleges.
Sheila had an excellent undergraduate career ending up a `Wrangler', as students who are placed first class in the examinations for the Mathematical Tripos are called - though this did not result in a Cambridge BA degree because women were ineligible until 1947. The following year, she was awarded a distinction in the notoriously demanding Part III of the Tripos. In a speech she gave at her 80th birthday dinner, she acknowledged that a key to her success was the thorough mathematical training she received from her Director of Studies at Newnham, Margaret Grimshaw, who was 11 years her senior and another of the old-style dons. *Newnham College web page

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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