## Monday 2 September 2024

### 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, $245={8}^{2}+{9}^{2}+{10}^{2}$

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

245 is also the 46th prime , 199+46=245 (is there a mathematical significance for these numbers, or just a nice curiosity?  Serious question.)

EVENTS

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

Some historians suggested there had been riots, the oft called the Calendar Riots of 1752.  These claims of civil unrest and rioters demanding “Give us our eleven days” may have arisen through a misinterpretation of a contemporary painting by William Hogarth. His 1755 painting entitled: “An Election Entertainment” refers to the elections of 1754 and depicts a tavern dinner organised by Whig candidates. A stolen Tory campaign banner with the slogan, “Give us our Eleven Days” can be seen lower right (on the black  banner on the floor under the seated gentleman’s foot). The Tories can be seen outside the window, demonstrating.Claims of civil unrest and rioters demanding “Give us our eleven days” may have arisen through a misinterpretation of a contemporary painting by William Hogarth. His 1755 painting entitled: “An Election Entertainment” refers to the elections of 1754 and depicts a tavern dinner organised by Whig candidates. A stolen Tory campaign banner with the slogan, “Give us our Eleven Days” can be seen lower right (on the black banner on the floor under the seated gentleman’s foot). The Tories can be seen outside the window, demonstrating.

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

The year 1957 also coincided with an acute shortage of mathematicians in the United States. The electronic computer created a demand for mathematicians as programmers and it also shortened the lead time between the development of a new mathematical theory and its practical application, thereby making their work more valuable. The United States could no longer rely on European refugees for all of its mathematicians, though they remained an important source, so it had to drastically increase the domestic supply. At the time, "mathematics" was interpreted as pure mathematics rather than applied mathematics. The problem in the 1950s and 1960s was that industry, including defense, was absorbing the mathematicians who were also needed at high schools and universities training the next generation. At the university level, even more recently, there have been years when it was difficult to hire applied mathematicians and computer scientists because of the rate that industry was absorbing them.

This chart shows the number of PhDs in the US by year from 1900.  The linearity across the 20th Century of the semi-log graph may make one wonder if the program really had much impact.  In fact the slope of growth rate drops significantly around the 70's (Which could be from age distribution in the country or numerous other causes.)

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

 a Deep Blue Processor, *Wik

2023  Dennis Austin, the principal software developer of PowerPoint, passed away from lung cancer on Sept. 1. He was 76. The Washington Post reports:

Released in 1987 by Forethought, a small software firm, PowerPoint was the digital successor to overhead projectors, transforming the labor-intensive process of creating slides -- a task typically assigned to design departments or outsourced -- to one where any employee with a computer could point, click and rearrange information with a mouse. "Our users were familiar with computers, but probably not graphics software," Mr. Austin wrote in an unpublished history of the software's development. "They were highly motivated to look their best in front of others, but they weren't savvy in graphics design."

Working alongside Robert Gaskins, the Forethought executive who conceived the software, it was Mr. Austin's job as the software engineer to make PowerPoint (originally called Presenter) easy to operate. He accomplished this with a "direct-manipulation interface," he wrote, meaning that "what you are editing looks exactly like the final product." Originally targeted for Macintosh computers, which had a graphical interface, Presenter included ways for users to incorporate graphics, clip art and multiple fonts. In addition, the slides could be uniform with graphic borders, corporate logos and slide numbers. The goal, Mr. Austin wrote, was "to create presentations -- not simply slides."

In his book "Sweating Bullets: Notes about Inventing PowerPoint" (2012), Gaskins wrote that "Dennis came up with at least half of the major design ideas," and was "completely responsible for the fluid performance and the polished finish of the implementation." "It's a good bet," Gaskins added, "that if Dennis had not been the person designing PowerPoint, no one would ever have heard of it."

BIRTHS

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

Despite his large body of works, Laurent series expansions for complex functions were not named after him, but after Pierre Alphonse Laurent.

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.  Sometime around 1908 he ran away to sea, jumped ship after a week of chipping paint when the ship failed to sail, and hid out for years from the imagined consequences of this desertion in the back country of West Virginia, first as an oil well worker, then as a tree surgeon. A trip to Boston to hone the latter skills at a forestry school fizzled when it turned out that the school had closed. Finally returning home, he was sent to the Pennsylvania Military College in 1917, another totally incompatible environment. His twin sister died in childbirth in 1918.

After a WW1 job with the Atlas Powder Company in Michigan, Wilcoxon entered Rutgers in 1920, and completed an MS in chemistry in 1921; he then shifted to Cornell and physical chemistry, and got his PhD in 1924.

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".)

At the time of his death, Wilcoxon was working on a multivariate generalization of his two-sample rank sum test. His proposals were described posthumously (by Bradley, 1967). They have not been taken up by the statistical community.

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

1913 Israel Moiseevich Gelfand, (2 September [O.S. 20 August] 1913 – 5 October 2009) was a prominent Soviet-American mathematician. He made significant contributions to many branches of mathematics, including group theory, representation theory and functional analysis. The recipient of many awards, including the Order of Lenin and the first Wolf Prize, he was a Foreign Fellow of the Royal Society and professor at Moscow State University and, after immigrating to the United States shortly before his 76th birthday, at Rutgers University. Gelfand is also a 1994 MacArthur Fellow.

His legacy continues through his students, who include Endre Szemerédi, Alexandre Kirillov, Edward Frenkel, Joseph Bernstein, David Kazhdan, as well as his own son, Sergei Gelfand.

Gelfand is known for many developments including:

the book Calculus of Variations (1963), which he co-authored with Sergei Fomin;

Gelfand's formula, which expresses the spectral radius as a limit of matrix norms.

the Gelfand representation in Banach algebra theory;

the Gelfand–Mazur theorem in Banach algebra theory;

the Gelfand–Naimark theorem;

the Gelfand–Naimark–Segal construction;

Gelfand–Shilov spaces;

the Gelfand–Pettis integral;

the representation theory of the complex classical Lie groups;

contributions to the theory of Verma modules in the representation theory of semisimple Lie algebras (with I. N. Bernstein and S. I. Gelfand);

contributions to distribution theory and measures on infinite-dimensional spaces;[5]

the first observation of the connection of automorphic forms with representations (with Sergei Fomin);

conjectures about the Atiyah–Singer index theorem;

ordinary differential equations (Gelfand–Levitan theory);

work on calculus of variations and soliton theory (Gelfand–Dikii equations);

contributions to the philosophy of cusp forms;

Gelfand–Fuchs cohomology of Lie algebras;

Gelfand–Kirillov dimension;

integral geometry;

combinatorial definition of the Pontryagin class;

Coxeter functors;

general hypergeometric functions;

Gelfand–Tsetlin patterns;

Gelfand–Lokutsievski method;

and many other results, particularly in the representation theory of classical groups.

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 (September 1, 1925 – December 26, 2018)  was an American theoretical physicist. He was 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

DEATHS

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

1834 Thomas Telford (9 August 1757 Glendinning, Westerkirk, Eskdale, Dumfriesshire, Scotland - 2 September 1834 (aged 77) 24 Abingdon Street, Westminster, London) He is the founder of modern bridge construction, his crowning achievement being the Menai suspension bridge in Wales. Do you know the shape of the cables on a suspension bridge? *VFR

 Menai Suspension Bridge *Wik

Telford's reputation in Shropshire led to his appointment in 1793 to manage the detailed design and construction of the Ellesmere Canal, linking the ironworks and collieries of Wrexham via the north-west Shropshire town of Ellesmere, with Chester, utilising the existing Chester Canal, and then the River Mersey.

Among other structures, this involved the spectacular Pontcysyllte Aqueduct over the River Dee in the Vale of Llangollen, where Telford used a new method of construction consisting of troughs made from cast iron plates and fixed in masonry. Extending for over 1,000 feet (300 metres) with an altitude of 126 ft (38 m) above the valley floor, the Pontcysyllte Aqueduct consists of nineteen arches, each with a 45 ft (14 m) span. Being a pioneer in the use of cast-iron for large scaled structures, Telford had to invent new techniques, such as using boiling sugar and lead as a sealant on the iron connections. Eminent canal engineer William Jessop oversaw the project, but he left the detailed execution of the project in Telford's hands. The aqueduct was designated a UNESCO World Heritage Site in 2009. *Wik

A canal boat traverses the Pontcysyllte aqueduct in North Wales

1836 William Henry FRS (12 December 1774 – 2 September 1836) was an English chemist. He was the son of Thomas Henry and was born in Manchester England. He developed what is known today as Henry's Law.

William Henry was apprenticed to Thomas Percival and later worked with John Ferriar & John Huit at the Manchesters Infirmary.[citation needed] He began to study medicine at University of Edinburgh in 1795, taking his medical in 1807, but ill-health interrupted his practice as a physician, and he devoted his time mainly to chemical research, especially with regard to gases. One of his best-known papers (published in Philosophical Transactions of the Royal Society, 1803) describes experiments on the quantity of gases absorbed by water at different temperatures and under different pressures. His results are known today as Henry's law. His other papers deal with gas-analysis, fire-damp, illuminating gas, the composition of hydrochloric acid and of ammonia, urinary and other morbid concretions, and the disinfecting powers of heat. His Elements of Experimental Chemistry (1799) enjoyed considerable vogue in its day, going through eleven editions in 30 years. He was one of the founders of the Mechanics' Institute, the original precursor of University of Manchester Institute of Science and Technology.

He was elected a Fellow of the Royal Society in February 1809, having been awarded their prestigious Copley Medal in 1808.

He shot himself in his private chapel at Pendlebury, near Manchester, in 1836.

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   (1 April 1916 – 2 September 2002) 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