## Friday 10 November 2023

### On This Day in Math - November 10

“Composição em Vermelho e Preto” - Aluisio Carvão - Oil on canvas

My work always tried to unite the true with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.
~Herman Weyl

The 314th day of the year; 314 is the smallest number that can be written as the sum of 3 positive distinct squares in 6 ways. *What's Special about this number
(Students, can you find the smallest number that can be written as the sum of two distinct squares in at least two ways?)

314 = 5^2 + 17^2

314 is a semi-prime, and 3142 +1 is prime

EVENTS

In 1619, Descartes had enlisted in the army of the Duke of Bavaria. On 10 Nov 1619, at Neuberg on the Danube (presumably Neuberg, Bayern, about 20km west of Ingolstadt), he found the cold, which he never liked, so bad that he locked himself in a heated room and began his contemplations. He and others consider this the most significant date of his entire life and the birth date of analytic geometry! At the end of the winter, he continued his wanderings.

1664, Robert Hooke wrote to Robert Boyle about his experiment in which he had opened the chest of a living dog.
In his letter, he described how he ‘opened the thorax, and cut off all the ribs’ of the dog, and ‘handled…all the other parts of its body, as I pleased’. But despite these rather horrific details, we see through Hooke’s words a man deeply moved by the suffering he had caused, for he ends, ‘I shall hardly be induced to make any further trials of this kind, because of the torture of this creature’. What Hooke hadn’t realized before he began his experiment was that lungs were not muscles, and that by removing the animal’s chest, he had removed the dog’s ability to breathe on its own. To keep the animal alive, Hooke pushed a hollow cane down the dog’s throat and into its windpipe. He then pumped air into the animal’s lungs with a bellow for over an hour, carefully studying the way in which the organs expanded and contracted with each artificial breath. All-the-while, the dog stared at him in horror, unable to whimper or cry out in agony
*Lindsey Bracken, The Chirurgeon's Apprentice

1719 London gets a light show from the Aurora Borealis. Halley describes "An Account of the Phaenomena of a Very Extraordinary Aurora Borealis, Seen at London on November 10. 1719. Both Morning and Evening." By Dr. Edmond Halley. R.S. Secr. *Philosophical Transactions

1742 Euler writes to Niklaus I Bernoulli on November 10, 1742. This is the last letter in their correspondence that deals with the pentagonal number theorem. Euler writes: “This expression $\left(1-n\right)\left(1-{n}^{2}\right)\left(1-{n}^{3}\right)\left(1-{n}^{4}\right)$ etc. by expansion shall give the series $1-n-{n}^{2}+{n}^{5}+{n}^{7}-etc$ . in which no other exponents occur unless they are contained in $\frac{3xx±x}{2}$

which I have for my part concluded with legitimate induction, even if I have not been able to find a demonstration in any manner, however, although I have notdevoted enough time to this

1872 Stanley found Livingstone. VFR

1918 A marble monument to Niccolo Fontana known as Tartaglia
(1499-1557) was unveiled at Brescia, his birthplace. *VFR

1957 GIGO first used in print? The Times Daily of Hammond, Indiana printed an article that opened : “BIZMAC UNIVAC, GARBAGE IN-GARBAGE OUT — all new terms in the Army… These colorful expressions are part of the working vocabulary of the military mathematicians who man the Army’s electronic computors [sic].” *Robert Stenson, Atlas Obscura

In 1983, U.S. student Fred Cohen presented to a security seminar the results of his test - the first documented virus, created as an experiment in computer security. Cohen created this first virus when studying for a PhD at the University of Southern California. Others had written about the potential for creating pernicious programs but he was the first to demonstrate a working example. In the paper, he defined a virus as "a program that can 'infect' other programs by modifying them to include a ... version of itself". Cohen added his virus to a graphics program called VD, written for a Vax mini-computer. The virus hid inside VD and used the permissions users had to look at other parts of the Vax computer to spread around the system.*TIS

1983 Microsoft announces a new product, Windows, to compete with other graphical environments for computers, such as interface on the Apple Lisa. After several delays, Windows 1.0 finally became available to the public in 1985. Its major features included pull-down menus, tiled windows, mouse support, and cooperative multitasking of the program’s applications. Although Windows 1.0 saw some use, the Windows interface did not gain general acceptance until version 3.0*CHM

1984 Evariste Galois was commemorated as a revolutionary and geometrician on a French postal stamp issued on 10 Nov 1984. He was born in the little village of Bourg-la-Reine, near Paris, France. He is remembered for his contributions to the part of higher algebra known as group theory. His theory solved many long-standing unanswered questions, including the impossibility of trisecting the angle and squaring the circle. *TIS

2015  "
While most people associate the mathematical constant π (pi) with arcs and circles, mathematicians are accustomed to seeing it in a variety of fields. But two University scientists were still surprised to find it lurking in a quantum mechanics formula for the energy states of the hydrogen atom.
“We didn’t just find pi,” said Tamar Friedmann, a visiting assistant professor of mathematics and a research associate of high energy physics, and co-author of a paper published this week in the Journal of Mathematical Physics. “We found the classic seventeenth century Wallis formula for pi, making us the first to derive it from physics, in general, and quantum mechanics, in particular.”
The Wallis formula—developed by British mathematician John Wallis in his book Arithmetica Infinitorum—defines π as the product of an infinite string of ratios made up of integers. For Friedmann, discovering the Wallis formula for π in a quantum mechanics formula for the hydrogen atom’s energy states underscores π’s omnipresence in math and science."  *News Center, University of Rochester

BIRTHS

1829 Elwin Bruno Christoffel (10 Nov 1829 in Montjoie Aachen (now Monschau), Germany - 15 March 1900 in Strasbourg, France) Christoffel published works on conformal mappings, Riemann's o-function, the theory of invariants, and the Christoffel reduction theorem.*SAU

1861 Robert Thorburn Ayton Innes (10 Nov 1861; 13 Mar 1933) was a Scottish astronomer who discovered Proxima Centauri (1915), the closest star to earth after the Sun. Invited by David Gill to the Cape Observatory, South Africa (1894), he became a successful binary star observer with the 7-inch refractor (1628 discoveries). His most famous discovery, Proxima Centauri is a faint star near the binary star Alpha Centauri, which is so far south it is not visible from most of the northern hemisphere. He was also the first to see the Daylight Comet of 1910, though this comet was found independently by so many people in the Southern Hemisphere that no single "original" discoverer could be named. Innes recorded it on 17 Jan 1910. *TIS

1896 Ernst Paul Heinz Prüfer (10 Nov 1896 in Wilhelmshaven, Germany
- 7 April 1934 in Münster, Germany) was a German mathematician who proved important results about abelian groups.*SAU

1902 Thomas Gerald Room FRS FAA (10 November 1902 – 2 April 1986) was an Australian mathematician who is best known for Room squares. He was a Foundation Fellow of the Australian Academy of Science.He studied mathematics in St John's College, Cambridge, and was a wrangler in 1923. He continued at Cambridge as a graduate student, and was elected as a fellow in 1925, but instead took a position at the University of Liverpool. He returned to Cambridge in 1927, at which time he completed his PhD, with a thesis supervised by H. F. Baker.  Room remained at Cambridge until 1935, when he moved to the University of Sydney, where he accepted the position of Chair of the Mathematics Department, a position he held until his retirement in 1968.
During World War II he worked for the Australian government, helping to decrypt Japanese communications.
Room's PhD work concerned generalizations of the Schläfli double six, a configuration formed by the 27 lines on a cubic algebraic surface.
In 1938 he published the book The geometry of determinantal loci through the Cambridge University Press. Nearly 500 pages long, the book combines methods of synthetic geometry and algebraic geometry to study higher-dimensional generalizations of quartic surfaces and cubic surfaces. It describes many infinite families of algebraic varieties, and individual varieties in these families, following a unifying principle that nearly all loci arising in algebraic geometry can be expressed as the solution to an equation involving the determinant of an appropriate matrix.
Room invented Room squares in a brief note published in 1955.

A Room square, named after Thomas Gerald Room, is an n × n array filled with n + 1 different symbols in such a way that:

Each cell of the array is either empty or contains an unordered pair from the set of symbols
Each symbol occurs exactly once in each row and column of the array
Every unordered pair of symbols occurs in exactly one cell of the array.
An example, a Room square of order seven, if the set of symbols is integers from 0 to 7:
(It is known that a Room square (or squares) exist if and only if n is odd but not 3 or 5.)

DEATHS

1683 John Collins (5 March 1624 in Wood Eaton (4km north of Oxford), England - 10 Nov 1683 in London, England) was an accountant and publisher who corresponded extensively with the mathematicians of his day. Collins's importance is, as Barrow said, being "the English Mersenne" . He corresponded with Barrow, David Gregory, James Gregory, Newton, Wallis, Borelli, Huygens, Leibniz, Tschirnhaus and Sluze.
Collins published books by Barrow and Wallis and left a collection of 2000 books and an uncounted number of manuscripts.
He did publish works of his own, however. For instance he published works on sundials, trigonometry for navigation and the use of the quadrant. He had a paper on cartography published and also wrote on accounting, compound interest and annuities. His major works were An introduction to merchant's accounts (1652), The sector on a quadrant (1658), Geometrical dialling (1659), The mariner's plain scale new plained (1659) and, in 1664, he published Doctrine of Decimal Arithmetick. *SAU

1914 Nils Christofer Dunér (21 May 1839, 10 Nov 1914)Swedish astronomer who studied the rotational period of the Sun when he became director of the Uppsala Observatory (1888). By measuring the Doppler shift of the spectral lines of light from the approaching and receding edges of the sun, he made the significant discovery that the rotational period differs from about 25.5 days near the Sun's equator but up to 38.5 days near the Sun's poles.*TIS

1931 Charlotte Angas Scott (8 June 1858 in Lincoln, England
- 10 Nov 1931 in Cambridge, England) studied at Cambridge but was not allowed to take her degree. After graduate work at Cambridge she became the first Head of Mathematics at Bryn Mawr College in Pennsylvania USA. In 1894 Scott published an important textbook An Introductory Account of Certain Modern Ideas and Methods in Plane Analytical Geometry. In 1899 she became an editor of the American Journal of Mathematics and continued an impressive publication record. She also served on the Council of the American Mathematical Society and served as its vice-president in 1905. *SAU

1950 Jacques Inaudi (October 15, 1867 – November 10, 1950) Born to a poor family in the Italian Piedmont, Jacques Inaudi began life as a shepherd but soon discovered a prodigious talent for calculation, and soon he was giving exhibitions in large cities.
Camille Flammarion wrote, “He was asked, for example, how many minutes have elapsed since the birth of Jesus Christ, or what the population would be if the dead from the past ten centuries were resurrected, or the square root of a number of twelve digits, and he gave the response accurately and in two or three minutes — while amusing himself with another activity.”
“The subtraction of numbers consisting of twenty-four figures is an easy matter for him,” reported Scientific American. “Problems for which logarithm tables are generally used he solves mentally with wonderful precision.”
Unlike other prodigies, Inaudi did not visualize his work. “I hear the figures,” he told Alfred Binet, “and it is my ear which retains them; I hear them resounding after I have repeated them, and this interior sensation remains for a long time.”
Inaudi’s father had approached Flammarion hoping that his son could be educated toward a career in astronomy. “It had been an error, whichever way one looked at it,” Flammarion wrote 10 years later. “In science, one cannot make use of his methods, of his adapted formulae, which are tailored to mental calculation.” It was just as well: “Regarding his financial position, he now has, as a result of the curiosity his ability has aroused, a salary, which is over three times that of the Director of the Paris Observatory.” *Greg Ross, Futlty Closet

1970 Heinz Rutishauser (30 January 1918 in Weinfelden, Switzerland; 10 November 1970 in Zürich) was a Swiss mathematician and a pioneer of modern numerical mathematics and computer science. *Wik

1986 Leona Woods (August 9, 1919;La Grange, Illinois, – November 10, 1986; Santa Monica, California), later known as Leona Woods Marshall and Leona Woods Marshall Libby, was an American physicist who helped build the first nuclear reactor and the first atomic bomb.
At age 23, she was the youngest and only female member of the team which built and experimented with the world's first nuclear reactor (then called a pile ), Chicago Pile-1, in a project led by her mentor Enrico Fermi. In particular, Woods was instrumental in the construction and then utilization of geiger counters for analysis during experimentation. She was the only woman present when the reactor went critical. She worked with Fermi on the Manhattan Project, and, together with her first husband John Marshall, she subsequently helped solve the problem of xenon poisoning at the Hanford plutonium production site, and supervised the construction and operation of Hanford's plutonium production reactors.
After the war, she became a fellow at Fermi's Institute for Nuclear Studies. She later worked at the Institute for Advanced Studies in Princeton, New Jersey, the Brookhaven National Laboratory, and New York University, where she became a professor in 1962. Her research involved high-energy physics, astrophysics and cosmology. In 1966 she divorced Marshall and married Nobel laureate Willard Libby. She became a professor at the University of Colorado, and a staff member at RAND Corporation. In later life she became interested in ecological and environmental issues, and she devised a method of using the isotope ratios in tree rings to study climate change. She was a strong advocate of food irradiation as a means of killing harmful bacteria.
She died at St. John's Medical Center from an anesthesia-induced stroke.*Wik

1994 William Higinbotham (25 Oct 1910, 10 Nov 1994)American physicist who invented the first video game, Tennis for Two, as entertainment for the 1958 visitor day at Brookhaven National Laboratory, where he worked (1947-84) then as head of the Instrumentation Division. It used a small analogue computer with ten direct-connected operational amplifiers and output a side view of the curved flight of the tennis ball on an oscilloscope only five inches in diameter. Each player had a control knob and a button. Late in WW II he became electronics group leader at Los Alamos, New Mexico, where the nuclear bomb was developed. After the war, he became active with other nuclear scientists in establishing the Federation of American Scientists to promote nuclear non-proliferation.*TIS

1998 Jean Leray (7 Nov 1906 in Chantenay, near Nantes, Loire-Inférieure, France
- 10 Nov 1998 in La Baule, Loire-Atlantique, France) mathematician who worked on algebraic topology and differential equations. *SAU

2008 Kiyoshi Itō (September 7, 1915 – 10 November 2008) was a Japanese mathematician whose work is now called Itō calculus. The basic concept of this calculus is the Itō integral, and among the most important results is Itō's lemma. The Itō calculus facilitates mathematical understanding of random events. His theory is widely applied in various fields, and is perhaps best known for its use in financial mathematics.*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