Friday 9 February 2024

On This Day in Math - February 9


da Vinci's Stellated Dodecahedron from divina proportione

To argue with a man who has renounced the use of authority of reason is like administering medicine to the dead.
~Thomas Paine, American Patriot, and a pretty good bridge builder, perhaps pointing out something still very relevant to today's political discussions.

The 40th day of the year; in English forty is the only number whose letters are in alphabetical order.

There are 40 solutions on for the 7 queens problem.  placing seven chess queens on a 7x7 chessboard so that no two queens threaten each other.

-40 is the temperature at which the Fahrenheit and Celsius scales correspond; that is, −40 °F = −40 °C.

Euler first noticed (in 1772) that the quadratic polynomial P(n) = n2 + n + 41 is prime for all non-negative numbers less than 40.
Paul Halcke noted in 1719 that the product of the aliquot parts of 40 is equal to 40 cubed. 1*2*4*5*8*10*20 = 64000 = 403. He found the same is true for 24.

forty (quaranta)  is the root of the word quarantine, for the forty day period of isolation for visitors to Venice to control the plague.

And.... forty is the highest number ever counted to on Sesame Street.

The expanded collection of Number Factoids for Day 1-60  are available here


1498 Luca Pacioli was professor at Milan. He was inspired to start his Divina Proportione on 9 Feb 1498 and completed it on 14 Dec 1498, though it was not published (in an expanded form) until 1509. (J Tennenbaum in 2005 said that it was completed by the Feb 9 date.)  He was a good friend of Leonardo da Vinci. It was Leonardo who drew the pictures for Pacioli's book. Pacioli may have advised Leonardo on the perspective for the painting of The Last Supper. Certainly Pacioli stimulated Leonardo's interest in perspective and it is possible that Leonardo's famous drawing of the proportions of the human body was inspired by Pacioli's comment on classical architecture; "For in the human body they found the two main figures ..., namely the perfect circle and the square." Pacioli seems to have made models of the polyhedra illustrated in his book, though we don't know if Leonardo used these for his drawings. A set was probably given to Pacioli's earlier patron, the Duke of Urbino, in 1494. Another set was paid for by Florence in 1504. *Unknown Internet Source
I was just reminded by a tweet from @IanMegaw that Pacioli also published the first description of double-entry bookkeeping. (thanks Ian)

Another first, or two, for Pacioli is found in a paper on the origins of the game of Nim by Lisa Rougetet.  "The oldest simplified variation of Nim found to date in Europe is in a manuscript of the Renaissance,De Viribus Quantitatis(On the powers of numbers) , a treatise written between 1496 and 1508 by the Italian mathematician Fra Luca Bartolomeo dePacioli , one of the most famous mathematicians of his time. ... TheDe Viribus Quantitatiscan be considered to be one of the first works entirely devoted to mathematical recreations 

I received a comment that included this un-cited quote with two more firsts about the book.

"The world's oldest magic text, De viribus quantitatis (On the Powers of Numbers), was penned by Luca Pacioli, a Franciscan monk who shared lodgings with da Vinci. ...  and contains the first ever reference to card tricks as well as guidance on how to juggle, eat fire and make coins dance. It is also the first work to note that da Vinci was left-handed."

1849 After the death of Lord Kelvin’s Father, James Thomson, his replacement was the subject of a letter from William Hopkins to discuss the merits of G.G. Stokes and Hugh Blackburn for the position, “if you determine … to elect a man who is sure to hereafter to dignify his postion by the highest scientific distinction, Stokes is unquestionably your man.” * The correspondence between Sir George Gabriel Stokes and Sir William Thomson, pg 59

In 1829 the honorary degree of LLD was conferred upon James Thomson by the University of Glasgow, where in 1832 he was appointed professor of mathematics. He held this post till his death on 12 January 1849.

In 1870, the U.S. Weather Bureau (later named the Weather Service) was authorized by Congress, and placed under the direction of the Signal Service. Cleveland Abbe had inaugurated a private weather reporting and warning service at Cincinnati and had been issuing weather reports or bulletins since 1 Sep 1869. Hence, Abbe was the only person in the country who was already experienced in drawing weather maps from telegraphic reports and forecasting from them. Naturally, he was offered an important position in this new service which he accepted, beginning 3 Jan 1871, and was often the official forecaster of the weather. He was the first U.S. meteorologist, and known as the "father of the U.S. Weather Bureau."*TIS  

1883 The very first issue of Science is published. The first item in the “Weekly summary of the progress of science” contains a report by Thomas Craig that “Lindemann gave a proof of the fact that π cannot be a root of an equation of any degree with rational co-eficients. This is a most remarkable paper, as it thus contains the first direct, absolute proof that has ever been given of the impossibility of the quadrature of the circle. ... Lindemann has certainly done a splendid piece of work in thus absolutely proving the impossibility of ‘squaring the circle’; and it is only to be regretted that his work will not carry conviction to the minds of those mistaken individuals, the ‘circle-squarers.’ But it is hardly to be supposed that they will be convinced of the futility of their task, any more than the perpetual-motion inventors were convinced by the discovery and enunciation of the principles of the conservation of energy.” [p. 15] *VFR

1912 The Salt Lake Tribune, reporting on the 1912 theory that Mars was populated by a giant vegetable that possessed a single giant eye, accompanied by a remarkable diagram. *Paul Fairie

J F Ptak wrote, "The Giant All-Seeing Eyeball was hoisted high in the Tribune, given supposed life by the very highly capable astronomer W.W. Campbell (1862-1930, with his biography here at the National Academy of Science), who is quoted by the paper as being the source of this preposterous theory.  Campbell was not pleased by this--not at all.  And I can well imagine why. "

"I can't consider the Salt Lake paper's story a hoax (as in the case of the great Moon hoax perpetrated in the pages of the New York Sun in 1835), mainly because it is surrounded by other crazy/funny stories--and it didn't try to present the story as a piece of non-fiction, as is classically the case with hoaxes. The Tribune followed up this story on the very next page with one on how the English aristocracy was turning into gorillas. "

J F Ptak

On this day in 1937, Ruth Moufang habilitated, being only the third German woman to habilitate in mathematics. However, the Nazis refused her permission to teach (because she was a woman), so from 1937 she became an industrial mathematician working on elasticity theory. In fact this gives Moufang the unique position of being the first German woman with a doctorate to be employed in industry. She may actually be the first ever such woman anywhere.

 At the end of World War II she was leading the Department of Applied Mathematics at the arms industry of Krupp.

In 1946 she was finally allowed to accept a teaching position at the University of Frankfurt, and in 1957 she became the first woman professor at the university.

In 1933, Moufang showed Desargues's theorem does not hold in the Cayley plane. The Cayley plane uses octonion coordinates which do not satisfy the associative law. Such connections between geometry and algebra had been previously noted by Karl von Staudt and David Hilbert. Ruth Moufang thus initiated a new branch of geometry called Moufang planes.

1986 Halley’s comet last reached perihelion. The next return to perihelion will be on 28 July 2061. *Wik (I am still amazed that we can mathematically predict such an event with such precision.)


1489 Georg Hartmann (sometimes spelled Hartman; February 9, 1489 – April 9, 1564) was a German engineer, instrument maker, author, printer, humanist, churchman, and astronomer. After finishing his studies, he travelled through Italy and finally settled in Nuremberg in 1518. There he constructed astrolabes, globes, sundials, and quadrants. In addition to these traditional scientific instruments Hartmann also made gunner's levels and sights. Hartmann was possibly the first to discover the inclination of Earth's magnetic field. He died in Nuremberg.
His two published works were Perspectiva Communis (Nuremberg, 1542), a reprint of John Peckham's 1292 book on optics and Directorium (Nuremberg, 1554), a book on astrology. He also left Collectanea mathematica praeprimis gnomonicam spectania, 151 f. MS Vienna, Österreichische Nationalbibliothek, Quarto, Saec. 16 (1527–1528), an unpublished work on sundials and astrolabes that was translated by John Lamprey and published under the title of Hartmann's Practika in 2002. *Wik

1775 Farkas Bolyai (9 Feb 1775, 20 Nov 1856) Hungarian mathematician, poet, and dramatist who spent a lifetime trying to prove Euclid's (fifth) postulate that parallel lines do not meet. While studying at the University of Göttingen, he met as a fellow student, the noted German mathematician Carl F. Gauss, with whom he corresponded as a life-long friend. Bolyai taught mathematics, physics and chemistry at Marosvásárhely all his life. He discouraged his son, János Bolyai, from studying the parallel axiom as he had, writing in a letter to him: "For God's sake, please give it up. Fear it no less than the sensual passion, because it, too, may take up all your time and deprive you of your health, peace of mind and happiness in life." *TIS (In 1804 he believed that he had a proof the Euclid's fifth postulate could be deduced from the other axioms. He sent this proof to C. F. Gauss who found an error. His Son, Janos, would ignore his father's warnings and go on to discover a non-Euclidean Geometry. ).

1880 Lipót Fejér (9 Feb 1880, 15 Oct 1959) Fejér's main work was in harmonic analysis working on Fourier series and their singularities. Fejér collaborated to produce important papers with Carathéodory on entire functions and with Riesz on conformal mappings. *SAU In 1897 he won a prize in one of the first mathematical competitions held in Hungary. *VFR

1907 Harold Scott MacDonald Coxeter (9 Feb 1907 in London, England - 31 March 2003 in Toronto, Canada) graduated from Cambridge and worked most of his life in Canada. His work was mainly in geometry. In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics. Among his most famous geometry books are The real projective plane (1955), Introduction to geometry (1961), Regular polytopes (1963), Non-euclidean geometry (1965) and, written jointly with S L Greitzer, Geometry revisited (1967). He also published a famous work on group presentations, which was written jointly with his first doctoral student W O J Moser, Generators and relations for discrete groups.
His 12 books and 167 published articles cover more than mathematical research. Coxeter met Escher in 1954 and the two became lifelong friends. Another friend, R Buckminister Fuller, used Coxeter's ideas in his architecture. In 1938 Coxeter revised and updated Rouse Ball's Mathematical recreations and essays, a book which Rouse Ball first published in 1892. *SAU
Considered by many as the greatest geometer of the 20th Century.  

1908 Alexander Dinghas (February 9, 1908 – April 19, 1974) was a Turkish mathematician. He is known for his work in different areas of mathematics including differential equations, functions of a complex variable, functions of several complex variables, measure theory and differential geometry. His most important contribution was his work in function theory, in particular Nevanlinna theory and the growth of subharmonic functions.*Wik

Lloyd Noel Ferguson (February 9, 1918 – November 30, 2011) was an American chemist. 

Many chemists came into the field after being given a chemistry set as a kid, but Ferguson's family was too poor for such niceties, so Ferguson built his own chemistry lab in his backyard, financing it by making insect repellants and stain removers and selling them to neighbors.  And he remembers, naturally, that he liked blowing up things.  He skipped several grades in high school and used the years thus gained to work as a porter for the railroads to raise money for college. He was accepted into the University of California at Berkeley as an undergraduate, and did so well that they took him into their PhD program, which most graduate programs will not do except under exceptional circumstances.  Ferguson apparently warranted the exception.  He worked under Melvin Calvin, future Nobelist, and this being the war years (1940-43), they worked on a military project, trying to develop an inorganic compound, like organic hemoglobin, that would release oxygen on demand and then re-oxygenate itself.  This might provide a supply of oxygen for welding onboard ship, where oxygen tanks were too dangerous if damaged by gunfire. 

After he received a PhD in 1943, Ferguson found it difficult to find a teaching position in white America, just as his advisor had predicted, who suggested that he go into industry instead.  But Ferguson found a small North Carolina black college that needed a chemistry professor, and he started his career there.  He then moved on to Howard University, where he founded a PhD program in chemistry, the first such program in any black college anywhere.  After twenty years at Howard, he was invited to become chair of the chemistry department at California State University, Los Angeles, were he would work until retirement in 1986.

His finest achievement was in promoting interest in chemistry in young black Americans.  He founded the National Organization for the Professional Advancement of Black Chemists and Chemical Engineers (NOBCChE) in 1972, mainly for the purpose of youth education, and, for the American Chemical Society, he founded the SEED project in 1968, which provided financial assistance to black high school students who lacked the resources to pursue higher education.   The organization he founded, NOBCChE, later established the Lloyd N. Ferguson Young Scientist Award, given annually to a promising young black chemist. *Linda Hall Org

1919 Irene Anne Stegun (February 9, 1919 – January 27, 2008) was a mathematician at the National Bureau of Standards who, with Milton Abramowitz, edited a classic book of mathematical tables called A Handbook of Mathematical Functions, widely known as Abramowitz and Stegun. When Abramowitz died of a heart attack in 1958, Stegun took over management of the project and finished the work by 1964, working under the direction of the NBS Chief of Numerical Analysis Philip J. Davis, who was also a contributor to the book. *Wik

1927 David John Wheeler FRS (9 February 1927–13 December 2004) the Inventor of the Wheeler Jump, is Born. In 1951, he introduced the concept of the subroutine to computer programming, is born. He concentrated his work on assembly programming language and invoked the subroutine in his Wheeler jump technique. For this work Wheeler received the IEEE Computer Society Pioneer Award. *CHM
He was born in Birmingham and gained a scholarship at Trinity College, Cambridge to read mathematics, graduating in 1948. He completed the world's first PhD in computer science in 1951. His contributions to the field included work on the EDSAC and the Burrows-Wheeler transform. Along with Maurice Wilkes and Stanley Gill he is credited with the invention of the subroutine (which they referred to as the closed subroutine), because of which a jump to subroutine instruction is often called Wheeler Jump. He was responsible for the implementation of the CAP computer, the first to be based on security capabilities. In cryptography, he was the designer of WAKE and the co-designer of the TEA and XTEA encryption algorithms together with Roger Needham. In 2003 he was a Computer History Museum Fellow Award recipient.
Wheeler is often quoted as saying "All problems in computer science can be solved by another level of indirection... Except for the problem of too many layers of indirection." *Wik


1734 Pierre Polinière (8 September 1671, Coulonces, France - 9 February 1734, Coulonces, France) was an early investigator of electricity and electrical phenomena, notably "barometric light", a form of gas-discharge light, which suggested the possibility of electric lighting. He also helped to introduce the scientific method in French universities. *Wik

1811 Nevil Maskelyne (6 Oct 1732, 9 Feb 1811) (SAU gives 5 Oct for birhtdate)
British astronomer noted for his contribution to the science of navigation. In 1761 the Royal Society sent Maskelyne to the island of St Helena to make accurate measurements of a transit of Venus. This in turn gives the distance from the Earth to the Sun, and the scale of the solar system. During the voyage he also experimented with the lunar position method of determining longitude. In 1764 he went on a voyage to Barbados to carry out trials of Harrison's timepiece, followed by appointment as Astronomer Royal (1765). In 1774, he carried out an experiment on a Scottish mountain with the use of a plumb line to determine the Earth's density. He found it was approximately 4.5 times that of water. *TIS (the current scientific value of the Earth's density is about 5.2 times that of water.) He was the fifth English Astronomer Royal. He held the office from 1765 to 1811.*Wik

1865 James Melville Gilliss (6 Sep 1811; 9 Feb 1865) U.S. naval officer and astronomer who founded the Naval Observatory in Washington, D.C., the first U.S. observatory devoted entirely to research. Gilliss joined the Navy as a midshipman at the age of 15. He taught himself astronomy, at a time when there was no fixed astronomical observatory in the U.S., and very little formal instruction. In 1838, when Charles Wilkes left on the famous South Seas Exploring Expedition, Gilliss became officer-in-charge of the Depot of Charts and Instruments, forerunner of the U. S. Naval Observatory. Gilliss' astronomical observations made during this time in connection with determining longitude differences with the Wilkes Expedition, resulted in the first star catalogue published in the United States. *TIS

1883 Henry John Stephen Smith (2 Nov 1826 in Dublin, Ireland, 9 Feb 1883 in Oxford, England) was an Irish mathematician whose most important contributions are in number theory where he worked on elementary divisors. Henry John Stephen Smith In addition to solving these cases explicitly, he gave a method which would yield the number of ways that an integer can be expressed as the sum of k squares for any fixed k. He published his results in The orders and genera of quadratic forms containing more than three indeterminates published in the Proceedings of the Royal Society in 1867. Eisenstein had earlier proved the result for 3 squares and Jacobi for 2, 4 and 6 squares. Smith also extended Gauss's theorem on real quadratic forms to complex quadratic forms. *SAU He posthumously received the Grand Prix des Sciences Mathematiques of the Paris Academy of Science for his proof that every positive integer is the sum of five squares. He shared the prize with the eighteen year old Hermann Minkowski.*VFR The prize was awarded on April 2, less than two months after his death.

1937 Francis Sowerby Macaulay FRS (11 February 1862 – 9 February 1937) was an English mathematician who made significant contributions to algebraic geometry. He is most famous for his 1916 book, The Algebraic Theory of Modular Systems, which greatly influenced the later course of algebraic geometry. Both Cohen-Macaulay rings and the Macaulay resultant are named for Macaulay.
Macaulay was educated at Kingswood School and graduated with distinction from St John's College, Cambridge. He taught top mathematics class in St Paul's School in London from 1885 to 1911. His students included J. E. Littlewood and G. N. Watson.*Wik Littlewood consulted the examinations record and wrote, "In the 25 years from [Macaulay's] appointment to St Paul's in 1885 to his resignation in 1911 there were 41 scholarships (34 at Cambridge) and 11 exhibitions; and in the 20 years available there were 4 senior wranglers, one second, and one fourth among his former pupils." *SAU

1970 Leo Moser (April 11, 1921, Vienna—February 9, 1970, Edmonton) was an Austrian-Canadian mathematician, best known for his polygon notation.
A native of Vienna, Leo Moser immigrated with his parents to Canada at the age of three. He received his Bachelor of Science degree from the University of Manitoba in 1943, and a Master of Science from the University of Toronto in 1945. After two years of teaching he went to the University of North Carolina to complete a Ph.D., supervised by Alfred Brauer.[1] There, in 1950, he began suffering recurrent heart problems. He took a position at Texas Technical College for one year, and joined the faculty of the University of Alberta in 1951, where he remained until his death at the age of 48. *Wik In mathematics, Steinhaus–Moser notation is a means of expressing certain extremely large numbers. It is an extension of Steinhaus’s polygon notation.

n in a triangle a number n in a triangle means nn.
n in a square a number n in a square is equivalent with "the number n inside n triangles, which are all nested."
n in a pentagon a number n in a pentagon is equivalent with "the number n inside n squares, which are all nested."

1988 Israel Nathan Herstein (March 28, 1923, Lublin, Poland – February 9, 1988, Chicago, Illinois) was a mathematician, appointed as professor at the University of Chicago in 1951. He worked on a variety of areas of algebra, including ring theory, with over 100 research papers and over a dozen books.
He is known for his lucid style of writing, as exemplified by the classic and widely influential Topics in Algebra, an undergraduate introduction to abstract algebra that was published in 1964, which dominated the field for 20 years. A more advanced classic text is his Noncommutative Rings in the Carus Mathematical Monographs series. His primary interest was in noncommutative ring theory, but he also wrote papers on finite groups, linear algebra, and mathematical economics.

 His family emigrated to Canada in 1926, and he grew up in a harsh and underprivileged environment where, according to him, "you either became a gangster or a college professor." During his school years he played football, ice hockey, golf, tennis, and pool. He also worked as a steeplejack and as a barker at a fair. He received his B.S. degree from the University of Manitoba and his M.A. from the University of Toronto. He received his Ph.D from Indiana University in 1948. His advisor was Max Zorn. He held positions at the University of Kansas, Ohio State University, University of Pennsylvania, and Cornell University before permanently settling at the University of Chicago in 1962. He was a Guggenheim Fellow for the academic year 1960–1961.


2001 Herbert Alexander Simon (15 Jun 1916, 9 Feb 2001 at age 84) American social scientist who was a pioneer of the development of computer artificial intelligence. In 1956, with his long-time colleague Allen Newell, Simon produced the computer program, The Logic Theorist, a computer program that could discover proofs of geometric theorems. It was the first computer program capable of thinking, and marked the beginning of what would become known as artificial intelligence. It proved many of the theorems of symbolic logic in Whitehead and Russell's Principia Mathematica. He is further known for his contributions in fields including psychology, mathematics, statistics, and operations research, all of which he synthesized in a key theory for which he won the 1978 Nobel Prize for economics. *TIS

2003 Masatoşi Gündüz İkeda (25 February 1926, Tokyo. - 9 February 2003, Ankara), was a Turkish mathematician of Japanese ancestry, known for his contributions to the field of algebraic number theory. *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

No comments: