## Wednesday, 16 December 2020

### On This Day in Math - December 16

The fact that the author thinks slowly is not serious, but the fact that he publishes faster than he thinks is inexcusable.
~Wolfgang Pauli

The 351st day of the year; 351 is a triangular number, and the sum of five consecutive primes. It is also an element in the Padovan sequence, an interesting exploration for students.

351 ca NOT be written as the sum of three non-zero squares.  It is the 85th day of the year for which that is true.  It is also not the sum of two squares, or of a single square.

351 is the smallest number n so that n, n+1, and n+2 are all the product of four or more primes.

EVENTS

1627 Cavalieri announced to Galileo and Cardinal Borromeo that he had completed his Geometria, which contains his method of indivisibles, now known as Cavalieri’s principle. *VFR

1752 Goldbach wrote Euler with a conjecture that every odd number greater than 3 is the sum of an odd number and twice a square (he allowed 02). Euler would reply on Dec 16 that it was true for the first 1000 odd numbers, and then again on April 3, 1753, to confirm it for the first 2500. A hundred years later, German mathematician Moritz Stern found two contradictions, 5777 and 5993. The story appears in Alfred S. Posamentier's Magnificent Mistakes in Mathematics, (but gloriously, has a mistake for the date, using 1852, but such a wonderful book can forgive a print error.)

1799 Gauss wrote Wolfgang Bolyai that he was sorry they had not discussed the theory of parallels during their student days together at Gottingen (1796–1798). *G. E. Martin, Foundations of Geometry and the Non-Euclidean Plane, p. 306
In the says  he has not sent his doctoral thesis (the foundation of  his classic "Disquisitiones") because he had been critical of two many French mathematicians and feared it would not be well received.  *G Waldo Dunnington,National Mathematics Magazine, Mathematical Association of America

1861 Weierstrass, who for twelve years had endured painful attacks of vertigo, suﬀered a complete collapse of his health due to overwork. Henceforth, he always lectured while seated, consigning the blackboard work to an advanced student. Nevertheless, he eventually became a recognized master teacher. *VFR

1897 Marie Curie began her research in an unheated abandoned shed with the piezo-quartz electrometer invented by her husband Pierre and his brother Jacques, a minerology professor.  *Brody & Brody, The Science Class You Wish You Had

1926 In September of this year Samuel Goudsmit and George Eugene Uhlenbeck – both graduate students working under Paul Ehrenfest at the University of Leiden, published a paper on electron spin. The article caught the attention of Warner Heisenberg who wrote a letter to Samuel Goudsmit regarding the concept on December 16. The letter was subsequently misplaced and not found until March of 2017. Esther Goudsmit, daughter of Samuel Goudsmit, sent the letter (in German) and its translation to the Niels Bohr Library & Archives. She had found it in a drawer of miscellany and decided it was important that it be united with the rest of her father’s papers. NBL&A

1941 Pope Pius XII declared Albertus Magnus the patron of all who cultivate the natural sciences. *VFR

BIRTHS

1625 Erhard Weigel (December 16, 1625 – March 21, 1699) was a German mathematician, astronomer and philosopher. He earned his Ph.D. from the University of Leipzig. From 1653 until his death he was professor of mathematics at Jena University. He was the teacher of Leibniz in 1663, and other notable students. He also worked to make science more widely accessible to the public, and what would today be considered a populariser of science. Through Leibniz, Weigel is the intellectual forefather of a long tradition of mathematicians that connects a great number of professionals to this day. The Mathematics Genealogy Project lists more than 50,000 "descendants" of Weigel's, including Lagrange, Euler, Poisson and several Fields Medalists. *Wik
A post at the Renaissance Mathematicus about Weigel and some of his lesser known students (most student's would be "lesser known" compared to Leibniz) also pointed out that "Another Weigel innovation in celestial cartography was his eclipse map from 1654. An eclipse map is a map that shows the path on the surface of the earth from which a solar eclipse will be visible. Weigel’s was the first such printed map ever produced. This honour is usually falsely accredited to Edmund Halley for his 1715 eclipse map."
For religious reasons, he wanted to rename all the constellations, and made several globes of the sky with his renamed constellations. The one below is from the Franklin Institute.

1776 Johann Wilhelm Ritter (16 Dec 1776; 23 Jan 1810) German physicist who discovered the ultraviolet region of the spectrum (1801) and thus helped broaden man's view beyond the narrow region of visible light to encompass the entire electromagnetic spectrum from the shortest gamma rays to the longest radio waves. After studying Herschel's discovery of infrared radiation, he observed the effects of solar radiation on silver salts and deduced the existence of radiation outside the visible spectrum. He also made contributions to spectroscopy and the study of electricity. *TIS

1804 Viktor Bunyakovsky (16 Dec 1804 in Bar, Podolskaya gubernia (now Vinnitsa oblast), Ukraine - 12 Dec 1889 in St Petersburg, Russia) worked on Number Theory as well as geometry, mechanics and hydrostatics. He discovered the Cauchy-Schwarz inequality 25 years before Cauchy or Schwarz.*SAU

1826 Giovanni Battista Donati (16 Dec 1826; 20 Sep 1873) Italian astronomer who, on 5 Aug 1864, was first to observe the spectrum of a comet (Tempel 1864 II), showing not merely reflected sunlight but also spectral lines from luminous gas forming the comet tail when near the Sun. Earlier, he discovered the comet known as Donati's Comet at Florence, on 2 Jun 1858. When the comet was nearest the earth, its triple tail had an apparent length of 50°, more than half the distance from the horizon to the zenith and corresponding to the enormous linear figure of more than 72 million km (about 45 million mi). With an orbital period estimated at more than 2000 years, it will not return until about the year 4000.*TIS

1828 Alexander Ross Clarke (16 Dec 1828; 11 Feb 1914) English geodesist with the Army Ordnance Survey who made calculations of the size and shape of the Earth (the Clarke ellipsoid) were the first to approximate accepted modern values with respect to both polar flattening and equatorial radius. The figures from his second determination (1866) became a standard reference for U.S. geodesy for most of the twentieth century until satellites could improve accuracy. In 1880, Clarke coined the term "Geodesy" when he published his famous book by that title. He wrote articles on mathematical geography and geodesy and also contributed "The Figure of the Earth" in the Encyclopedia Britannica. His military service with the Ordnance Survey lasted 27 years.*TIS

1849 Gyula Kőnig (16 December 1849 – 8 April 1913) was a Hungarian mathematician. He was born in Győr, Hungary and died in Budapest. His mathematical publications in foreign languages appeared under the name Julius König. His son Denes Konig is the famous graph theorist.Kőnig worked in many mathematical fields. His work on polynomial ideals, discriminants and elimination theory can be considered as a link between Leopold Kronecker and David Hilbert as well as Emmy Noether. Later on his ideas were simplified considerably, to the extent that today they are only of historical interest.
Kőnig already considered material influences on scientific thinking and the mechanisms which stand behind thinking.
“ The foundations of set theory are a formalization and legalization of facts which are taken from the internal view of our consciousness, such that our 'scientific thinking' itself is an object of scientific thinking."
But mainly he is remembered for his contributions to and his opposition against set theory.*Wik

1857 Edward Emerson Barnard (16 Dec 1857; 6 Feb 1923)
astronomer who pioneered in celestial photography, specializing in wide-field photography. From the time he began observing in 1881, his skill and keen eyesight combined to make him one of the greatest observers. Barnard came to prominence as an astronomer through the discovery of numerous comets. In the 1880s, a patron of astronomy in Rochester, N.Y. awarded \$200 per new comet was found. Barnard discovered eight - enough to build a "comet house" for his bride. At Lick Observatory (1888-95) he made the first photographic discovery of a comet; photographed the Milky Way; and discovered the fifth moon of Jupiter. Then he joined Yerkes Observatory, making his Photographic Atlas of Selected Regions of the Milky Way.*TIS

1887 Johann Radon (16 Dec 1887 in Tetschen, Bohemia (now Decin, Czech Republic)
- 25 May 1956 in Vienna, Austria) Radon applied the calculus of variations to differential geometry which led to applications in number theory. It was while he was studying applications of the calculus of variations to differential geometry that he discovered curves which are now named Radon curves. His best known results involve combining the integration theories of Lebesgue and Stieltjes which first appeared in his habilitation dissertation and then in a second important work Über lineare Funktionaltransformationen und Funktionalgleichungen (1919).
During 1918-19 he worked on affine differential geometry, then in 1926 he considered conformal differential geometry. His wide interests led him to study Riemannian geometry and geometrical problems which arose in the study of relativity. *SAU

1905 Piet Hein (December 16, 1905–April 17, 1996) was a Danish scientist, mathematician, inventor, designer, author, and poet, often writing under the Old Norse pseudonym "Kumbel" meaning "tombstone". His short poems, known as gruks or grooks (Danish: Gruk), first started to appear in the daily newspaper "Politiken" shortly after the Nazi occupation in April 1940 under the pseudonym "Kumbel Kumbell"
The Soma cube is a solid dissection puzzle invented by Piet Hein in 1933 during a lecture on quantum mechanics conducted by Werner Heisenberg. Seven pieces made out of unit cubes must be assembled into a 3x3x3 cube. The pieces can also be used to make a variety of other 3D shapes. Piet Hein created the superellipse which became the hallmark of modern Scandinavian architecture.
In addition to the thousands of grooks he wrote, Piet Hein devised the games of Hex, Tangloids, Morra, Tower, Polytaire, TacTix, Nimbi, Qrazy Qube, Pyramystery, and the Soma cube. He advocated the use of the superellipse curve in city planning, furniture making and other realms. He also invented a perpetual calendar called the Astro Calendar and marketed housewares based on the superellipse and Superegg. *Wik
My Favorite of his grooks is this one:
Problems worthy
of attack
prove their worth
by hitting back.

1925 IBM-701 Team Member William F. McClelland is born in Bronxville, N.Y. He received a BS from MIT in 1947 and immediately joined IBM Watson Laboratory. At IBM he programmed the SSEC (Selective Sequence Electronic Calculator) for John von Neumann and was chairman of the Mathematics Planning Group in 1951-1953. This group developed computer specifications to solve complex mathematical problems, performed basic research in the use of a stored-binary calculator, and wrote and tested programs that were supplied to the customers of the 701.
McClelland had held various management and marketing position at IBM until his retirement in 1982. *CHM

1968 Valérie Berthé (16 December 1968) French mathematician who works as a director of research for the Centre national de la recherche scientifique (CNRS) at the Institut de Recherche en Informatique Fondamentale (IRIF), a joint project between CNRS and Paris Diderot University. Her research involves symbolic dynamics, combinatorics on words, discrete geometry, numeral systems, tessellations, and fractals.
Berthé completed her baccalauréat at age 16, and studied at the École Normale Supérieure from 1988 to 1993. She earned a licentiate and master's degree in pure mathematics from Pierre and Marie Curie University in 1989, a Diplôme d'études approfondies from University of Paris-Sud in 1991, completed her agrégation in 1992, and was recruited by CNRS in 1993. Continuing her graduate studies, she defended a doctoral thesis in 1994 at the University of Bordeaux. Her dissertation, Fonctions de Carlitz et automates: Entropies conditionnelles was supervised by Jean-Paul Allouche. She completed a habilitation in 1999, again under the supervision of Allouche, at the University of the Mediterranean Aix-Marseille II; her habilitation thesis was Étude arithmétique et dynamique de suites algorithmiques.
In 2013, she was elevated to the Legion of Honour. *Wik

DEATHS
1687 Sir William Petty FRS (26 May 1623 – 16 December 1687) was an English economist, scientist and philosopher. He first became prominent serving Oliver Cromwell and Commonwealth in Ireland. He developed efficient methods to survey the land that was to be confiscated and given to Cromwell's soldiers. He also managed to remain prominent under King Charles II and King James II, as did many others who had served Cromwell.
He was Member of the Parliament of England briefly and was also a scientist, inventor, and entrepreneur, and was a charter member of the Royal Society. It is for his theories on economics and his methods of political arithmetic that he is best remembered, however, and to him is attributed the philosophy of 'laissez-faire' in relation to government activity. He was knighted in 1661. He was the great-grandfather of Prime Minister William Petty Fitzmaurice, 2nd Earl of Shelburne and 1st Marquess of Lansdowne.
Petty was a founder member of The Royal Society. He was born and buried in Romsey, and was a friend of Samuel Pepys.
He is best known for economic history and statistic writings, pre-Adam Smith. Of particular interest were Petty's forays into statistical analysis. Petty's work in political arithmetic, along with the work of John Graunt, laid the foundation for modern census techniques. Moreover, this work in statistical analysis, when further expanded by writers like Josiah Child documented some of the first expositions of modern insurance. Vernon Louis Parrington notes him as an early expositor of the labour theory of value as discussed in Treatise of Taxes in 1692.
Petty was knighted in 1661 by Charles II and returned to Ireland in 1666, where he remained for most of the next twenty years. *Wik

1933 Ludwig Schlesinger (1 Nov 1864 in Nagyszombat, Hungary (now Trnava, Tyrnau, Slovakia)- 16 Dec 1933 in Giessen, Germany was a mathematician, born in what is now Slovakia, who worked on differential equations. *SAU

1934 Gustav de Vries (22 Jan 1866 in Amsterdam, The Netherlands
- 16 Dec 1934 in Haarlem, The Netherlands) was a Dutch mathematician who introduced the famous Korteweg-de Vries equation which characterizes traveling waves. *SAU

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