## Thursday, 22 December 2016

### On This Day in Math - December 22

*Wik

Scientists are the true driving force of civilization.
~James Burke

The 357th day of the year; there are 357 odd numbers in the first 46 rows of Pascal's Arithmetic triangle. (How many evens?)

357 is made up of three consecutive prime digits, and is the product of three distinct primes, 3 x 7 x 17=357

EVENTS,
968 First clear description of the corona seen during a total eclipse, by a chronicler in Constantinople. The first mention of the corona may have been due to Plutarch, who lived from about AD 46 to 120. Plutarch's book 'On the Face in the Orb of the Moon' contains a reference to 'a certain splendour' round the eclipsed Sun which could well have been the corona. *Patrick Poitevin ‏@PatrickPoitevin

1666 Seven mathematicians and seven physicists met at the king’s Library to inaugurate the French Academy of sciences. They would not receive a formal decree of protection from Louis XIV until 1699. For three centuries women were not allowed as members of the Academy. The first female full member was Yvonne Choquet-Bruhat in 1979. *VFR The society was an outgrowth of an informal community of scientists who coordinated their research efforts through the efforts of Marin Mersenne, a monk at the Minim monastery, who had exchanged 10,000 letters with them. *TIS

1669 John Wallis in a letter to Thomas Smith of Madalene College writes “In a dark night, in bed, without pen, ink or paper or anything equivalent, I did by memory extract the square root of 30000,00000,00000,00000,00000,00000,00000,00000, which I found to be 1,73205,08075,68077,29353, etc. and did the next day commit it to writing.” (Wallis wrote this some 12 years after the event, but there is sufficient evidence elsewhere of his prodigious powers of calculation to lend the story some credence.) *Jacqueline A. Stedall, Our Own Nation

1680 The Great Comet of 1680, sometimes called Kirch's Comet was the first comet discovered by telescope, but it was visible to the naked eye for several months, some say even in the daylight. The image at right is a drawing of comet as it appeared on December 22, 1680 over Beverwijk, attributed to Rochus van Even *@rijksmuseum.

1831 The first use of Sir Francis Beaufort's scale of wind force in an official log was by Captain Robert Fitzroy on the first day of the voyage of exploration of the HMS Beagle that included a young naturalist named Charles Darwin. *Isaac's Storm, Erik Larson

1866 L E Becker wrote to Darwin to ask if he would “be so very good as to send us a paper to be read at our first meeting”. “Of course we are not so unreasonable as to desire that you should write anything specially for us” Becker said, “but I think it possible you may have by you a copy of some paper such as that on the Linum which you have communicated to the learned societies but which is unknown and inaccessible to us unless through your kindness.”
Darwin responded by sending not one but three papers to be read at the ladies’ inaugural meeting. Whether Darwin realized that he was providing materials for a feminist organization is unclear, although Becker’s use of headed paper and the enclosure in her letter to Darwin of the society’s first pamphlet certainly made no secret of her political affiliations.
Regardless, what is interesting is that despite what he said in the public context about women’s intellectual in-capabilities and designated social role, in private his thoughts and actions were very different. Darwin was happy to work in collaboration with many women like Becker. He encouraged women’s scientific interests wherever possible, frequently sharing observations, samples and reading materials with women across the world. In some rare instances he was even happy to acknowledge that a woman’s scientific skill and knowledge might be superior to his own! *Darwin and Gender, the blog)

In 1870, Charles Augustus Young, an American astronomer, made the first observations of the flash spectrum of the Sun. He was a pioneer in the study of the spectrum of the sun and experimented in photographing solar prominences in full sunlight. On 22 Dec 1870, at the eclipse in Spain, he saw the lines of the solar spectrum all become bright for perhaps a second and a half (the "flash spectrum") and announced the "reversing layer." In his career, he also proved the gaseous nature of the sun's corona. By exploring from the high altitude of Sherman, Wy. (1872), he more than doubled the number of bright lines he had observed in the chromosphere. By a comparison of observations, he concluded that magnetic conditions on the earth respond to solar disturbances.

1877 Alfred Beach, editor of Scientific American wrote, "Mr. Thomas A. Edison recently came into this office, placed a little machine on our desk, turned a crank, and the machine inquired as to our health, asked how we liked the phonograph, informed us that it was well, and bid us a cordial good night. These remarks were not only perfectly audible to ourselves, but to a dozen or more persons gathered around." *TIS

1882 First electrical lights for a Christmas tree. Edward Hibberd Johnson, an American electrical engineer and inventor,spent many years in various business projects with Thomas Edison. Johnson created the first electric lights on a Christmas tree on 22 Dec 1882.*TIS

In 1885, a U.S. patent for a gravity switchback railway was issued to La Marcus Adna Thompson of Coney Island, N.Y. (No. 332,762). In 1884, Thompson, the "Father of the Gravity Ride," opened a 600-ft roller-coaster at Coney Island at 6-mph maximum. Its popularity enabled him to recoup his \$1,600 investment in only three weeks. In this patent he described a railway on trestles with two parallel tracks undulating vertically. At the end of the first track, a switch automatically allowed the car to return on the second track. His design in an earlier patent (20 Jan 1885, No. 310,966) needed passengers to temporarily get out of the car at the end of the first track while assistants prepared it to return on the second track.) *TIS

1955 The FINAC, the Italian Mark I*, is inaugurated in Rome. The Mark I*, the commercial prototype of Manchester's Mark I, was built by English Ferranti Ltd., for UNESCO's International Computational Center in Rome. This completely electronic computer arrived. *CHM

2006 The journal Science honored Grigori Perelman Perelman's proof of the Poincaré conjecture as the scientific "Breakthrough of the Year", the first time this had been bestowed in the area of mathematics. *Wik

2010 India issued a stamp featuring Srinivasa Ramanujan, who was born on this day, to celebrate their National Mathematics Day.

BIRTHS

1765 Johann Friedrich Pfaff born in Stuttgart, Germany. Laplace, when asked who the greatest mathematician in Germany, replied, Pfaﬀ. When the questioner said he should have thought Gauss was, Laplace replied: “Pfaff is the greatest mathematician in Germany; but Gauss is the greatest in all Europe.” [Quoted from Cajori, A History of Mathemtics, in AMM 8(1901), p. 26] *VFR (22 Dec 1765; 21 Apr 1825) He proposed the first general method of integrating partial differential equations of the first order. Pfaff did important work on special functions and the theory of series. He developed Taylor's Theorem using the form with remainder as given by Lagrange. In 1810 he contributed to the solution of a problem due to Gauss concerning the ellipse of greatest area which could be drawn inside a given quadrilateral. His most important work on Pfaffian forms was published in 1815 when he was nearly 50, but its importance was not recognised until 1827 when Jacobi published a paper on Pfaff's method. *TIS

1799 Nicholas Joseph Callan (22 Dec 1799; 10 Jan 1864) Irish pioneering scientist in electrical science, who invented the induction coil (1836) before that of better-known Heinrich Ruhmkorff. Callan's coil was built using a horseshoe shaped iron bar wound with a secondary coil of thin insulated wire under a separate winding of thick insulated wire as the "primary" coil. Each time a battery's current through the "primary" coil was interrupted, a high voltage current was produced in the electrically separate "secondary" coil. By 1837, Callan used a clock mechanism to rock a wire in and out of a small cup of mercury to interrupt the circuit 20 times/sec on a giant induction machine, producing 15-inch sparks (estimated at 600,000 volts)*TIS

1819  Pierre-Ossian Bonnet whose favorite ﬁeld was differential geometry, a ﬁeld opened by Euler, Monge, and Gauss, but lacking systematic treatment when Bonnet took it up in the 1840s. *VFR

1824 Francesco Brioschi (22 Dec 1824 in Milan, Lombardo-Veneto (now Italy)- 14 Dec 1897 in Milan, Italy) a professor at Pavia who contributed to the study of mathematical physics.*SAU

1859 Otto Ludwig Hölder (22 Dec 1859 in Stuttgart, Germany - 29 Aug 1937 in Leipzig, Germany) worked on the convergence of Fourier series and in 1884 he discovered the inequality now named after him. He became interested in group theory through Kronecker and Klein and proved the uniqueness of the factor groups in a composition series.*SAU

1859 Enrico Barone (22 Dec 1859; 14 May 1924) Italian mathematical economist who built on the general equilibrium theory of Léon Walras and was instrumental in convincing Walras to incorporate variable production techniques - and, by extension, marginal productivity theory - into the Walras theory. Barone's greatest contribution was in getting the "Socialist Calculation" debate started with his famous 1908 article. His position was that it was indeed possible in a collectivist state for a planning agency to calculate prices for maximum efficiency. He was the first to apply indifference curve analysis to compare the relative burdens of income taxes and excise taxes (1912). He opposed "progressive" taxation schemes as based on dubious utilitarian calculations.*TIS

1887 Srinivasa Ramanujan (22 Dec 1887; 26 Apr 1920) Indian mathematician known for his work on hypergeometric series and continued fractions. In number theory, he discovered properties of the partition function. Although self-taught, he was one of India's greatest mathematical geniuses. He worked on elliptic functions, continued fractions, and infinite series. His remarkable familiarity with numbers, was shown by the following incident. While Ramanujan was in hospital in England, his Cambridge professor, G. H. Hardy, visited and remarked that he had taken taxi number 1729, a singularly unexceptional number. Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=13+123=93+103. *TIS Ramanujan's recognition of 1729 could be partly due to his studying examples of numbers such that $a^3 + b^3 = c^3 + 1$His papers had several examples of them.

1897 Vojtěch Jarník ( 22 Dec 1897 in Prague, Bohemia (now Czech Republic) - 22 Sept 1970 in Prague, Czechoslovakia) was a Czech mathematician.
His main area of work was in number theory and mathematical analysis; he proved a number of results on lattice point problems. He also developed the graph theory algorithm known as Prim's algorithm.
The Vojtěch Jarník International Mathematical Competition, held each year in Ostrava, is named in his honor.*Wik

1898 Vladimir Aleksandrovich Fock​ (December 22, 1898 – December 27, 1974) was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics.*Wik

1936 James Burke (22 December 1936, ) is a British broadcaster, science historian, author and television producer known amongst other things for his documentary television series Connections (1978) and its more philosophical oriented companion production, The Day the Universe Changed (1985), focusing on the history of science and technology leavened with a sense of humour. The Washington Post​ has called him "one of the most intriguing minds in the Western world".*Wik

1937 Arthur Jaffe (December 22, 1937, ) is an American mathematical physicist and a professor at Harvard University. He attended Princeton University as an undergraduate obtaining a degree in chemistry, and later Clare College, Cambridge, as a Marshall Scholar, obtaining a degree in mathematics. He then returned to Princeton, obtaining a doctorate in physics.
With James Glimm, he founded the subject called constructive quantum field theory. One of their major achievements was to show the mathematical compatibility of quantum theory, special relativity, and interaction. They did this by proving the existence of the first examples of non-linear, relativistic quantum fields with non-trivial scattering. Jaffe's work in several related fields of mathematics and physics is well-known, including contributions to gauge theory and to non-commutative geometry.
For several years Jaffe was president of the International Association of Mathematical Physics, and later of the American Mathematical Society. He chaired the Council of Scientific Society Presidents.
Jaffe conceived the idea of the Clay Mathematics Institute and its programs, including the employment of research fellows and the Millennium Prizes in mathematics. The latter immediately captured public imagination worldwide. He served as a founding Member, a founding member of the Board, and the founding President of that organization.
Currently Jaffe teaches Mathematical Physics and pursues research at Harvard University. His doctoral students include Joel Feldman, Ezra Getzler, and Clifford Taubes. *Wik

DEATHS

1640 Jean Beaugrand (about 1590 in Paris, France - 22 Dec 1640 in Paris, France) was a French mathematician who published works on Geostatics as well as mathematics. *SAU

1660 André Tacquet (23 June 1612 Antwerp – 22 December 1660 Antwerp, also referred to by his Latinized name Andrea Tacquet[) was a Flemish mathematician and Jesuit Priest. His work prepared ground for the eventual discovery of the calculus.
He was born in Antwerp, and entered the Jesuit Order in 1629. From 1631 to 1635, he studied mathematics, physics and logic at Leuven. Two of his teachers were Saint-Vincent and Francois d'Aguilon.
Tacquet became a brilliant mathematician of international fame and his works were often reprinted and translated (into Italian and English). He helped articulate some of the preliminary concepts necessary for Isaac Newton and Gottfried Leibniz to recognize the inverse nature of the quadrature and the tangent. He was one of the precursors of the infinitesimal calculus, developed by John Wallis. His most famous work, which influenced the thinking of Blaise Pascal and his contemporaries, is Cylindricorum et annularium (1651). In this book Tacquet presented how a moving point could generate a curve and the theories of area and volume. *Wik

1693 Elisabetha Koopman (17 Jan 1647 in Danzig, now Gdańsk, Poland - 22 Dec 1693 in Danzig, now Gdańsk, Poland) was the wife of the Polish astronomer Johannes Hevelius and helped him with his observations.*SAU

1828 William Hyde Wollaston (6 Aug 1766, 22 Dec 1828) English scientist who discovered palladium (1803) and rhodium (1804), during his investigation of platinum ore. He developed a method of forming platinum - powder-metallurgy - and was the first to produce malleable and ductile platinum on a commercial scale. He made his method public at the Royal Society on 28 Nov 1828, shortly before his death. In 1801 he proved experimentally that frictional and current electricity are the same. He is particularly noted for being the first to observe dark lines in the spectrum of the sun which eventually led to the discovery of the elements in the Sun. He constructed the Wollaston prism, a polarizing beam splitter (now applied in the CD player), and invented the camera lucida. *TIS

1867 Jean-Victor Poncelet (1 Jul 1788, 22 Dec 1867). French mathematician and engineer whose study of the pole and polar lines associated with conic led to the principle of duality. While serving as an engineer in Napoleon's 1812 Russian campaign, he was left for dead at Krasnoy, but then captured. During his imprisonment he studied projective geometry and wrote a treatise on analytic geometry. Released in 1814, he returned to France, and in 1822 published Traité des propriétés projectives des figures in which he presented his fundamental ideas of projective geometry such as the cross-ratio, perspective, involution and the circular points at infinity. As a professor of mechanics (1825-35), he applied mechanics to improve waterwheels and was able to double their efficiency. *TIS

1928 Henry Burchard Fine born in Chambersburg, Pennsylvania. After earning his Ph.D. in Germany he joined the Princeton faculty. He is responsible for building that department into a world class mathematics department. The mathematics building at Princeton is named in his honor.*VFR (Fine Hall is the tallest building on the campus) He was president of the American Mathematical Society in 1911-12.Fine wrote:

Euclid's Elements (1891)
The Number System of Algebra (1891; second edition, 1903) PDF/DjVu copy from Internet Archive.
A College Algebra (1904)
Coördinate Geometry, with Henry Dallas Thompson (1909) PDF Copy from University of Michigan Historical Math Collection.
Calculus (1927)
*Wik

1955 Jules-Émile Verschaffelt (27 January 1870, Ghent – 22 December 1955) was a Belgian physicist. He worked at Kamerlingh Onnes’s laboratory in Leiden from 1894 to 1906 and once again from 1914 to 1923. From 1906 to 1914 he worked at the Vrije Universiteit Brussel and from 1923 to 1940 at the Ghent University. *Wik

1994 John Arthur Todd FRS (23 August 1908 – 22 December 1994) was a British geometer. He was born in Liverpool, and went to Trinity College of the University of Cambridge in 1925. He did research under H.F. Baker, and in 1931 took a position at the University of Manchester. He became a lecturer at Cambridge in 1937. He remained at Cambridge for the rest of his working life.[2]
The Todd class in the theory of the higher-dimensional Riemann–Roch theorem is an example of a characteristic class (or, more accurately, a reciprocal of one) that was discovered by Todd in work published in 1937. It used the methods of the Italian school of algebraic geometry. The Todd–Coxeter process for coset enumeration is a major method of computational algebra, and dates from a collaboration with H.S.M. Coxeter in 1936. In 1953 he and Coxeter discovered the Coxeter–Todd lattice. In 1954 he and G. C. Shephard classified the finite complex reflection groups.
In March 1948 he was elected a Fellow of the Royal Society. *Wik

2001 Luís Antoni Santaló Sors (October 9, 1911 – November 22, 2001) was a Spanish mathematician.
He graduated from the University of Madrid and he studied at the University of Hamburg, where he received his Ph.D. in 1936. His advisor was Wilhelm Blaschke. Because of the Spanish Civil War, he moved to Argentina where he became a very famous mathematician.
He studied integral geometry and many other topics of mathematics and science.
He worked as a teacher in the National University of the Littoral, National University of La Plata and University of Buenos Aires. *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