Saturday, 16 December 2017

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 350th day of the year; 350 is S(7,4), a Stirling Number of the second kind.

3502+1 = 122,501 is prime. The last day of the year for which n2 + 1 is prime.

Lucky Sevens, 350 = 73 + 7

Both 350 and 351 are the product of four primes. 350 = 2x5x5x7 and 351 = 3x3x3x13. They are the third, and last pair of consecutive year days that are the product of four primes. (Don't just sit there, find the others!")


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

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

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

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


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.

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.)

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

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

Friday, 15 December 2017

On This Day in Math - December 15

The reason why new concepts in any branch of science are hard to grasp is always the same; contemporary scientists try to picture the new concept in terms of ideas which existed before.
~Freeman Dyson

The 349th day of the year; 349 is a prime, and the sum of three consecutive primes.

349 is the last day-number of the year that will be a member of a twin prime.

349 is also the largest day-number that is a prime such that p- product of its digits and p+product of its digits are both also prime; for 349, 349 + 3*4*9 = 457 and 349 - 3*4*9 = 241.. and 349, 457 and 241 are all prime. *Ben Vitale


1610 Father Christoph Clavius SJ writes Galileo to ask about why his large aperture was partly covered; Galileo would answer on the 30th that he did this for two reasons:
The first is to make it possible to work it more accurately because a large surface is
more easily kept in the proper shape than a smaller one. The other reason is that if
one wants to see a larger space in one glance, the glass can be uncovered, but it is then
necessary to put a less acute glass near the eye and shorten the tube, otherwise the
objects will appear very fuzzy. *Aalbert Vvan Helden, Galileo and the Telescope; Origins of the Telescope - Royal Netherlands Academy of Arts and Sciences, 2010

In 1612, Simon Marius, namer of Jupiter's 4 inner satellites, is first to observe Andromeda galaxy through a telescope. He described it in the preface to his Mundus Jovialis as, 'like the flame of a candle seen through horn'. Marius vrs Galileo is well covered in this blog at the Renaissance Mathematicus  .

1693 The House of Commons established the British National Debt by issuing one-million GBP of annuities. *Against the Gods: The Remarkable Story of Risk By Peter L. Bernstein

1742 Euler gave the first clear statement of the fundamental theorem of algebra: every algebraic equation of degree n has exactly n complex roots. Imprecise statements of the result were given earlier by Peter Rothe (1608) and Albert Girard (1629). Incorrect proofs were given by d’Alembert (1746), Euler (1749), Foncenex (1759), Lagrange (1772) and Laplace (1795), but a correct proof (and the name) had to await Gauss’s doctoral dissertation of 1799, who discovered it in the fall of 1797 when he was 20. * E. Smith, Source Book, p. 292

1859 Gustav R. Kirchhoff distillated from the sun spectra which elements are present in the sun. *SOLAR ECLIPSE NEWSLETTER

1887 Nature quotes J. J. Sylvester: “Perhaps I may, without immodesty, lay claim to the appellation of the mathematical Adam, as I believe that I have given more names (passed into general circulation) to the creatures of the mathematical reason than all the other mathematicians of the age combined.” [p. 162] *VFR (Among the many terms he created were matrix, discriminant, invariant, totient, and Jacobian)

1890 Karl Pearson is appointed Gresham Professor of Geometry. The first whose name is commonly known since Robert Hooke died in 1703. The terms “standard deviation” and “histogram” were first used in his lectures at Gresham College. *Gresham Geometry lecture by Robin Wilson, 2008

1896 Hollerith Agrees to Supply Machines for Russian Census:
Hollerith’s Census Machine was first employed by the U.S. Census Bureau in 1890 as the result of a crisis in counting a rapidly-increasing U.S. population. Methods based on Hollerith's machine served for almost 60 years until the Bureau adopted electron.*CHM (Image at Top, from

1928 To commemorate the International Congress of Medicine at Cairo, Egypt issued a postage stamp picturing Imhotep (c. 3000 BC). [Scott #153] *VFR

1965 Richard Feynman, having just won the Nobel Prize, makes a bet with CERN Director Viktor Weisskop that he will not hold a "responsible" position within the next ten years. A wager he will win. *Brain Pickings

1983 Grace Hopper was presented with the star to signify her promotion to Commodore (later Rear Admiral) by President Ronald Regan in a special White house ceremony. *WM

In 2001, the Leaning Tower of Pisa, Italy, was reopened to the public after a $27 million realignment that took over a decade. *TIS (sotto voce "But still, it leans!")


1732 Wenceslaus Johann Gustav Karsten (15 Dec 1732 in Neubrandenburg, Mecklenburg-Strelitz, Germany - 17 April 1787 in Halle, Germany) He wrote an important article in 1768 Von den Logarithmen vermeinter Grössen in which he discussed logarithms of negative and imaginary numbers, giving a geometric interpretation of logarithms of complex numbers as hyperbolic sectors, based on the similarity of the equations of the circle and of the equilateral hyperbola. *SAU

1802 János Bolyai (15 Dec 1802; 27 Jan 1860) Hungarian mathematician and one of the founders of non-Euclidean geometry - geometry that does not include Euclid's axiom that only one line can be drawn parallel to a given line through a point not on the given line. His father, Farkas Bolyai, had devoted his life to trying to prove Euclid's famous parallel postulate. Despite his father's warnings that it would ruin his health and peace of mind, János followed in working on this axiom until, in about 1820, he came to the conclusion that it could not be proved. He went on to develop a consistent geometry (published 1882) in which the parallel postulate is not used, thus establishing the independence of this axiom from the others. He also did valuable work in the theory of complex numbers. *TIS

1823 Mikhail Vasilyevich Ostrogradsky , (September 24, 1801 – January 1, 1862) was an Russian / Ukrainian mathematician, mechanician and physicist. Ostrogradsky is considered to be a disciple of Leonhard Euler and one of the leading mathematicians of Imperial Russia.
Ostrogradsky was born in Pashennaya, Poltava Governorate, Russian Empire (today Ukraine). From 1816 to 1820 he studied under Timofei Fedorovich Osipovsky (1765–1832) and graduated from the University of Kharkiv. When 1820 Osipovsky was suspended on religious grounds, Ostrogradsky refused to be examined and he never received his Doctor's degree. From 1822 to 1826 he studied at the Sorbonne and at the Collège de France in Paris, France. In 1828 he returned to the Russian Empire and settled in Saint Petersburg, where he was elected a member of the Academy of Sciences, Also he becomes the professor of the Main military engineering School of the Russian empire.
He worked mainly in the mathematical fields of calculus of variations, integration of algebraic functions, number theory, algebra, geometry, probability theory and in the fields of mathematical physics and classical mechanics. In the latter his most important work includes researches of the motion of an elastic body and the development of methods for integration of the equations of dynamics. Here he continued works of Euler, Joseph Louis Lagrange, Siméon-Denis Poisson and Augustin Louis Cauchy. His work in these fields was in Russia continued by Nikolay Dmitrievich Brashman (1796–1866), August Yulevich Davidov (1823–1885) and specially by the brilliant work of Nikolai Yegorovich Zhukovsky (1847–1921).
Ostrogradsky did not appreciate the work on non-Euclidean geometry of Nikolay Ivanovich Lobachevsky from 1823 and he rejected it, when it was submitted for publication in the Saint Petersburg Academy of Sciences.*Wik

1827 Samuel Roberts FRS (15 December 1827, Horncastle, Lincolnshire – 18 September 1913, London) was a British mathematician.
Roberts studied at Queen Elizabeth's Grammar School, Horncastle. He matriculated in 1845 at the University of London, where he earned in 1847 his bachelor's degree in mathematics and in 1849 his master's degree in mathematics and physics, as first in his class. Next he studied law and became a solicitor in 1853. After a few years of law practice he abandoned his law career and returned to mathematics, although he never had an academic position. He had his first mathematical paper published in 1848. In 1865 he was an important participant in the founding of the London Mathematical Society (LMS). From 1866 to 1892 he acted as legal counsel for LMS, from 1872 to 1880 he was the organization's treasurer, and from 1880 to 1882 its president. In 1896 he received the De Morgan Medal of the LMS. In 1878 he was elected FRS.
Roberts published papers in several fields of mathematics, including geometry, interpolation theory, and Diophantine equations.
Roberts and Pafnuty Chebyschev are jointly credited with the Roberts-Chebyshev theorem related to four-bar linkages *Wik

1834 Charles Augustus Young (15 Dec 1834; 3 Jan 1908) American astronomer who made the first observations of the flash spectrum of the Sun, proved the gaseous nature of the sun's corona and discovered the reversing layer of the solar atmosphere. 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." 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. *TIS

1847 Achille Marie Gaston Floquet (December 15, 1847, Épinal–October 7, 1920, Nancy) was a French mathematician, best known for his work in mathematical analysis, especially in theory of differential equations.*Wik

1852 Antoine-Henri Becquerel (15 Dec 1852; 25 Aug 1908) was a French physicist who discovered radioactivity. In 1903 he shared the Nobel Prize for Physics with Pierre and Marie Curie. His early researches were in optics, then in 1896 he accidentally discovered radioactivity in fluorescent salts of uranium. He left some uranium mineral crystals in a drawer on a plate in black paper. Later, he developed the plate and found it was fogged, even though the crystals without ultraviolet radiation from sunlight were not fluorescing. Thus the salt was a source of a penetrating radiation. Three years afterwards he showed that it consists of charged particles that are deflected by a magnetic field. Initially, the rays emitted by radioactive substances were named after him. *TIS

1912 Reuben Louis Goodstein (15 December 1912 in London – 8 March 1985 in Leicester) was an English mathematician with a strong interest in the philosophy and teaching of mathematics. He earned his PhD from the University of London in 1946 while still working in Reading. Goodstein also studied under Wittgenstein and John Littlewood.
He published many works on finitism and the reconstruction of analysis from a finitistic viewpoint, for example "Constructive Formalism. Essays on the foundations of mathematics." Goodstein's theorem was among the earliest examples of theorems found to be unprovable in Peano arithmetic but provable in stronger logical systems (such as second order arithmetic). He also introduced a variant of the Ackermann function that is now known as the hyperoperation sequence, together with the naming convention now used for these operations (tetration, pentation, etc.).*Wik

1912 Emil Grosswald (December 15, 1912 – April 11, 1989) was a Romanian-American mathematician who worked primarily in number theory. His career is closely associated with that of his teacher, Hans Rademacher. *Wik

1916 Maurice Hugh Frederick Wilkins (15 Dec 1916; 5 Oct 2004) was a New Zealand-born British biophysicist, whose X-ray diffraction studies of deoxyribonucleic acid (DNA) were significant in the determination of the molecular structure of DNA accomplished by James Watson and Sir Francis Crick. For this work the three scientists shared the 1962 Nobel Prize for Physiology or Medicine. *TIS

1923 Freeman (John) Dyson (15 Dec 1923, ) is an English-born American physicist and educator best known for his speculative work on extraterrestrial civilizations. As an imaginative scientist he proposed that a highly advanced technological civilization would ultimately completely surround its host star with a huge shell to capture 100% of the useful radiant energy. This "Dyson shell", would have a gigantic cluster of artificial planetoids ("Dyson cloud") with billions of billions of inhabitants who would make use of the energy captured by the Dyson shell. He also made the intriguing speculation that a Dyson shell viewed from other galaxies would have a highly distinctive, unnatural light. He suggests astronomers search for such tell-tale colored stars, which should signify advanced, intelligent life. *TIS (One of Dyson's earliest memories of his calculating power was at a time when he was still being put down for naps. He set about summing the fractions 1+1/2 + 1/4 ... and realized that they added up to two. At a time when most of us were still trying to figure out what fractions were, Dyson summed an infinite converging sequence.)
I came across another beautiful anecdote about Dyson's incredible mental computational ability on the Math Frolic blog Posted by "Shecky Riemann":
Freeman Dyson sitting around a table with a bunch of scientists where the question arises, is there an integer such that by moving the last digit to the front (say 1234 to 4123) you can arrive at a result such that the new integer is exactly double the value of the original integer? In a matter of seconds, Dyson essentially responds (to a stunned group), “Oh, that’s not difficult, but of course the smallest such number is 18 digits long.” AND, he was right!


1921 Leo Königsberger (15 October 1837 – 15 December 1921) was a German mathematician, and historian of science. He is best known for his three-volume biography of Hermann von Helmholtz, which remains the standard reference on the subject.
The biography of Helmholtz was published in 1902 and 1903. He also wrote a biography of C. G. J. Jacobi.
Königsberger's own research was primarily on elliptic functions and differential equations. He worked closely with Lazarus Fuchs, a childhood friend. *Wik

1958 Wolfgang Pauli (25 Apr 1900, 15 Dec 1958) Austrian-born American winner of the Nobel Prize for Physics in 1945 for his discovery in 1925 of the Pauli exclusion principle, which states that in an atom no two electrons can occupy the same quantum state simultaneously. This principle clearly relates the quantum theory to the observed properties of atoms. *TIS

1970 Sir Ernest Marsden (19 Feb 1889, 15 Dec 1970) British-born New Zealand nuclear physicist who worked under Ernest Rutherford investigating atomic structure with Hans Geiger. Marsden visually counted scintillations from alpha particles after passing through gold foil and striking a phosphorescent screen. That some of these were observed scattered at surprisingly large angles led to Rutherford's theory of the nucleus as the massive, tiny centre of the atom. Later, Marsden's own experiments, working in New Zealand, hinted suggested transmutation of elements was possible when alpha particles bombarding nitrogen nuclei produced scattered particles of greater speed than the original radiation. *TIS

1970 Theodore Samuel Motzkin (26 March 1908–15 December 1970) was an Israeli-American mathematician. Motzkin received his Ph.D. in 1934 from the University of Basel under the supervision of Alexander Ostrowski.
He was appointed at UCLA in 1950 and worked there until retirement.
The Motzkin transposition theorem, Motzkin numbers and the Fourier–Motzkin elimination are named after him. Motzkin first developed the "double description" algorithm of polyhedral combinatorics and computational geometry.[3] He was the first to prove the existence of principal ideal domains that are not Euclidean domains.
The quote "complete disorder is impossible," describing Ramsey theory is attributed to him. *Wik

1971 Paul Pierre Lévy (15 Sep 1886, 15 Dec 1971) was a French mining engineer and mathematician. He contributed to probability, functional analysis, partial differential equations and series. He also studied geometry. In 1926 he extended Laplace transforms to broader function classes. He undertook a large-scale work on generalized differential equations in functional derivatives. *TIS

2000 George Eric Deacon Alcock (August 28, 1912 – December 15, 2000)
George Alcock was an English astronomer. He was one of the most successful visual discoverers of novae and comets. He was also a very good (probably under-respected) teacher of the 4th year at Southfields Junior School in Stanground, Peterborough. In 1953 he decided to start searching for comets and in 1955 began searching for novae. His technique was to memorize the patterns of thousands of stars, so that he would visually recognize any intruder.
In 1959 he discovered comet C/1959 Q1 (Alcock), the first comet discovered in Britain since 1894, and only five days later discovered another, C/1959 Q2 (Alcock). He discovered two more comets in 1963 and 1965. He later discovered his first nova, Nova Delphini 1967 (HR Delphini), which turned out to have an unusual light curve. He discovered two more novas, LV Vul (in 1968) and V368 Sct (in 1970). He found his fifth and final comet in 1983: C/1983 H1 (IRAS-Araki-Alcock). In 1991 he found the nova V838 Her.
Alcock won the Jackson-Gwilt Medal of the Royal Astronomical Society in 1963 and Amateur Achievement Award of the Astronomical Society of the Pacific in 1981. After his death, a plaque was placed in Peterborough Cathedral in his memory. *TIA

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

Thursday, 14 December 2017

On This Day in Math - December 14

Those who study the stars have God for a teacher.
~Tycho Brahe

The 348th day of the year; 348 is the sum of four consecutive primes. It is the last day of the year that is of such distinction.

348 is the smallest number whose fifth power contains exactly the same digits as another fifth power... find it.


1498 Luca Pacioli was professor in Milan 1496-1499. 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 . The period in Milan was the high point of his career, being a leading member of the glittering intellectual court of Lodovico Sforza. He lived at the monastery of San Simpliciano, writing his Divina Proportione, and De Viribus Quantitatis here . He was a good friend of LEONARDO DA VINCI who drew the pictures for Pacioli's book. Pacioli is our leading witness to Leonardo's work at this time, particularly the Last Supper in the Refectory of the Monastery of Santa Maria delle Grazie during 1495 1497, and he may well have advised on the perspective of the painting. 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. *VFR
The first known printing of the Rhombicubeoctahedron, an Archimedian Solid with 26 faces, was Leonardo da Vinci's drawing in Divina Proportione

In 1807, the first meteorite strike to be recorded in the U.S. fell at Weston (now called Easton), Conn., at 6:30 a.m., making a hole 5-ft long and 4.5-ft wide. This was the New World's first witnessed fall of a meteorite, with subsequent recovery of specimens, since the arrival of the European settlers. Yale Professor Benjamin Silliman's description of the fall and his chemical analysis of the stone meteorite, the first performed in the U.S., received much attention in the national and international press. A thirty-pound fragment of this Chondrite H4 became the nucleus of Yale University’s Peabody Museum. This meteorite collection, the oldest in the country, was begun by Silliman.*TIS

1844 Grassman had sent a copy of his book to Gauss who replied that a) I already did that fifty years ago, and b) I didn’t actually read it because I’m very busy and the terminology is difficult. Michael Cro. we described Grassmann’s book, “Grassmann’s Die lineale Ausdehnungslehre (Linear Extension Theory) demonstrated deep mathematical insights. It also in one sense contained much of the modern system of vector analysis. This, however, was embedded within a far broader system, which included n-dimensional spaces and as many as sixteen different products of his base entities (including his inner and outer products, which are respectively somewhat close to the our modern dot and cross products). Moreover, Grassmann justifies his system by philosophical discussions that may have put off many of his readers.” *A history of vector analysis: the evolution of the idea of a vectorial system, By Michael J. Crowe pg 78

1893 The American, Dorothea Klumpke defended her thesis on Saturn’s rings for a doctorate in mathematics at the Sorbonne, before an expectant gathering of professors and several hundred spectators. “Your thesis,” said one of the examining professors during the awards ceremony, “is the first which a woman has presented and successfully sustained with our faculty to obtain this degree. You worthily open the way.” Indeed she did, for she became a distinguished astronomer. *Sky & Telescope, August 1986, pp. 109–110. Reprinted in AWM Newsletter, 17, no. 5, p. 12-13.

In 1900, German physicist Max Planck made public his ideas on quantum physics at a meeting of the German Physics Society, revolutionizing scientists' understanding of physics. Planck demonstrated that in certain situations energy exhibits characteristics of physical matter, something unthinkable at the time. He suggested the explanation energy exists in discrete packets, which he called "quanta."*TIS

1911 “So we arrived and were able to plant our flag at the geographical South Pole. God be thanked!” From the diary of the Norwegian explorer, Roald Amundsen, the first person to reach the South Pole. He was accompanied by four companions and fifty-two sled dogs. *VFR

In 1933, Rutherford suggested the names diplogen for the newly discovered heavy hydrogen isotope and diplon for its nucleus. He presented these ideas in the Discussion on Heavy Hydrogen at the Royal Society. For ordinary hydrogen, the lightest of the atoms, having a nuclues of a sole proton, he coined a related name: haplogen. (Greek: haploos, single; diploos, double.) In 1931, Harold Urey had discovered small quantities of atoms of heavy hydrogen wherever ordinary hydrogen occurred. The mass of its nucleus was double that of ordinary hydrogen. This hydrogen-2 is now called deuterium, as named by Urey (Greek: deuteros, second). Its nucleus, named a deuteron, has a neutron in addition to a proton. *TIS

1946 Denmark issued a stamp commemorating the 400th anniversary of the birth of the mathematician and astronomer Tycho Brahe. [Scott #300]. (TOP)*VFR

1981 The New Yorker carried a long interview with Marvin Minsky, tracing his biography and the development of artificial intelligence. [Mathematics Magazine 55(1982), p. 245]. *VFR

1952 U.S. Navy Approaches MIT to create Whirlwind
U.S. Navy issues a formal Letter of Intent to MIT for development of the Airplane Stability and Control Analyzer (ASCA) program, the beginning of the project Whirlwind. Constructed under the leadership of Jay. W. Forrester, the Whirlwind was the first high-speed electronic digital computer that was able to operate in real time with the remarkable electronic reliability. By December 1954, the computer comprised 12,500 vacuum tubes and 23,800 crystal diodes, occupying a two-story building. It operated until 1959.
Whirlwind served as an experimental prototype for the IBM’s AN/FSQ-7 manufactured for the SAGE air defense system, and influenced the early IBM 700 series computers and computers developed by Digital Equipment Corporation. *CHM

In 1967, the first synthesis of biologically active DNA in a test tube was announced at a press conference by Arthur Kornberg who had worked with Mehran Goulian at Stanford and Robert L. Sinsheimer of MIT. Kornberg chose to replicate the relatively simple DNA chain of the Phi X174 virus, which infects bacteria (a bacteriophage). It has a single strand of DNA only about 5500 nucleotide building blocks long, and with about 11 genes, it was easier to purify without breaking it up. Having isolated the Phi X174 DNA, they used the DNA from E. coli, a common bacterium in the human intestine that could copy a DNA template from any organism. The viral DNA template thus copied was found to be able to infect bacteria - it was error-free, active DNA. *TIS

2009 On 14 December 2009, the Orient Express ceased to operate and the route disappeared from European railway timetables, reportedly a "victim of high-speed trains and cut-rate airlines" *Wik

2014. The annual Geminids meteor shower will reach its peak late on Saturday night and into early sunday morning.
The meteors will appear to radiate from a point near the star Castor, in the constellation Gemini.
In the Northern hemisphere, that will be westward and nearly overhead in the early hours of Sunday. *BBC News


1503 The astrologer Nostradamus is born. [Muller] *VFR

1546 Tycho Brahe (14 Dec 1546; 24 Oct 1601) Danish astronomer whose work in developing astronomical instruments and in measuring and fixing the positions of stars paved the way for future discoveries. He studied the nova of 1572 ("Tycho's star") showed that it was a fixed star. His report, De nova...stella (1573), was taken by many as proof of the inadequacy of the traditional Aristotelian cosmology. In 1577, he moved to his own observatory on Hven Island (financed by King Frederick II). Before the invention of the telescope, using his nine-foot armillary sphere and his fourteen-foot mural quadrant, he charted the positions of 777 stars with an unparallelled accuracy. In 1599 he moved to Prague, with Johannes Kepler as his assistant. *TIS

1760 The Very Reverend James Wood (14 December 1760 – 23 April 1839) was a mathematician, Dean of Ely and Master of St John's College, Cambridge.
Wood was born in Holcombe where his father ran an evening school and taught his son the elements of arithmetic and algebra. From Bury Grammar School he proceeded to St John's College, Cambridge in 1778, graduating as senior wrangler in 1782. On graduating he became a fellow of the college and in his long tenure there produced several successful academic textbooks for students of mathematics. (The Elements of Algebra (1795); The Principles of Mechanics (1796); The Elements of Optics (1798))
Wood remained for sixty years at St. John's, serving as both President (1802–1815) and Master (1815–1839); on his death in 1839 he was interred in the college chapel and bequeathed his extensive library to the college, comprising almost 4,500 printed books on classics, history, mathematics, theology and travel, dating from the 17th to the 19th centuries.[3]
Wood was also ordained as a priest in 1787 and served as Dean of Ely from 1820 until his death.{He was succeeded by another eminent mathematician, George Peacock)*Wik

1904 Nikolai Grigor'evich Chudakov (1904–1986) was a Russian and Soviet mathematician. He was born in Lysovsk, Novo-Burassk, Saratov, Russian Empire. His father worked as a medical assistant.
He first studied at the Faculty of Physics and Mathematics at Saratov State University, but then he transferred to Moscow University. He then graduated in 1927. In 1930, he was named head of higher mathematics at Saratov University. In 1936, he successfully defended his thesis and became a Doctor of Science. Among others, he considerably improved a result from Guido Hoheisel and Hans Heilbronn on an upper bound for prime gaps. *Wik

1914 Solomon Spiegelman (14 Dec 1914; 21 Jan 1983) American microbiologist and geneticist who discovered that only one of two strands of molecules that make up DNA, carried the genetic information to produce new substances. The carrier was called ribonucleic acid (RNA). In 1962, he developed a technique that allowed the detection of specific RNA and DNA molecules in cells. This technique, called nucleic acid hybridization, is credited for helping to lay the groundwork for current advances in recombinant DNA technology. Much earlier, his Ph.D. thesis (1944) was the first work to establish that genes are activated and deactivated by compounds that he called inducers, which thus radically affect the pattern of proteins that a cell fabricates without actually altering the genes themselves. *TIS

1922 Nikolay Gennadiyevich Basov (14 Dec 1922, )Soviet physicist, best known for the development of the maser, the precursor of the laser. In 1955, while working as a research student with Aleksandr Prokhorov (1916- ) at the Soviet Academy of Sciences, he devised a microwave amplifier based on ammonia molecules. The two scientists shared the 1964 Nobel Prize (with American Charles Townes (1915- ), who independently developed a maser), for basic research in quantum electronics that led to the development of both the maser and the laser. These devices produce monochromatic, parallel, coherent beams of microwaves and light, respectively. Basov went on to develop the laser principle, and introduced the idea of using semiconductors to achieve laser action (1958). *TIS

1936 Charles Terence Clegg ("Terry") Wall (born 14 December 1936 in Bristol, England) is a leading British mathematician, educated at Marlborough and Trinity College, Cambridge. He is an emeritus professor of the University of Liverpool, where he was first appointed Professor in 1965. From 1978 to 1980 he was the President of the London Mathematical Society.
His early work was in cobordism theory in algebraic topology; this includes his 1959 Cambridge Ph.D thesis entitled "Algebraic aspects of cobordism", written under the direction of Frank Adams and Christopher Zeeman. His research was then mainly in the area of manifolds, particularly geometric topology and related abstract algebra included in surgery theory, of which he was one of the founders. His 1970 research monograph "Surgery on Compact Manifolds" is a major reference work in geometric topology.
In 1971 he conjectured that every finitely generated group is accessible. This conjecture is known as "Wall's conjecture". It motivated much progress in the understanding of splittings of groups. In 1985 Martin J. Dunwoody proved the conjecture for the class of finitely presented groups. The resolution of the full conjecture took until 1991 when, surprising to most mathematicians at the time, Dunwoody found a finitely generated group that is not accessible and hence the conjecture turned out to be not correct in its general formulation.
C.T.C Wall's work since the mid-1970s has mostly been in singularity theory as developed by R. Thom, J. Milnor and V. Arnold, and especially concerns the classification of isolated singularities of differentiable maps and of algebraic varieties. He has written two research monographs on singularity theory, "The Geometry of Topological Stability" (1989) (containing a great deal of original work) with Andrew du Plessis, and "Singular Points of Plane Curves" (2004).*Wik


1710 Henry Aldrich (1647 – 14 December 1710) was an English theologian and philosopher.He had wide interests including mathematics, music, and architecture. He was well known as a humorist and Suttle describes him as".. a punner of the first value. "
In 1674 he published Elementa geometricae which led to him being described by his Christ Church colleagues as ".. a great mathematician of our house."
In 1691 he published Artis logicae compendium a treatise on logic which was to be the main text on the topic for 150 years in England. Even when Richard Whately published Elements of logic in 1826 it still took Aldrich's work as his starting point. *SAU

1897 Francesco Brioschi (22 December 1824 – 13 December 1897) was an Italian mathematician born in Milan in 1824. From 1850 he taught analytical mechanics in the University of Pavia. After the Italian unification in 1861, he was elected depute in the Parliament of Italy and then appointed twice secretary of the Education Minister. In 1863 he founded the Politecnico di Milano university, where he worked until death. In 1870 he became member of the National Academy of the Lincei and in 1884 he succeed Quintino Sella as president of the National Academy of the Lincei. He directed the Il Politecnico (English translation: The Polytechnic) review and, between 1867 and 1877, Annali di matematica pura e applicata (English translation: Annals of pure and applied mathematics). He died in Milan in 1897.
As mathematician, Brioschi publicized in Italy various algebraic theories and studied the problem of solving fifth and sixth grade equations using elliptic functions. Brioschi is also remembered as a distinguished teacher: among his students in the University of Pavia there were Eugenio Beltrami, Luigi Cremona and Felice Casorati.*Wik

1927 Yulian-Karl Vasilievich Sokhotsky (2 Feb 1842 in Warsaw, Poland - 14 Dec 1927 in Leningrad, USSR (now St Petersburg, Russia)) The magister's thesis of Sokhotskii was the first research paper on complex analysis published in Russian. It contains many important results which were later ascribed to other mathematicians. First of all, there is the famous theorem on the behaviour of an analytic function in a neighbourhood of an essential singularity. This theorem was published by Sokhotskii (in his magister's thesis) and by Casorati in 1868, whereas Weierstrass published it eight years later - in 1876. Furthermore, Sokhotskii was the first to apply the calculus of residues to Legendre polynomials. The credit for this procedure is usually given to Hermann Laurent. Finally, the so-called Plemelj formulas are also due to Sokhotskii, who published them in his doctor's thesis in 1873, that is to say 35 years before Plemelj. *SAU

1976 Donald H(oward) Menzel (11 Apr 1901, 14 Dec 1976) was an American astronomer best known for his arguments against the existance of extraterrestrial UFO's. Menzel was one of the first practitioners of theoretical astrophysics in the United States and pioneered the application of quantum mechanics to astronomical spectroscopy. An authority on the sun's chromosphere, he discovered with J. C. Boyce (1933) that the sun's corona contains oxygen. With W. W. Salisbury he made (1941) the first of the calculations that led to radio contact with the moon in 1946. He supervised the assignment of names to newly discovered lunar features. *TIS

1989 Andrey Dmitriyevich Sakharov (21 May 1921, 14 Dec 1989) Soviet nuclear physicist, an outspoken advocate of human rights in the Soviet Union. At the end of World War II, Sakharov returned to pure science and the study of cosmic rays. Two years later, he began work with a secret research group on the development of the hydrogen bomb, and he is believed to have been principally responsible for the Soviets' success in exploding their first thermonuclear bomb (1954). With I.E. Tamm, he proposed controlled thermonuclear fusion by confining an extremely hot ionized plasma in a torus-shaped magnetic bottle, known as a tokamak device. He became politically more active in the 1960s, campaigned against nuclear proliferation, and from 1980 to 1986, he was banished and kept under police surveillance.*TIS

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

Wednesday, 13 December 2017

On This Day in Math - December 13

Scottish Café (Polish: Kawiarnia Szkocka) in Lwów

Once a sage asked why scholars always flock to the doors of the rich, whilst the rich are not inclined to call at the doors of scholars. "The scholars" he answered, "are well aware of the use of money, but the rich are ignorant of the nobility of science".

The 347th day of the year; 347 is a safe prime, one more than twice a Sophie Germain Prime, 173. There is only one more safe prime this year.
And from Derek at @MathYearRound, "Adding 2 to any digit of 347 keeps it prime (547, 367 and 349 are prime)."

Derek's comment also points out that 347 is the smaller of a pair of twin primes. I just found out that, "(p, p+2) are twin primes if and only if p + 2 can be represented as the sum of two primes. Brun (1919)" (Brun showed that even if there are an infinity of prime pairs, the sum of their reciprocals converges.)

There are 347 even digits before the 347th odd digit of π. (How often is it true that after 2n digits of π there are n even and n odd digits?)


Not the Actual Aurora from 1128  ;-}
 1128 “In the third year of Lothar, emperor of the Romans, in the twenty-eighth year of King Henry of the English…on Saturday, 8 December, there appeared from the morning right up to the evening two black spheres against the sun.” This description of sunspots, and the earliest known drawing of sunspots, appears in John of Worcester’s Chronicle recorded in 1128. On the night of 13 December 1128, astronomers in Songdo, Korea, witnessed a red vapour that “soared and filled the sky” from the northwest to the southwest. A delay of five days is the average delay between the occurrence of a large sunspot group near the center of the Sun – exactly as witnessed by John of Worcester – and the appearance of the aurora borealis in the night sky at relatively low latitudes *Joe Hanson,

1883 Felix Klein notes in his references, "Received call to go to Baltimore. Great desire to go there -- at the least a new start." He had received an offer to replace J. J. Sylvester as the Professor of Mathematics at Johns Hopkins University in the form of a telegram from Danial Colt Gilman, President of the University. Klein's response contains two demands. The first is that he will not take less than the salary of the departing Sylvester, ($1000 a year more than the initial offer) and the second that his need for the economic security of his family should be somehow met (in Germany tenured positions included a pension that passed to the wife after the professor's death). Neither demand was met, and eventually Klein would go to Gottingen to develop his famous math institute. *Constance Reid, The Road Not Taken, Mathematical Intelligencer, 1978

1907 Emmy Noether received her Ph.D. degree, summa cum laude, from the University of Erlangen, for a dissertation on algebraic invariants directed by Paul Gordan. She went on to become the world’s greatest woman mathematician. [DSB 10, 137 and A. Dick, p. xiii] *VFR

In 1920, first U.S. measurement of the size of a fixed star was made on Betelgeuse, the bright red star in the right shoulder of Orion, which was found to be 260 million miles in diameter - 150 times greater than the Sun. Dr. Francis G. Pease made the measurement on the 100-inch telescope at the Mount Wilson Observatory using a beam interferometer designed by Professor A. A. Michelson. Betelgeuse was selected as the first test object since theoretical calculations had suggested that the star was unusually great in size. The apparent angular size of Betelgeuse was found to average about .044 arcseconds. Direct interferometer measurements can only be used with large stars. The majority of stars rely upon more indirect methods of determining stellar sizes. *TIS

1943 Croatia issued a pair of stamps to honor the Serbo-Croation mathematician and physicist Fr. Rugjer Boscovich (1711–1787). [Scott #59-60].*VFR

1957 Niels Bohr comes to Univ of Oklahoma for lecture on "Atoms and Human Knowledge." Jens Rud Nielsen, who joined the OU Physics Department in 1924, was an undergraduate student of Bohr in Denmark. Bohr, one of the founders of quantum mechanics, made two trips to the University of Oklahoma, first in 1937 and again in 1957. *U of Ok digital collection

1991 Stanford Linear Accelerator Center launches first Web site outside Europe
On December 13, 1991 the Stanford Linear Accelerator Center (SLAC) put up the first Web site outside Europe. It let physicists browse the full text of pre-publication scientific papers on SLAC's SPIRES database directly over the Web. This was a radical improvement over the old system, which involved submitting requests and waiting for fax or email versions to be sent back. As a vital service for the international physics community, the SLAC site became an important early step in helping the World Wide Web live up to its ambitious name *CHM


1724 Franz Maria Ulrich Theodor Hoch Aepinus (13 Dec 1724; 10 Aug 1802.)
Dutch physicist whose Tentamen theoriae electricitatis et magnetismi (1759; "An Attempt at a Theory of Electricity and Magnetism") was the first work to apply mathematics to the theory of electricity and magnetism. Aepinus' experiments led to the design of the parallel-plate capacitor, a device used to store energy in an electric field. He also discovered the electric properties of the mineral tourmaline and investigated pyroelectricity, the state of electrical polarization produced in tourmaline and various other crystals by a change of temperature. Other achievements of Aepinus include improvements to the microscope, and his demonstration of the effects of parallax in the transit of a planet across the Sun's disk (1764). *TIS

1753 William Nicholson (13 December 1753 – 21 May 1815) was a renowned English chemist and writer on "natural philosophy" and chemistry, as well as a translator, journalist, publisher, scientist, inventor, patent agent and civil engineer.
In 1797 he began to publish and contribute to the Journal of Natural Philosophy, Chemistry and the Arts, generally known as Nicholson's Journal, the earliest monthly scientific work of its kind in Great Britain— the publication continued until 1814. The journal included the first comprehensive descriptions of aerodynamics with George Cayley's "On Aerial Navigation", which inspired the Wright brothers a hundred years later. In May 1800 he with Anthony Carlisle discovered electrolysis, the decomposition of water into hydrogen and oxygen by voltaic current. The two were then appointed to a chemical investigation committee of the new Royal Institution. But his own interests shortly turned elsewhere.
Besides considerable contributions to the Philosophical Transactions, Nicholson wrote translations of Fourcroy's Chemistry (1787) and Chaptal's Chemistry (1788), First Principles of Chemistry (1788) and a Chemical Dictionary (1795); he also edited the British Encyclopaedia, or Dictionary of Arts and Sciences (6 vols., London, 1809).
Nicholson died in Bloomsbury at the age of 61 on 21 May 1815. *Wik

1759 John Hailstone (13 Dec, 1759– 9 June, 1847), English geologist, born near London, was placed at an early age under the care of a maternal uncle at York, and was sent to Beverley school in the East Riding. Samuel Hailstone was a younger brother. John went to Cambridge, entering first at Catharine Hall, and afterwards at Trinity College, and was second wrangler and second in the Smith Prize of his year (1782). He was second in both competitions to James Wood who became master of Saint Johns, and Dean of Ely. Hailstone was elected fellow of Trinity in 1784, and four years later became Woodwardian Professor of Geology, an office which he held for thirty years.
He went to Germany, and studied geology under Werner at Freiburg for about twelve months. On his return to Cambridge he devoted himself to the study and collection of geological specimens, but did not deliver any lectures. He published, however, in 1792, ‘A Plan of a course of lectures.’
He married, and retired to the vicarage of Trumpington, near Cambridge, in 1818, and worked zealously for the education of the poor of his parish. He devoted much attention to chemistry and mineralogy, as well as to his favourite science, and kept for many years a meteorological diary. He made additions to the Woodwardian Museum, and left manuscript journals of his travels at home and abroad, and much correspondence on geological subjects. He was elected to the Linnean Society in 1800, and to the Royal Society in 1801, and was one of the original members of the Geological Society. Hailstone contributed papers to the ‘Transactions of the Geological Society’ (1816, iii. 243–50), the ‘Transactions of the Cambridge Philosophical Society’ (1822, i. 453–8), and the British Association (Report, 1834, p. 569). He died at Trumpington in his eighty-eighth year. *Wik

1805 Johann von Lamont (13 Dec 1805; 6 Aug 1879) Scottish-born German astronomer noted for discovering (1852) that the magnetic field of the Earth fluctuates with a 10.3-year activity cycle, but does not correlate it with the period of the sunspot cycle. From 1 Aug 1840, Johann von Lamont (as director of the Royal Astronomical Observatory in Munich) started regular and permanent observations of the earth's magnetic field. In the 1850's he started making regional magnetic surveys in the kingdom of Bavaria, later extended to other states in south Germany, France, Holland, Belgium, Spain, Portugal, Prussia and Denmark. His central European maps with isolines of geomagnetic elements, reduced to 1854, were the first worldwide. *TIS

1887 George Pólya (13 Dec 1887 in Budapest, Hungary - 7 Sept 1985 in Palo Alto, California, USA) Pólya was arguably the most influential mathematician of the 20th century. His basic research contributions span complex analysis, mathematical physics, probability theory, geometry, and combinatorics. He was a teacher par excellence who maintained a strong interest in pedagogical matters throughout his long career. Before going to the United States Pólya had a draft of a book How to solve it written in German. He had to try four publishers before finding one to publish the English version in the United States but it sold over one million copies over the years and has been translated in 17 languages. Schoenfeld described its importance, "For mathematics education and the world of problem solving it marked a line of demarcation between two eras, problem solving before and after Pólya."
Pólya explained in How to solve it that to solve problems required the study of heuristic"The aim of heuristic is to study the methods and rules of discovery and invention .... Heuristic, as an adjective, means 'serving to discover'. ... its purpose is to discover the solution of the present problem. ... What is good education? Systematically giving opportunity to the student to discover things by himself."
He also gave the wise advice, "If you can't solve a problem, then there is an easier problem you can't solve: find it."
Pólya published further books on the art of solving mathematical problems. For example Mathematics and plausible reasoning (1954), and Mathematical discovery which was published in two volumes (1962, 1965).*SAU (The student or teacher who has not read any of these books should go immediately and read them.)

1908 Leon Bankoff (December 13, 1908, New York City, NY -February 16, 1997, Los Angeles, CA), was an American dentist and mathematician.
After a visit to the City College of New York, Bankoff studied dentistry at New York University. Later, he moved to Los Angeles, California, where he taught at the University of Southern California; while there, he completed his studies. He practiced over 60 years as a dentist in Beverly Hills. Many of his patients were celebrities.
Along with Bankoff's interest in dentistry were the piano and the guitar. He was fluent in Esperanto, created artistic sculptures, and was interested in the progressive development of computer technology. Above all, he was a specialist in the mathematical world and highly respected as an expert in the field of flat geometry. Since the 1940s, he lectured and published many articles as a co-author. Bankoff collaborated with Paul Erdős in a mathematics paper and therefore has an Erdős number 1.
From 1968 to 1981, Bankoff was the editor of the Problem Department of Pi Mu Epsilon Journals, where he was responsible for the publication of some 300 top problems in the area of plane geometry, particularly Morley's trisector theorem, and the arbelos of Archimedes. Among his discoveries with the arbelos was the Bankoff circle, which is equal in area to Archimedes' twin circles. Martin Gardner called Bankoff, “one of the most remarkable mathematicians I have been privileged to know.” *Wik

1910 Charles Alfred Coulson FRS (13 December 1910, Dudley, England – 7 January 1974, Oxford, England) was a British applied mathematician, theoretical chemist and religious author.
His major scientific work was as a pioneer of the application of the quantum theory of valency to problems of molecular structure, dynamics and reactivity. He shared his deep religious belief, as a Methodist lay preacher, with the general public in radio broadcasts, served on the World Council of Churches from 1962 to 1968 and was Chairman of Oxfam from 1965 to 1971.
Coulson was a Senior Lecturer in the Mathematics Department of University College, Dundee, which was administratively part of the University of St. Andrews from 1938 to 1945. He held a Fellowship at the University of Oxford from 1945 to 1947, when he took up the newly appointed Chair of Theoretical Physics at King's College London. He returned to Oxford in 1952 as Rouse Ball Professor of Mathematics and Fellow of Wadham College. He set up and directed the Mathematical Institute. In 1972 he was appointed to the newly created Chair of Theoretical Chemistry, which has since been named for him.
He was elected a Fellow of the Royal Society of Edinburgh in 1941 and a Fellow of the Royal Society of London in 1950. He was awarded the Davy Medal of the Royal Society in 1970, the Faraday and Tilden Medals of the Chemical Society in 1968 and 1969 respectively, and received a dozen honorary degrees from English and other universities. He was a member of the International Academy of Quantum Molecular Science.
In each of his successive appointments, Coulson attracted an active and enthusiastic group of graduate students, short and long term visitors, many of whom held senior university and industrial positions in England and other countries. Many of his students went on to make major contributions in several fields of endeavour.
Coulson was an excellent cricketer and chess player, a warm family man and had a strong sense of humour. He and Eileen were gracious hosts to his students and his associates. The conference in his honour at Brasenose College in 1967 had an impressive international attendance, despite the difficulty of organizing it during a postal strike. *Wik

1921 David Gale (December 13, 1921 – March 7, 2008) was a distinguished American mathematician and economist. He was a Professor Emeritus at University of California, Berkeley, affiliated with departments of Mathematics, Economics, and Industrial Engineering​ and Operations Research. He has contributed to the fields of mathematical economics, game theory, and convex analysis.*Wik

1923 Philip Warren Anderson (13 Dec 1923, ) is an American physicist who (with John H. Van Vleck and Sir Nevill F. Mott) received the 1977 Nobel Prize for Physics for his research on semiconductors, superconductivity, and magnetism. He made contributions to the study of solid-state physics, and research on molecular interactions has been facilitated by his work on the spectroscopy of gases. He conceived a model (known as the Anderson model) to describe what happens when an impurity atom is present in a metal. He also investigated magnetism and superconductivity, and his work is of fundamental importance for modern solid-state electronics, making possible the development of inexpensive electronic switching and memory devices in computers. *TIS


1048 Abu Arrayhan Muhammad ibn Ahmad al-Biruni (15 Sept 973 in Kath, Khwarazm (now Kara-Kalpakskaya, Uzbekistan) - 13 Dec 1048 in Ghazna (now Ghazni, Afganistan)) one of the major figures of Islamic mathematics. He contributed to astronomy, mathematics, physics, medicine and history. the mathematical contributions of al-Biruni. These include: theoretical and practical arithmetic, summation of series, combinatorial analysis, the rule of three, irrational numbers, ratio theory, algebraic definitions, method of solving algebraic equations, geometry, Archimedes' theorems, trisection of the angle and other problems which cannot be solved with ruler and compass alone, conic sections, stereometry, stereographic projection, trigonometry, the sine theorem in the plane, and solving spherical triangles.
Important contributions to geodesy and geography were also made by al-Biruni. He introduced techniques to measure the earth and distances on it using triangulation. He found the radius of the earth to be 6339.6 km, a value not obtained in the West until the 16th century (see [50]). His Masudic canon contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge. Not all, however, were measured by al-Biruni himself, some being taken from a similar table given by al-Khwarizmi. The author of [27] remarks that al-Biruni seemed to realize that for places given by both al-Khwarizmi and Ptolemy, the value obtained by al-Khwarizmi is the more accurate.
Al-Biruni also wrote a treatise on time-keeping, wrote several treatises on the astrolabe and describes a mechanical calendar. He makes interesting observations on the velocity of light, stating that its velocity is immense compared with that of sound. He also describes the Milky Way as, "... a collection of countless fragments of the nature of nebulous stars. "
Topics in physics that were studied by al-Biruni included hydrostatics and made very accurate measurements of specific weights. He described the ratios between the densities of gold, mercury, lead, silver, bronze, copper, brass, iron, and tin. Al-Biruni displayed the results as combinations of integers and numbers of the form 1/n, n = 2, 3, 4, ... , 10. *SAU

1557 Niccolò Fontana Tartaglia (1499, 13 Dec 1557) Italian mathematician who originated the science of ballistics. His proper name was Niccolo Fontana although he is always known by his nickname, Tartaglia, which means the "stammerer." When the French sacked Brescia in 1512, soldiers killed his father and left young Tartaglia for dead with a sabre wound that cut his jaw and palate. In 1535, by winning a competition to solve cubic equations, he gained fame as the discoverer of the formula for their algebraic solution (which was published in Cardan's Ars Magna, 1545) Tartaglia wrote Nova Scientia (1537) on the application of mathematics to artillery fire. He described new ballistic methods and instruments, including the first firing tables. He was the first Italian translator and publisher of Euclid's Elements (1543).*TIS

1565 Conrad Gessner (Konrad Gessner, Conrad Geßner, Conrad von Gesner, Conradus Gesnerus, Conrad Gesner; 26 March 1516 – 13 December 1565) was a Swiss naturalist and bibliographer. His five-volume Historiae animalium (1551–1558) is considered the beginning of modern zoology, and the flowering plant genus Gesneria (Gesneriaceae) is named after him. He is denoted by the author abbreviation Gesner when citing a botanical name. Gessner in 1551 was the first to describe adipose tissue; and in 1565 the first to document the pencil. *Wik See more at The Renaissance Mathematicus blog.

1603 Seigneur (lord) De La Bigotiere François Viète (1540, 13 Dec 1603) French mathematician who introduced the first systematic algebraic notation and contributed to the theory of equations. As Henry IV's cryptographer, he broke an elaborate cipher used by Spanish agents. In algebra, he made a number of innovations in the use of symbolism and several technical terms still in use (e.g., coefficient) were introduced by him. By using algebraic rather than geometric methods, Viète was able to solve a number of geometrical problems. In his In artem analyticam isagoge (1591) Viète introduced such basic algebraic conventions as using letters to represent both known and unknown quantities, while improving the notation for the expression of square and cubic numbers. *TIS

1870 William Chauvenet (24 May 1820, Milford, Pennsylvania - 13 December 1870, St. Paul, Minnesota) was an early American educator. A professor of mathematics, astronomy, navigation, and surveying, he was always known and well liked among students and faculty. In 1841 he was appointed a professor of mathematics in the United States Navy, and for a while served on Mississippi. A year later, he was appointed to the chair of mathematics at the naval asylum in Philadelphia, Pennsylvania. He was instrumental in the founding of the United States Naval Academy at Annapolis, Maryland. In 1859, he was offered a professorship at his alma mater at the same time he was offered a position at Washington University in St. Louis as professor of mathematics and astronomy. He chose St. Louis over New Haven and brought with him a deep love of music and a familiarity with the classics, in addition to being an outstanding figure in the world of science, noted by many historians as one of the foremost mathematical minds in the U.S. prior to the Civil War. It was Chauvenet who mathematically confirmed James B. Eads' plans for the first bridge to span the Mississippi River at St. Louis. The directors of the University chose him to be chancellor when his friend and Yale classmate Joseph Hoyt died in 1862. He came to his chancellorship in the midst of the Civil War in a state divided by the question of slavery.
Washington University went through a great period of growth during his chancellorship, adding dozens of professors, hundreds of students, and several new programs, including the establishment in 1867 of the law school. He served terms as vice president of the United States National Academy of Sciences and president of the American Association for the Advancement of Science, and was a member of both the American Philosophical Society and the American Academy of Arts and Sciences. After his death, the Mathematical Association of America established a prestigious prize in his honor, the Naval Academy named a mathematics building for him, and the U.S. Navy christened two ships Chauvenet.

1921 Max Noether (24 Sept 1844 in Mannheim, Baden, Germany - 13 Dec 1921 in Erlangen, Germany) was one of the leaders of nineteenth century algebraic geometry. Although himself a very distinguished mathematician, his daughter Emmy Noether was to bring greater innovation to mathematics than did her father.*SAU

1950 Abraham Wald (October 31, 1902 – December 13, 1950) was a mathematician born in Cluj, in the then Austria–Hungary (present-day Romania) who contributed to decision theory, geometry, and econometrics, and founded the field of statistical sequential analysis. He spent his researching years at Columbia University.Wald applied his statistical skills in World War II​ to the problem of bomber losses to enemy fire. A study had been made of the damage to returning aircraft and it had been proposed that armor be added to those areas that showed the most damage. Wald's unique insight was that the holes from flak and bullets on the bombers that returned represented the areas where they were able to take damage. The data showed that there were similar patches on each returning B-29 where there was no damage from enemy fire, leading Wald to conclude that these patches were weak spots and that they must be reinforced. *Wik

2004 David Wheeler, Inventor of the Closed Subroutine, Dies. Wheeler, born February 9, 1927, was Emeritus Professor of Computer Science at Cambridge University and a computer science pioneer. He worked on the original Cambridge EDSAC computer and wrote the first computer program to be stored in a computer’s memory. He pioneered the use of subroutines and data compression. He earned his Ph.D. in 1951 from Cambridge’s Computer Laboratory. (reputed to be the first Ph.D. in computer science) He spent time at the University of Illinois where he made contributions to the architecture of the ILLIAC system there. He later returned to the Cambridge Computer Laboratory and invented the Cambridge Ring and advanced methods of computer testing. He continued to work there until his death, a decade after he had officially retired. *CHM

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