## Sunday, 19 November 2017

### On This Day in Math - November 19

A visitor to Niels Bohr's country cottage, noticing a horseshoe hanging on the wall, teasing the eminent scientist about this ancient superstition. 'Can it be true that you, of all people, believe it will bring you luck?'
'Of course not,' replied Bohr, 'but I understand it brings you luck whether you believe it or not.'

The 323rd day of the year; If you put drew every possible path from (0,0) to (8,0) that never dropped below the x-axis using only unit vectorial moves with slopes of 1, 0, or -1 there are 323 possible paths. (alternatively this is the number of different ways of drawing non-intersecting chords on a circle with eight points- this is deceptive because it counts each way of drawing a single chord, and drawing no chords at all, students might want to count how many ways this can be done using four chords.) These are called Motzkin numbers, after Theodore Motzkin.

3232 is the sum of nine consecutive primes 323 = 19 + 23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 *Derek Orr

323 is a palindrome and also the smallest composite number n that divides the (n+1)st Fibonacci number. *What's Special about this Number

When eight labled points are selected around a circle, there are 323 ways of drawing any number of nonintersecting chords joining them, such numbers are called Motzkin numbers

EVENTS

1857 Arhtur Cayley opens a letter to J. J. Sylvester with, "I have just obtained a theorem that appears to be very remarkable." The theorem would be the centerpiece of his Memoire on the Theory of Matrices. The theorem showed that a matrix was the solution of its own characteristic equation. *A. J. Crilly, Arthur Cayley: Mathematician Laureate of the Victorian Age

1982 Science has an article describing Friedman’s version of Kruskal’s theorem. The important thing is that this is a mathematical (rather than metamathematical) statement independent of arithmetic. *VFR

2010 Experts confirmed that the remains of the 16th-century Danish astronomer Tycho Brahe, his wife and another eight people, including five children, were buried in Prague's Church of Our Lady before Tyn. The tin coffin, tied up with a red ribbon, was deposited in the tomb in the overcrowded church that afternoon preceded by a church service celebrated by Prague Archbishop Dominik Duka and including prayers in Czech and Danish. *Wik The grave had been previously opened 1901, on the three hundredth anniversary of his death, the bodies of Tycho Brahe and his wife Kirstine were exhumed in Prague. They had been embalmed and were in remarkably good condition, but the astronomer’s artificial nose was missing, apparently filched by someone after his death. It had been made for him in gold and silver when his original nose was sliced off in a duel he fought in his youth at Rostock University after a quarrel over some obscure mathematical point.

BIRTHS

1894 Heinz Hopf (19 Nov 1894 in Gräbschen (near Breslau), Germany (now Wrocław, Poland) - 3 June 1971 in Zollikon, Switzerland) work was in algebraic topology. He studied vector fields and extended Lefschetz's fixed point formula. He also studied homotopy classes and defined what is now known as the 'Hopf invariant'.*SAU

1900 Mikhail Lavrentev (19 Nov 1900 in Kazan, Russia
- 15 Oct 1980 in Moscow, Russia) remembered for an outstanding book on conformal mappings and he made many important contributions to that topic.*SAU

1901 Nina Karlovna Bari (November 19, 1901, Moscow – July 15, 1961, Moscow) was a Soviet mathematician known for her work on trigonometric series. She was killed by a train in the Moscow Metro, and her colleagues speculated that she committed suicide, prompted by the death of her mentor Nikolai Luzin ten years earlier, a man who may have been her lover.*Wik

1907 Adrien Albert (19 November 1907, Sydney - 29 December 1989, Canberra) was a leading authority in the development of medicinal chemistry in Australia. Albert also authored many important books on chemistry, including one on selective toxicity.
He was awarded BSc with first class honours and the University Medal in 1932 at the University of Sydney. He gained a PhD in 1937 and a DSc in 1947 from the University of London. His appointments included Lecturer at the University of Sydney (1938-1947), advisor to the Medical Directorate of the Australian Army (1942-1947), research at the Wellcome Research Institute in London (1947-1948) and in 1948 the Foundation Chair of Medical Chemistry in the John Curtin School of Medical Research at the Australian National University in Canberra where he established the Department of Medical Chemistry. He was a Fellow of the Australian Academy of Science.
He was the author of Selective Toxicity: The Physico-Chemical Basis of Therapy, first published by Chapman and Hall in 1951.
The Adrien Albert Laboratory of Medicinal Chemistry at the University of Sydney was established in his honour in 1989.[1] His bequest funds the Adrien Albert Lectureship, awarded every two years by the Royal Society of Chemistry *Wik

1918 Hendrik Christoffel van de Hulst (19 Nov 1918; 31 Jul 2000) Dutch astronomer who predicted theoretically (1944) that in interstellar space the amount of neutral atomic hydrogen, which in its hyperfine transition radiates and absorbs at a wavelength of 21 cm, might be expected to occur at such high column densities as to provide a spectral line sufficiently strong as to be measurable. Shortly after the end of the war several groups set about to test this prediction. The 21-cm line of atomic hydrogen was detected in 1951, first at Harvard University followed within a few weeks by others. The discovery demonstrated that astronomical research, which at that time was limited to conventional light, could be complemented with observations at radio wavelengths, revealing a range of new physical processes.*TIS

DEATHS

1672 John Wilkins FRS (1 January 1614 – 19 November 1672) was an English clergyman, natural philosopher and author, as well as a founder of the Invisible College and one of the founders of the Royal Society, and Bishop of Chester from 1668 until his death. Along with his inventions (almost all of which were destroyed in the Great Fire) and assorted writings on philosophy, mathematics, and cryptography, John Wilkins distinguished himself by planning the first lunar expedition.(in the 17th century??? Yes… learn more here)
He wrote for the common reader the Discovery (1638) and the Discourse (1640) which showed how reason and experience supported Copernicus, Kepler and Galileo rather than Aristotlian or literal biblical doctrines. In 1641, he anonymously published a small but comprehensive treatise on cryptography. In Mathematical Magick (1648) he described and illustrated the balance lever, wheel, pulley, wedge and screw in a part called "Archimedes or Mechanical Powers" and in a second part "Daedalus or Mechanical Motions" such strange devices as flying machines, artificial spiders, a land yacht, and a submarine. *WIS

1998 Tetsuya Theodore Fujita(23 Oct 1920, 19 Nov 1998) was a Japanese-American meteorologist who increased the knowledge of severe storms. In 1953, he began research in the U.S. Shortly afterwards, he immigrated and established the Severe Local Storms Project. He was known as "Mr. Tornado" as a result of the Fujita scale (F-scale, Feb 1971), which he and his wife, Sumiko, developed for measuring tornadoes on the basis of their damage. Following the crash of Eastern flight 66 on 24 Jun 1975, he reviewed weather-related aircraft disasters and verified the downburst and the microburst (small downburst) phenomena, enabling airplane pilots to be trained on how to react to them. Late in his career, he turned to the study of storm tracks and El Nino. *TIS

*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

## Saturday, 18 November 2017

### On This Day in Math - November 18

Predictions can be very difficult—
— Niels Bohr

The 322nd day of the year; 322 is the 12th Lucas Number. The Lucas Sequence is similar to the Fibonacci sequence with L(1) = 1 and L(2) = 3 and each term is the sum of the two previous terms. L(n) is also the integer nearest to $\phi ^n$ This is the last day of the year that will be a Lucas Number.

322 is smallest number whose square has 6 diff digits (103684). *Derek Orr
322 is a sphenic number, which means that it is the area of  a rectangular box (parallelepiped) with prime lengths for its length, width, and height.

EVENTS

2349 B.C. Noah’s ﬂood began according to the English mathematician, William Whiston (1667–1752) who felt it was caused by a comet which passed over the equator causing extensive rains. *Claire L. Parkinson, Breakthroughs, p. 131 Whiston would follow Newton as the Lucasian Professor at Cambridge.*RMAT

1690 First use of catenary According to E. H. Lockwood (1961) and the University of St. Andrews website, this term was first used (in Latin as catenaria) by Christiaan Huygens (1629-1695) in a letter to Leibniz dated November 18, 1690. *Earliest Known Uses of Some of the Words of Mathematics The English word catenary is usually attributed to Thomas Jefferson (but see below****), who wrote in a letter to Thomas Paine on the construction of an arch for a bridge"I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to be a very scientifical work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the catenary is in perfect equilibrium."  (Dec. 23, 1788) *Jeff Miller  (Paine had previously used the term "catenarian" in earlier letter to Jefferson. (Sept. 15, 1788).
****Miller's web site now includes a single previous use of Catenary in English in 1725 in Lexicon Technicum: Or, An Universal English Dictionary of ARTS and SCIENCES: Fourth Edition Volume I*****

1752 Goldbach writes Euler with 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 that it was true for the first 1000 odd numbers, and then later 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.)

1812 Jean Victor Poncelet , a military engineer, was captured while Napoleon’s army was retreating from Moscow. He proﬁted from this enforced leisure (until his release in June 1814) by resuming his study of mathematics. While there he did important work on projective geometry. *VFR

1825 Birbeck writes to Gilmer regarding the application for professor at U Va of Charles Bonnycastle, son of John Bonneycastle.  “The name of Bonnycastle must be well known in America, and if known, must be highly valued; and the son I am persuaded will extend the fame of the parent.

1879  After the death of Maxwell, George Stokes writes to offer Lord Rayleigh the position of head of the Cavendish Laboratory in Cambridge.  *Memoir and scientific correspondence of the late Sir George Gabriel Stokes, pg 227

1883 At noon on this day the telegraphic time signals sent out daily from the Naval Observatory at Washington, D.C., were changed to standard time, a system adopted on the initiative of the American Railway Association. Standard time was suggested for the U.S. in 1869 by Charles Ferdinand Dowd, a schoolmaster from Saratoga, N.Y., but was not adopted then. He suggested dividing the continent into four time zones each one hour or ﬁfteen degrees of longitude wide. Standard Railroad Time had four time zones, Eastern, Central, Western, and Paciﬁc. Congress made these official in 1918. Some citizens grumbled about “railroad tyranny” and tampering with “God’s time.” See New York Times, 20 Nov. 1983. *VFR On April 1 of 1967, The Uniform Time Act divided the United States into eight time zones; Eastern, Central, Mountain, Pacific, Yukon, Alaska, Hawaii, and Bering.  *FFF, pg 149

1963 The first push-button telephone goes into service. @yovisto
The first electronic push-button system with Touch-Tone dialing was offered by Bell Telephone to customers in Carnegie and Greensburg, Pennsylvania.
Western Electric experimented as early as 1941 with methods of using mechanically activated reeds to produce two tones for each of the ten digits. But the technology proved unreliable and it was not until long after the invention of the transistor when the technology matured. On 18 November 1963 the Bell System in the United States officially introduced dual-tone multi-frequency (DTMF) technology under its registered Touch-Tone® mark. Over the next few decades Touch-Tone service replaced traditional pulse dialing technology and it eventually became a world-wide standard for telecommunication signaling.
The now standard layout of the keys on the Touch-Tone telephone was the result of research of the human-engineering department at Bell Laboratories in the 1950s under the leadership of South African-born psychologist John Elias Karlin (1918–2013), who was previously a leading proponent in the introduction of all-number-dialing in the Bell System. This research resulted in the design of the DTMF keypad that arranged the push-buttons into 12 positions in a 3-by-4 position rectangular array, and placed the 1, 2, and 3 keys in the top row for most accurate dialing.[18] The remaining digits occupied the lower rows in sequence from left to right, however, placing the 0 into the center of the fourth row, while omitting the lower left, and lower right positions. These two positions were later assigned to the asterisk and pound key when the keypad was expanded for twelve buttons in 1969. *Wik

1991 IBM and Siemens AG Announce 64M DRAM Chip Prototype : IBM and Siemens AG announce they have developed a prototype 64 megabyte DRAM chip. This development was in line with Moore’s Law which predicts a doubling of the number of transistors etched into silicon every 18 months. *CHM

BIRTHS

1839 August (Adolph Eduard Eberhard) Kundt (18 Nov 1839; 21 May 1894)  was a German physicist who developed a method (1866) to determine the  velocity of sound in gases and solids. He used a closed glass tube into  which a dry powder (such as lycopodium) has been sprinkled. The source  of sound in the original device was a metal rod clamped at its centre  with a piston at one end, which is inserted into the tube. When the rod  is stroked, sound waves generated by the piston enter the tube. If the  position of the piston in the tube is adjusted so that the gas column is  a whole number of half wavelengths long, the dust will be disturbed by  the resulting stationary waves forming a series of striations, enabling  distances between nodes to be measured. *TIS

1844 Albert Wangerin (November 18, 1844 – October 25, 1933) worked on potential theory, spherical functions and differential geometry.*SAU He wrote an important two volume treatise on potential theory and spherical functions. Theorie des Potentials und der Kugelfunktionen I was published in 1909 and Theorie des Potentials und der Kugelfunktionen II was published in 1921. Wangerin functions are named for him.
He was also known for writing of textbooks, encyclopaedias and his historical writings.*Wik

1872 Giovanni Enrico Eugenio Vacca (18 November 1872 – 6 January 1953) was an Italian mathematician, Sinologist and historian of science.
Vacca studied mathematics and graduated from the University of Genoa in 1897 under the guidance of G. B. Negri. He was a politically active student and was banished for that from Genoa in 1897. He moved to Turin and became an assistant to Giuseppe Peano. In 1899 he studied, at Hanover, unpublished manuscripts of Gottfried Wilhelm Leibniz, which he published in 1903. Around 1898 Vacca became interested in Chinese language and culture after attending a Chinese exhibition in Turin. He took private lessons of Chinese and continued to study it at the University of Florence. Vacca then traveled to China in 1907-8 and defended a PhD in Chinese studies in 1910. In 1911, he became a lecturer in Chinese literature at the University of Rome. In 1922, he moved to Florence and taught Chinese literature and language at university until 1947.
The interests of Vacca were almost equally split between mathematics, Sinology and history of science, with a corresponding number of papers being 38, 47 and 45. In 1910, Vacca developed a complex number iteration for pi. *Wik

1887 Gustav Theodor Fechner (19 Apr 1801, 18 Nov 1887) German physicist and philosopher who was a key figure in the founding of psychophysics, the science concerned with quantitative relations between sensations and the stimuli producing them. He formulated the rule known as Fechner’s law, that, within limits, the intensity of a sensation increases as the logarithm of the stimulus. He also proposed a mathematical expression of the theory concerning the difference between two stimuli, advanced by E. H. Weber. (These are now known to be only approximately true. However, as long as the stimulus is of moderate intensity, then the laws will give us a good estimate.) Under the name “Dr. Mises” he also wrote humorous satire. In philosophy he was an animist, maintaining that life is manifest in all objects of the universe. *TIS

1897 Patrick M.S. Blackett (18 Nov 1897; 13 Jul 1974) English scientist who won the Nobel Prize for Physics in 1948 for his discoveries in the field of cosmic radiation, which he accomplished primarily with cloud-chamber photographs that revealed the way in which a stable atomic nucleus can be disintegrated by bombarding it with alpha particles (helium nuclei). Although such nuclear disintegration had been observed previously, his data explained this phenomenon for the first time and were useful in explaining disintegration by other means. *TIS

1900 George Bogdanovich Kistiakowsky (November 18, 1900 – December 7, 1982) was a Ukrainian-American physical chemistry professor at Harvard who participated in the Manhattan Project and later served as President Dwight D. Eisenhower's Science Advisor.
Born in Kiev in the old Russian Empire, Kistiakowsky fled Russia during the Russian Civil War. He made his way to Germany, where he earned his PhD in physical chemistry under the supervision of Max Bodenstein at the University of Berlin. He emigrated to the United States in 1926, where he joined the faculty of Harvard University in 1930, and became a citizen in 1933.
During World War II, he was the head of the National Defense Research Committee (NDRC) section responsible for the development of explosives, and the technical director of the Explosives Research Laboratory (ERL), where he oversaw the development of new explosives, including RDX and HMX. He was involved in research into the hydrodynamic theory of explosions, and the development of shaped charges. In October 1943, he was brought into the Manhattan Project as a consultant. He was soon placed in charge of X Division, which was responsible for the development of the explosive lenses necessary for an implosion-type nuclear weapon. He watched an implosion weapon that was detonated in the Trinity test in July 1945. A few weeks later a Fat Man implosion weapon was dropped on Nagasaki.
From 1962 to 1965, he chaired the National Academy of Sciences's Committee on Science, Engineering, and Public Policy (COSEPUP), and was its vice president from 1965 to 1973.
In later years he was active in an antiwar organization, the Council for a Livable World. Kistiakowsky severed his connections with the government in protest against the US involvement in the war in Vietnam. In 1977, he assumed the chairmanship of the Council for Livable World, campaigning against nuclear proliferation. He died of cancer in Cambridge, Massachusetts, on December 17, 1982. His body was cremated, and his ashes were scattered near his summer home on Cape Cod, Massachusetts. His papers are in the Harvard University archives.*Wik

1901 George Horace Gallup (November 18, 1901 – July 26, 1984) was an American pioneer of survey sampling techniques and inventor of the Gallup poll, a successful statistical method of survey sampling for measuring public opinion.
Gallup was born in Jefferson, Iowa, the son of George Henry Gallup, a dairy farmer. His higher education took place at the University of Iowa. He served as a journalism professor at Drake and Northwestern for brief periods. In 1932 he moved to New York City to join the advertising agency of Young and Rubicam as director of research (later as vice president from 1937 to 1947). He was also professor of journalism at Columbia University, but he had to give up this position shortly after he formed his own polling company, the American Institute of Public Opinion (Gallup Poll), in 1935.
In 1936, his new organization achieved national recognition by correctly predicting, from the replies of only 50,000 respondents, that Franklin Roosevelt would defeat Alf Landon in the U.S. Presidential election. This was in direct contradiction to the widely respected Literary Digest magazine whose poll based on over two million returned questionnaires predicted that Landon would be the winner. Not only did Gallup get the election right, he correctly predicted the results of the Literary Digest poll as well using a random sample smaller than theirs but chosen to match it.
Twelve years later, his organization had its moment of greatest ignominy, when it predicted that Thomas Dewey would defeat Harry S. Truman in the 1948 election, by five to fifteen percentage points. Gallup believed the error was mostly due to ending his polling three weeks before Election Day.
Gallup died in 1984 of a heart attack at his summer home in Tschingel, a village in the Bernese Oberland of Switzerland. He was buried in Princeton Cemetery. *Wik

1912 Shigeo Sasaki 佐々木 (18 November 1912 Yamagata Prefecture, Japan – 14 August 1987 Tokyo) was a Japanese mathematician working on differential geometry who introduced Sasaki manifolds. *Wik

1916 Sir David Robert Bates, FRS(18 November 1916, Omagh, County Tyrone, Ireland – 5 January 1994) was an Irish mathematician and physicist.
During the Second World War he worked at the Admiralty Mining Establishment where he developed methods of protecting ships from magnetically activated mines.
His contributions to science include seminal works on atmospheric physics, molecular physics and the chemistry of interstellar clouds. He was knighted in 1978 for his services to science, was a Fellow of the Royal Society and vice-president of the Royal Irish Academy. In 1970 he won the Hughes Medal. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1974.
The Mathematics Building at Queens University Belfast, is named after him. *Wik

1923 Alan B. Shepard, Jr. (18 Nov 1923; 21 Jul 1998) Alan Bartlett Shepard, Jr. was America's first man in space and one of only 12 humans who walked on the Moon. Named as one of the nation's original seven Mercury astronauts in 1959, Shepard became the first American into space on 5 May 1961, riding a Redstone rocket on a 15-minute suborbital flight that took him and his Freedom 7 Mercury capsule 115 miles in altitude and 302 miles downrange from Cape Canaveral, FL. (His flight came three weeks after the launch of Soviet cosmonaut Yuri Gagarin, who on 12 Apr 1961, became the first human space traveler on a one-orbit flight lasting 108 minutes.) Although the flight of Freedom 7 was brief, it  was a major step for U.S. in a  race with the USSR. *TIS

1927 John Leslie Britton (November 18, 1927 – June 13, 1994) was an English mathematician from Yorkshire who worked in combinatorial group theory and was an expert on the word problem for groups. Britton was a member of the London Mathematical Society and was Secretary of Meetings and Membership with that organization from 1973-1976. Britton died in a climbing accident on the Isle of Skye. *Wik

DEATHS

1919 Adolf Hurwitz (26 March 1859 in Hildesheim, Lower Saxony, Germany
Died: 18 Nov 1919 in Zurich, Switzerland) Hurwitz studied the genus of the Riemann surface and worked on how class number relations could be derived from modular equations. Hurwitz did excellent work in algebraic number theory. For example he published a paper on a factorisation theory for integer quaternions in 1896 and applied it to the problem of representing an integer as the sum of four squares. A full proof of Hurwitz's ideas appears in a booklet published in the year of his death. This involves studying the ring of integer quaternions in which there are 24 units. He shows that one-sided ideals are principal and introduces prime and primary quaternions. *SAU

1928 Alexander Ziwet (February 8, 1853 -  No vember 18, 1928) born in Breslau. He became professor at the University of Michigan, an editor of the Bulletin of the AMS, and a collector of mathematics text who enriched the Michigan library. *VFR His early education was obtained in a German gymnasium. He afterwards studies in the universities of Warsaw and Moscow, one year at each, and then entered the Polytechnic School at Karlsruhe, where he received the degree of Civil Engineer in 1880.
He came immediately to the United States and received employment on the United States Lake Survey. Two years later he was transferred to the United States Coast and Geodetic Survey, computing division, where he remained five years.
In 1888 he was appointed Instructor in Mathematics in the University of Michigan. From this position he was advanced to Acting Assistant Professor in 1890, to Assistant Professor in 1891, to Junior Professor in 1896, and to Professor of Mathematics in 1904.
He was a member of the Council of the American Mathematical Society and an editor of the "Bulletin" of the society. In 1893-1894 he published an "Elementary Treatise on Theoretical Mechanics" in three parts, of which a revised edition appeared in 1904. He also translated from the Russian of I. Somoff "Theoretische Mechanik" (two volumes, 1878, 1879).
*Burke A. Hinsdale and Isaac Newton Demmon, History of the University of Michigan (Ann Arbor: University of Michigan Press, 1906), pp. 320-321.

1933 Robert Forsyth Scott (28 July 1849 in Leith, near Edinburgh, Scotland - 18 Nov 1933 in Cambridge, England) studied at Cambridge and was elected to a fellowship. After a short time teaching he studied to be a barrister. He spent most of his career as Bursar and Master of St John's College Cambridge. He published a book on Determinants. *SAU

1949 Frank Baldwin Jewett (5 Sep 1879, 18 Nov 1949) Frank Baldwin Jewett was the U.S. electrical engineer who directed research as the first president of the Bell Telephone Laboratories, Inc., (1925-40). Jewett believed that the best science and technology result from bringing together and nurturing the best minds. Under his tenure Bell Labs laid the foundation for a new scientific discipline, radio astronomy, and transformed movies by synchronizing sound to pictures. Bell Labs was the first to transmit television over a long distance in the U.S. and designed the first electrical digital computer. Bell Labs won its first Nobel Prize in physics for fundamental work demonstrating the wave nature of matter.*TIS

1959 Aleksandr Yakovlevich Khinchin (July 19, 1894, Kondrovo, Kaluga Oblast, Russia - November 18, 1959, Moscow, Russia) was a Russian mathematician who contributed to many fields including number theory and probability. Khinchin made significant contributions to the metric theory of Diophantine approximations and established an important result for simple real continued fractions, discovering a property of such numbers that leads to what is now known as Khinchin's constant. He also published several important works on statistical physics, where he used the methods of probability theory, and on information theory, queuing theory and mathematical analysis.*Wik

 *Niels Bohr Institute
1962 Niels Henrik David Bohr (7 Oct 1885, 18 Nov 1962) was a Danish physicist, born in Copenhagen, who was the first to apply the quantum theory, which restricts the energy of a system to certain discrete values, to the problem of atomic and molecular structure. For this work he received the Nobel Prize for Physics in 1922. He developed the so-called Bohr theory of the atom and liquid model of the nucleus. Bohr was of Jewish origin and when the Nazis occupied Denmark he escaped in 1943 to Sweden on a fishing boat. From there he was flown to England where he began to work on the project to make a nuclear fission bomb. After a few months he went with the British research team to Los Alamos in the USA where they continued work on the project. *TIS (Bohr was an excellent athlete in his youth, read more here.)
Niels and his mathematician brother Harald are buried in the same grave site at the Assistens cemetery in Copenhagen. I love the youthful picture of the two brothers shown at right.

1994 Nathan Jacob Fine (22 October 1916 in Philadelphia, USA - 18 Nov 1994 in Deerfield Beach, Florida, USA) He published on many different topics including number theory, logic, combinatorics, group theory, linear algebra, partitions and functional and classical analysis. He is perhaps best known for his book Basic hypergeometric series and applications published in the Mathematical Surveys and Monographs Series of the American Mathematical Society. The material which he presented in the Earle Raymond Hedrick Lectures twenty years earlier form the basis for the material in this text.*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, 17 November 2017

### On This Day in Math - November 17

 Central part of a large floor mosaic, from a Roman villa in Sentinum (now known as Sassoferrato, in Marche, Italy), ca. 200–250 C.E. Aion, the god of eternity, is standing inside a celestial sphere decorated with zodiac signs, in between a green tree and a bare tree (summer and winter, respectively). Sitting in front of him is the mother-earth goddess, Tellus (the Roman counterpart of Gaia) with her four children, who possibly represent the four seasons.*Wik

The unreasonable efficiency of mathematics in science is a gift we neither understand nor deserve.

~Eugene Paul Wigner

The 321st day of the year. 321 is the number of partitions of 13 into at most 4 parts. (7+3+2+1 would be one such)

321 is a Central Delannoy number. The Delannoy numbers are the number of lattice paths from (0, 0) to (b, a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed. Central Delannoy numbers are paths to (a,a). [Delannoy numbers are named for Henri Auguste Delannoy (1833–1915) who was a friend and correspondent of Edouard Lucas, editor of Récréations Mathématiques.]

EVENTS

1717 While making his rounds a gendarme found an infant on the steps of the Church of Saint Jean-le-Rond in Paris. The child was christened Jean-le-Rond. Later, for unknown reasons, he added the surname d’Alembert. Jean le Rond D'Alembert (1717 1783) was abandoned by his mother on the steps of Saint Jean le Rond, which was the baptistery of Notre-Dame. Foster parents were found and he was christened with the name of the saint. When he became famous, his mother attempted to reclaim him, but he rejected her. His father, we now know, was an artillery officer, Louis-Camus Destouches. His natural father did not want his paternity known, but paid for his education in secret. D'Alembert was a pioneer in the study of differential equations and their use of in physics. He studied the equilibrium and motion of fluids.

1767 At the commencement, the College of Philadelphia bestowed on David Rittenhouse, then present, the honorary degree of Master of Arts, Dr. William Smith, the Provost, addressing him as follows:
Sir,--The trustees of this College (the faculty of professors cheerfully concurring), being ever desirous to distinguish real merit, especially in the natives of this province,--and well-assured of the extraordinary progress and improvement which you have made, by a felicity of natural genius, in mechanics, mathematics, astronomy, and other liberal arts and sciences, all which you have adorned by singular modesty and irreproachable morals,--have authorized and required me to admit you to the honorary degree of Master of Arts, in this seminary: I do therefore, by virtue of this authority, most cheerfully admit, &c.
*U Penn Library web site

In 1797, the first patent in the U.S. for a clock was issued to Eli Terry of East Windsor, Conn. for an equation clock.The patent was signed by President John Adams. The clock had two minute hands, one of which showed the mean or true time, while the other "together with the striking part and hour hand showed the apparent time, as divided by the sun according to the table of variation of the sun and clock for each day of the year." He began making clocks in 1793, in Plymouth, Conn. Terry introduced wooden geared clocks using the ideas of Eli Whitney's new armory practice to produce interchangeable gears (1802) and mass production of very inexpensive household clocks. Terry developed ways to produce wooden clock works by machine. *TIS

1834 Astronomer Royal Airy receives suggestion to begin mathematical search for undiscovered planet that would be Neptune by the Reverend T.J. Hussey.
He mentions in his letter how he has heard of a possible planet beyond Uranus and looked for it using a reflector telescope, but to no avail. He presented the idea of using mathematics as a tool in the search but admitted to Airy that he would not be of much help in that regard. On Novemeber 23rd Airy writes back to the reverend and admits he too has been preoccupied with a possible planet. He had observed that Uranus' orbit deviated the most in 1750 and 1834, when it would be at the same point. This was strong evidence for an object pulling on the planet, but Airy felt that until more observations were made no mathematical tools would be of help
*from http://theoriginal1701.hubpages.com/hub/The-Drama-of-Neptunes-Discovery

1921 Fisher reads his famous Royal Society paper, On the Mathematical Foundations of Theoretical Statistics. Statistical Historian, Steven Stigler writes that, “in 1921 Fisher presented a major pathbreaking memoir to the Royal Society of London, a memoir that more than any other single work gave the framework and direction to twentieth century statistical theory.”
The paper begins with a list of definitions that, while almost unheard of before that paper, have become standard in even elementary statistics courses. Terms like estimation, likelihood, optimum, and not defined, but actually used in the descriptions of other terms was Fisher’s first public use of “parameter”. *Stigler, Fisher in 1921
At right the Fisher window from  from the Greatroom at Caius College., Cambridge

1930 Kurt Godel’s “On formally undecidable propositions of Principia Mathematica and related systems ” was received for publication. It contained the amazing result that there are true but unprovable statements in arithmetic.

In 1970, a U.S. patent was issued for the computer mouse - an "X-Y Position Indicator for a Display System" (No. 3541541). The inventor was Doug Engelbart. In the lab, he and his colleagues had called it a "mouse," after its tail-like cable. The first mouse was a simple hollowed-out wooden block, with a single push button on top. Engelbart had designed this as a tool to select text, move it around, and otherwise manipulate it. It was a key element of his larger project - the NLS (oN Line System), a computer he and some colleagues at the Stanford Research Institute had built. The NLS also allowed two or more users to work on the same document from different workstations.*TIS

2011  French law allows the ﬁrst taste of Beaujolais Nouveau on this date each year. In 1985 the law was changed to the third Thursday in November. Also permission was given to ship wine ahead of time to bonded warehouses outside of France. Thus in the US we can drink the Nouveau on the same day as the French. Get out now and buy several bottles for the holidays. *VFR

2012 The maximum of the Leonid activity in 2012 is expected during the night of the 17th November 2012. The Leonids are a prolific meteor shower. It tends to peak around November 17, but some are spread through several days on either side and the specific peak changing every year. *Cute-Calendar.com

BIRTHS

1597 Henry Gellibrand was an English clergyman who worked on magnetic declination and who made mathematical contributions to navigation.*SAU He discovered that magnetic declination – the angle of dip of a compass needle – is not constant but changes over time. He announced this in 1635, relying on previous observations by others, which had not yet been correctly interpreted.
He also devised a method for measuring longitude, based on eclipses. The mathematical tables of Henry Briggs, consisting of logarithms of trigonometric functions, were published by Gellibrand in 1633 as Trigonometria Britannica.
He was Professor at Gresham College, succeeding Edward Gunter in 1626. He was buried in St Peter Le Poer. (London, demolished in 1907) *Wik

1790 August Möbius (17 Nov 1790; 26 Sep 1868)August Ferdinand Möbius was a German astronomer, mathematician and author. He is best known for his work in analytic geometry and in topology, especially remembered as one of the discoverers of the Möbius strip, which he had discovered in 1858. A Möbius strip is a two-dimensional surface with only one side. It can be constructed in three dimensions as follows. Take a rectangular strip of paper and join the two ends of the strip together so that it has a 180 degree twist. It is now possible to start at a point A on the surface and trace out a path that passes through the point which is apparently on the other side of the surface from A. Although his most famous work is in mathematics, Möbius did publish important work on astronomy.*TIS

1865 John Stanley Plaskett (17 Nov 1865; 17 Oct 1941) Canadian astronomer known for his expert design of instruments and his extensive spectroscopic observations. He designed an exceptionally efficient spectrograph for the 15-inch refractor and measured radial velocities and found orbits of spectroscopic binary stars. He designed and supervised construction of the 72-inch reflector built for the new Dominion Astrophysical Observatory in Victoria and was appointed its first director in 1917. There he extended the work on radial velocities and spectroscopic binaries and studied spectra of O and B-type stars. In the 1930s he published the first detailed analysis of the rotation of the Milky Way, demonstrating that the sun is two-thirds out from the center of our galaxy about which it revolves once in 220 million years. *TIS

1902 Eugene Paul Wigner (17 Nov 1902; 1 Jan 1995) Hungarian-born American physicist who was the joint winner of the 1963 Nobel Prize for Physics (with Maria Goeppert Mayer and Johannes Hans Jensen) for his insight into quantum mechanics, for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles. He made many contributions to nuclear physics and played a prominent role in the development of the atomic bomb and nuclear energy. *TIS I love this story about Wigner as a child, "When he was ten years old ... he was told that he had tuberculosis. The cure was to be found in sending him to a sanatorium in Breitenstein in Austria and he spent six weeks there before being told that the diagnosis had been wrong and that he had never had tuberculosis. However, one advantage of his six weeks was that he began to think about mathematical problems "I had to lie on a deck chair for days on end, and I worked terribly hard on constructing a triangle if the three altitudes are given." *SAU

1917 Ruth Aaronson Bari (November 17, 1917 – August 25, 2005) was an American mathematician known for her work in graph theory and homomorphisms. The daughter of Polish-Jewish immigrants to the U.S., she was a professor at George Washington University beginning in 1966. She was the mother of environmental activist Judi Bari, science reporter Gina Kolata and art historian Martha Bari.*Wik

DEATHS
1704 Valentin Heins (May 15th 1637 in Hamburg - November 17 1704 ) was a German arithmetician (Reckoner)
The son of a linen weaver, the source of his education is unknown. From 1651 Heins was licensed to provide instruction in commercial computing (accounting, bookkeeping, arithmetic, etc). In the years 1658 and 1659 Heins studied theology for several semesters at the universities of Jena and Leipzig , but then returned to Hamburg. There he married and had a vicariate (financial endoument) in 1661 at the Cathedral. Whether Heins performed for a service is not known.
In 1670 he became writing and arithmetic master of the German Church School St. Michaelis . He was also from 1663-1672 accountant of the Guinean-African Company.
He wrote several textbooks, which made him known beyond national boundaries. They were reprinted up to the beginning of the 19th Century. Particularly popular was his tyrocinium mercatorio arithmeticum, a commercial arithmetic and accounting book.
Heins founded in 1690, with the calculation of the parish school master of St. Jacobi Henry Meissner , the art-loving Societät billing. This later became the Mathematical Society of Hamburg, the worlds oldest existing mathematical society. *Wik

1929 Herman Hollerith (29 Feb 1860, 17 Nov 1929) American inventor of a tabulating machine that was an important precursor of the electronic computer. For the 1890 U.S. census, he invented several punched-card machines to automate the sorting of data. The machine which read the cards used a pin going through a hole in the card to make an electrical connection with mercury placed beneath. The resulting electrical current activated a mechanical counter. It saved the United States 5 million dollars for the 1890 census by completing the analysis of the data in a fraction of the time it would have taken without it and with a smaller amount of manpower than would have been necessary otherwise. In 1896, he formed the Tabulating Machine Company, a precursor of IBM. *TIS

1953 Pierre Humbert (13 June 1891 in Paris, France, 17 Nov 1953 in Paris, France) graduated from the École Polytechnique in Paris and then moved to Edinburgh to do research under Whittaker. He spent most of his career in the University of Montpellier.  He specialized in the history of the seventeenth century he wrote particularly on the French astronomers of that period.
He also made contributions to mathematics, in particular he wrote on elliptic functions, Lamé functions, and Mathieu functions. His main mathematical work from the mid 1930s onwards was in developing the symbolic calculus. He also wrote on applications of the symbolic calculus to mathematical physics.
*SAU

1954 Tadeusz Banachiewicz (13 February 1882, Warsaw, Congress Poland, Russian Empire – 17 November 1954, Kraków) was a Polish astronomer, mathematician and geodesist.

He was educated at Warsaw University and his thesis was on "reduction constants of the Repsold heliometer". In 1905, after the closure of the University by the Russians, he moved to Göttingen and in 1906 to the Pulkowa Observatory. He also worked at the Engel'gardt Observatory at Kazan University from 1910–1915.
In 1919, after Poland regained her independence, Banachiewicz moved to Kraków, becoming a professor at the Jagiellonian University and the director of Kraków Observatory. He authored approximately 180 research papers and modified the method of determining parabolic orbits. In 1925, he invented a theory of "cracovians" — a special kind of matrix algebra — which brought him international recognition. This theory solved several astronomical, geodesic, mechanical and mathematical problems.
In 1922 he became a member of PAU (Polska Akademia Umiejętności) and from 1932 to 1938 was the vice-president of the International Astronomical Union. He was also the first President of the Polish Astronomical Society, the vice-president of the Geodesic Committee of The Baltic States and, from 1952 to his death, a member of the Polish Academy of Sciences. He was also the founder of the journal Acta Astronomica. He was the recipient of Doctor Honoris Causa titles from the University of Warsaw, the University of Poznań and the University of Sofia in Bulgaria.[citation needed]
Banachiewicz invented a chronocinematograph. The lunar crater Banachiewicz is named after him. He wrote over 230 scientific works. *Wik

1956 John Evershed (26 Feb 1864, 17 Nov 1956) English astronomer who discovered (1909) the Evershed effect - the horizontal motion of gases outward from the centres of sunspots. While photographing solar prominences and sunspot spectra, he noticed that many of the Fraunhofer lines in the sunspot spectra were shifted to the red. By showing that these were Doppler shifts, he proved the motion of the source gases. This discovery came to be known as the Evershed effect. He also gave his name to a spectroheliograph, the Evershed spectroscope.*TIS

1958 Yutaka Taniyama (November 12, 1927, Kisai near Tokyo – November 17, 1958, Tokyo) was a Japanese mathematician known for the Taniyama-Shimura conjecture.
Taniyama was best known for conjecturing, in modern language, automorphic properties of L-functions of elliptic curves over any number field. A partial and refined case of this conjecture for elliptic curves over rationals is called the Taniyama-Shimura conjecture or the modularity theorem whose statement he subsequently refined in collaboration with Goro Shimura. The names Taniyama, Shimura and Weil have all been attached to this conjecture, but the idea is essentially due to Taniyama.
In 1986 Ribet proved that if the Taniyama-Shimura conjecture held, then so would Fermat's last theorem, which inspired Andrew Wiles to work for a number of years in secrecy on it, and to prove enough of it to prove Fermat's Last Theorem. Due to the pioneering contribution of Wiles and the efforts of a number of mathematicians the Taniyama-Shimura conjecture was finally proven in 1999. The original Taniyama conjecture for elliptic curves over arbitrary number fields remains open, and the method of Wiles and others cannot be extended to provide its proof.*Wik

1990 Robert Hofstadter (5 Feb 1915, 17 Nov 1990) American scientist who was a joint recipient of the Nobel Prize for Physics in 1961 for his investigations in which he measured the sizes of the neutron and proton in the nuclei of atoms. He revealed the hitherto unknown structure of these particles and helped create an identifying order for subatomic particles. He also correctly predicted the existence of hte omega-meson and rho-meson. He also studied controlled nuclear fission. Hofstadter was one of the driving forces behind the creation of the Stanford Linear Accelerator. He also made substantial contributions to gamma ray spectroscopy, leading to the use of radioactive tracers to locate tumors and other disorders.*TIS

2000 Louis-Eugène-Félix Néel (22 Nov 1904, 17 Nov 2000) French physicist, corecipient (with the Swedish astrophysicist Hannes Alfvén) of the Nobel Prize for Physics in 1970 for his pioneering studies of the magnetic properties of solids. His contributions to solid-state physics have found numerous useful applications, particularly in the development of improved computer memory units. About 1930 he suggested that a new form of magnetic behavior might exist - called antiferromagnetism. Above a certain temperature (the Néel temperature) this behaviour stops. Néel pointed out (1947) that materials could also exist showing ferrimagnetism. Néel has also given an explanation of the weak magnetism of certain rocks, making possible the study of the past history of the Earth's magnetic field.*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

## Thursday, 16 November 2017

### On This Day in Math - November 16

Ramanujan, the Chuck Norris of math,
~John D. Cook

The 320th day of the year; 320 is the maximum value of the determinant of a 10x10 binary matrix (all entries are either one or zero). (Students might explore all possible determinants of smaller matrices looking for a pattern)

320!+1 is prime.

EVENTS

In 1904, the first electron tube, a diode thermionic valve, was invented by John Ambrose Fleming. The valve consists of a carbon or tungsten filament lamp, to which is added a metal plate (insulated from the filament), and a connecting wire brought through the glass wall of the bulb to a third terminal outside. When battery current is applied to the filament making it incandescent, the space between the filament and the insulated plate will be found to conduct elecrons in only one direction. That means if the valve is connected in a circuit in with an oscillating current, its one-way conductivity will convert the oscillating current into a unidirectional current capable of actuating a telephone receiver. He notified Marconi in a 30 Nov 1904 letter.*TIS

In 1942, work began on an experimental atomic pile to investigate the world's first artificial nuclear chain reaction. In a makeshift lab underneath the University's football stands at Stagg Field, physicists and staffers, worked around the clock to built a lattice of 57 layers of uranium metal and uranium oxide embedded in graphite blocks. A wooden structure supported the graphite pile. The research would be an important contribution to the Manhattan Project, a secret wartime project to develop nuclear weapons, which initiated the modern nuclear age. Little more than two weeks later, on 2 Dec 1942, the first self-sustained nuclear chain reaction was achieved by Enrico Fermi and his team*TIS

1945 The discovery of americium (Am) was announced on this day. This element is named after the Americas. Americium can be produced from intense neutron irradiation of pure plutonium (Pu). It is used in smoke detectors and as a portable source for gamma radiography. *rsc.org

1954 After a visit with Albert Einstein at Princeton on November 16, 1954, Linus Pauling wrote in his diary: "He said that he had made one great mistake -- when he signed the letter to Pres. Roosevelt (see Aug 10) recommending that atom bombs be made; but that there was some justification -- the danger that the Germans would make them." *Rebecca J. Rosen,The Atlantic.

BIRTHS

1717Jean le Rond D'Alembert (16 Nov 1717, 29 Oct 1783) was abandoned by his parents on the steps of Saint Jean le Rond, which was the baptistery of Notre-Dame, qv in Section 7-A-1. Foster parents were found and he was christened with the name of the saint. [Eves, vol. II, pp. 32 33. Okey, p. 297.] When he became famous, his mother attempted to reclaim him, but he rejected her. *VFR Known for his work in various fields of applied mathematics, in particular dynamics. In 1743 he published his Traité de dynamique (Treatise on Dynamics). The d'Alembert principle extends Newton's third law of motion, that Newton's law holds not only for fixed bodies but also for free moving bodies. D'Alembert also wrote on fluid dynamics, the theory of winds, the properties of vibrating strings and conducted experiments on the properties of sound . His most significant purely mathematical innovation was his invention and development of the theory of partial differential equations. He published eight volumes of mathematical studies (1761-80). He was editor of the mathematical and scientific articles for Denis Diderot's Encyclopédie.*TIS

1823 Birthdate of Jakob Amsler (b.11 November 1823 - d. 3 January 1912)inventor, in 1854, of the polar planimeter, a device for measuring areas enclosed by plane curves. *VFR Tracing around the perimeter of a surface induces a movement in another part of the instrument and a reading of this is used to establish the area of the shape. The planimeter contains a measuring wheel that rolls along the drawing as the operator traces the contour. He was a mathematician, physicist, engineer and the founder of his own factory . [A nice article about this instrument is at the MAA]
Amsler was born on the Stalden near the village of Schinznach in the district of Brugg, canton Aargau, and died in Schaffhausen, Switzerland. His father was Jakob Amsler-Amsler (1779–1869).
On graduating from school in 1843, he went to the University of Jena and then to the University of Königsberg to study theology. At Königsberg he changed courses, deciding to focus on mathematics and physics after meeting the inspiring Franz Neumann. Among Amsler's fellow students at Königsberg were Gustav Robert Kirchhoff and Siegfried Heinrich Aronhold. Amsler gained his doctorate from Königsberg in 1848 and returned to Switzerland in the same year. In 1851 he became a Privatdozent at the University of Zürich and later in that year accepted a position as a mathematics teacher at the Gymnasium in Schaffhausen.*Wik Amsler set up a workshop in Schaffhausen in 1854 specially designed to produce his polar planimeter. Three years later he had given up al his other interests to concentrate fully on producing instruments in the workshop. His shop produced 50 000 such instruments during his lifetime. *SAU

1835 Eugenio Beltrami (November 16, 1835, Cremona – February 18, 1900, Rome) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to prove consistency of non-Euclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and in the interior of an n-dimensional unit sphere, the so-called Beltrami–Klein model. He also developed singular value decomposition for matrices, which has been subsequently rediscovered several times. Beltrami's use of differential calculus for problems of mathematical physics indirectly influenced development of tensor calculus by Gregorio Ricci-Curbastro and Tullio Levi-Civita.*Wik

1841 Jules Louis Gabriel Violle (November 16, 1841, Langres, Haute-Marne - September 12, 1923, Fixin) was a French physicist and inventor.
He is notable for having determined the solar constant at Mont Blanc in 1875, and, in 1881, for proposing a standard for luminous intensity, called the Violle, equal to the light emitted by 1 cm² of platinum at its melting point. (It was notable as the first unit of light intensity that did not depend on the properties of a particular lamp, but it was made obsolete by the candela, the standard SI unit.)
Throughout his life, Violle taught at several colleges including the University of Lyon and the Conservatoire des Arts et Métiers in Paris. He was one of the founders of the Institut d'optique théorique et appliquée and the École supérieure d'optique. He improved and invented a number of devices for measuring radiation, and determined the freezing and melting points of palladium.
Violle is believed by some to be the secret identity of Fulcanelli, a contemporary French alchemist whose true identity is still debated. You can find his biography with this book "A l'ombre des chênes, l'alchimiste de la République (in the shade of the oak)*Wik

1886 Marcel Riesz (November 16, 1886 – September 4, 1969) was a Hungarian mathematician who was born in Győr, Hungary (Austria-Hungary). He moved to Sweden in 1908 and spent the rest of his life there, dying in Lund, where he was a professor from 1926 at Lund University. He was known for work on classical analysis, on fundamental solutions of partial differential equations, on divergent series, Clifford algebras, and number theory. Riesz was elected a member of Royal Swedish Academy of Sciences in 1936.
He was the younger brother of the mathematician Frigyes Riesz. *Wik

1897 Josif Zakharovich Shtokalo (16 Nov 1897 in Skomorokhy, Sokal, Galicia (now Ukraine) - 5 Jan 1987 in Kiev, Ukraine) Shtokalo worked mainly in the areas of differential equations, operational calculus and the history of mathematics.
Shtokalo's work had a particular impact on linear ordinary differential equations with almost periodic and quasi-periodic solutions. He extended the applications of the operational method to linear ordinary differential equations with variable coefficients.
He is regarded as one of the founders of the history of Soviet mathematics and particularly of the history in Ukraine and articles about M Ostrogradski and H Voronoy, he edited the three volume collections of Voronoy's (1952-3) and Ostrogradski's works (1959-61), a Russian-Ukrainian mathematical dictionary (1960) and approximately eighteen other Russian-Ukrainian terminology dictionaries. *SAU

1922 IBM System/360 hardware designer Gene Amdahl is born in Flandreau, SD. The System/360 marked IBM’s transition from discrete transistors to integrated circuits, as well as its move to a focus on electronic computer systems rather than punch card equipment. Amdahl went on from IBM to found his own company, Amdahl Computer Corp., which was very successful in making the first IBM-compatible mainframe systems.*CHM

DEATHS

1672 John Wilkins (14 February 1614 – 19 November 1672) was an English mathematician who was one of the founders of the Royal Society. He wrote on astronomy and mechanical machines.*SAU Wilkins is one of the few persons to have headed a college at both the University of Oxford and the University of Cambridge. He was a polymath, although not one of the most important scientific innovators of the period. His personal qualities were brought out, and obvious to his contemporaries, in reducing political tension in Interregnum Oxford, in founding the Royal Society on non-partisan lines, and in efforts to reach out to religious nonconformists. He was one of the founders of the new natural theology compatible with the science of the time.
He is particularly known for An Essay towards a Real Character and a Philosophical Language in which, amongst other things, he proposed a universal language and a decimal system of measure not unlike the modern metric system.*Wik

1786 István Hatvani was a Hungarian mathematician who wrote a pioneering work on probability and statistics. Hatvani was the first Hungarian to present work on statistics. In Introductio ad principia philosophicae solidioris in 1757 he presents tables for the number of births in Debrecen for the years 1750 to 1753 inclusive. He records the number of children who died within a year of being born and, finding a mortality rate of 34.2% which was well above that in other European countries (around 19%), he seeks medical reasons to explain the findings. *SAU

1922 Max Abraham (26 Mar 1875, 16 Nov 1922) German physicist whose life work was almost all related to Maxwell's theory. The text he wrote was the standard work on electrodynamics in Germany for a long time. Throughout his life, he remained strongly opposed to Einstein's Theory of Relativity, objecting to its postulates which he felt were contrary to classical common sense. He further held that the experimental evidence did not support that theory. In 1902, he had developed a theory of the electron in which he held that an electron was a perfectly rigid sphere with a charge distributed evenly over its surface. He also believed in the ether theory, thought that future astronomical data would validate it, and thus relativity was not in fact a good description of the real world. *TIS

1982 Pavel Sergeevich Aleksandrov (25 Apr 1896, 16 Nov 1982) Soviet mathematician who made important contributions to the field of topology (the study of related physical or abstract elements that remain unchanged under certain distortions) and one of the founders of the theory of compact and bicompact spaces. Aleksandrov introduced many of the basic concepts of topology, such as the notion that an arbitrarily general topological space can be approximated to an arbitrary degree of accuracy by simple geometric figures such as polyhedrons. Giving support to international cooperation, he supervised the publication of an English-Russian dictionary of mathematical terminology (1962).*TIS

2002 Frank Smithies FRSE (10 March 1912 Edinburgh, Scotland – 16 November 2002 Cambridge, England) was a British mathematician who worked on integral equations, functional analysis, and the history of mathematics. He was elected as a fellow of the Royal Society of Edinburgh in 1961.*Wik

2007 Gene Howard Golub (February 29, 1932 – November 16, 2007), Fletcher Jones Professor of Computer Science (and, by courtesy, of Electrical Engineering) at Stanford University, was one of the preeminent numerical analysts of his generation.
Credits. *Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*rsc.org Royal Society of Chemistry
*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