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| Pearls of Sluze, *Mathworld Wolfram |
There is no reason why the history and philosophy of science should not be taught in such a way as to bring home to all pupils the grandeur of science and the scope of its discoveries.
~Prince Louis-Victor de Broglie
The 78th day of the year; 78 is the smallest number that can be written as the sum of 4 distinct squares in 3 ways. *What's Special About This Number
In his pamphlet, "The Thousand Yard Model," Guy Ottewell creates a sacale model universe with the sun as a bowling ball. 78 feet away, the Earth is represented by a peppercorn.
In his doctoral thesis in the early 60's, Ron Graham proved that 78, and every number greater than 78 can be partitioned into distinct numbers so that the sum of their reciprocals is one. 78=2+6+8+10+12+40, and the reciprocals of all these distinct integers add up to one. There are at least two smaller numbers for which this is true. Can you find them?
78 is the sum of the first twelve integers, and thus a triangular number.
90 = 21+22+23+24, 78= 25+26 + 27, but 21^2 + 22^2 + 23^2 + 24^2 = 25^2 + 26^2 + 27^2 = 2030
The cube of 78 is equal to the sum of three distinct cubes, 783 = 393 + 523 + 653
(Historically, it seems Ramanujan was inspired by a much smaller such triplet 63 = 33 + 43 + 53
77 and 78 form the fourth Ruth-Aaron pair, named for the number of home runs hit by Babe Ruth, 714, and the number when Aaron broke the record, 715 (he hit more afterward). They are consecutive numbers that have the same sums of their prime factors (77 = 7*11, 78 = 2*3*13, and 7+11 = 2+3+13).
EVENTS
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| *Mark Jardine, |
1706 Advertisement in English Tabloid for William Jones's Synopsis Palmariorum Matheseos, or A New Introduction to the Mathematics. This is the book in which Jones introduces the symbol pi for the ratio of the circumference to diameter of a circle.
1752 Following the death of her father on March 19, 1752, a new phase of Maria Agnesi’s life began that lasted until her death. She restricted her study to theology and gave her time, effort, and money to devotional and charitable activities. Although continuing to live with her family, she kept a separate apartment, where she cared for a few poor, sick people. From 1759 she lived in a rented house with four of her poor people; and when money was needed for her charitable activity, she sold her gifts from the Empress Maria Theresa to a rich Englishman. Besides caring for the sick and indigent, she often taught catechism to working-class people. *Hubert Kennedy, Eight Mathematical Biographies, Pg 8
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| *Selected witch of Agnesi curves |
1791 Prior to 1784, when Jefferson arrived in France, most if not all of his drawings were made in ink. In Paris, Jefferson began to use pencil for drawing, and adopted the use of coordinate, or graph, paper. He treasured the coordinate paper that he brought back to the United States with him and used it sparingly over the course of many years. He gave a few sheets to his good friend David Rittenhouse, the astronomer and inventor:
"I send for your acceptance some sheets of drawing-paper, which being laid off in squares representing feet or what you please, saves the necessity of using the rule and dividers in all rectangular draughts and those whose angles have their sines and cosines in the proportion of any integral numbers. Using a black lead pencil the lines are very visible, and easily effaced with Indian rubber to be used for any other draught."
A few precious sheets of the paper survive today. *Monticello.org
Jefferson was widely interested in Science. For those who wish to know more about his scientific interest, I can recommend this book
1791 Report made to the Paris Academy of Sciences advocating the metric system, including the decimal subdivision of the circle. The committee consisted of J. C. Borda, J. Lagrange, P. S. Laplace, G. Monge, and de Condorcet. [Cajori, History of Mathematics 266] See April 14, 1790. *VFR
A metric system of angles was brought in, with 400 degrees in a full turn (100 degrees in a right angle). Now the earth would rotate 40 degrees in an hour and, since the metre had been designed so that one quarter meridian was 10 million metres, each degree of latitude would be 100 kilometres long. It was certainly a rational system but its introduction would require all watches, all clocks, all trigonometric tables, all charts etc. to be changed. Condorcet proposed that teams of out of work wig makers should be used to recalculate new mathematical tables with the new units. Why, one might ask, were the wig makers out of work? Well they had been employed by the aristocrats who, following the Revolution, no longer required their services! *SAU
The resolution found some traction in angle measures."In 1857, Mathematical Dictionary and Cyclopedia of Mathematical Science has: "The French have proposed to divide the right angle into 100 equal parts, called grades, but the suggestion has not been extensively adopted." In 1987 Mathographics by Robert Dixon has: “360° = 400 gradians = 2π radians.” And for those who have, or had, one, "The Texas Instruments TI-89 Titanium calculator has three modes, radians, degrees, and gradians."
*Jeff Miller "Angle: Units in which angle values are interpreted and displayed: RADIAN, DEGREE or GRADIAN* (* not available on the TI-92 family). *TI Knowledge Base web page
1797 The date of the entry in Gauss’s scientific diary showing that he had already discovered the double periodicity of certain elliptic functions. *VFR Gauss was investigating the lemniscate. Two days later he would show how to divide the lemniscate into five equal parts by ruler and compass. This means he must have had some sense of complex multiplication of elliptic functions. Abel would generalize this in 1826.
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| Lemniscate of Bernoulli |
1892 E. Hastings Moore, of Northwestern University, was elected professor of mathematics by the Board of Trustees of the new University of Chicago. *T. W. Goodspeed, The Story of the University of Chicago
1915 The first image of Pluto was taken by astronomer Thomas Gill at Lowell Observatory in 1915 using a nine-inch telescope borrowed from Swarthmore College. Percival undertook a passionate search for what he called “Planet X.” He took photographs of the sky where Planet X was predicted to be lurking, but failed to recognize Pluto because it was much fainter than expected. Percival died suddenly in 1916, not knowing he had in fact taken an image of Pluto. Only with the lens of history can we look back and recognize those photographs as containing some of the first images of Pluto. The calculations for the place to search for the undiscovered planet were directed by Elizabeth Williams, the head human computer, performing mathematical calculations on where Lowell should search for an unknown object and its size based on the differences in the orbits of Neptune and Uranus. Her calculations led to predictions for the location of the unknown planet. Lowell died unexpectedly in 1916 and the search was discontinued. In 1930 the search would resume, leading to the recognition of Pluto as a planet. Williams and her husband were then dismissed from their positions at the observatory by Percival Lowell's widow, Constance, because it was considered inappropriate to employ a married woman.
1918 "An Act to preserve daylight and provide standard time for the United States" was enacted on March 19, 1918. It both established standard time zones and set summer DST to begin on March 31, 1918. *WebExhibits
1937 John von Neumann gave a popular lecture at Princeton on the game of poker. Game Theory became one of his substantial contributions to mathematics. [A. Hodges, Alan Turing. The Enigma, p. 550]The Book that inspired the movie.
1937 John von Neumann gave a popular lecture at Princeton on the game of poker. Game Theory became one of his substantial contributions to mathematics. [A. Hodges, Alan Turing. The Enigma, p. 550]The Book that inspired the movie.
In 1921, Emile Borel, a French mathematician, published several papers on the theory of games. He used poker as an example and addressed the problem of bluffing and second-guessing the opponent in a game of imperfect information. Borel envisioned game theory as being used in economic and military applications. Borel's ultimate goal was to determine whether a "best" strategy for a given game exists and to find that strategy. While Borel could be arguably called as the first mathematician to envision an organized system for playing games, he did not develop his ideas very far. For that reason, most historians give the credit for developing and popularizing game theory to John Von Neumann, who published his first paper on game theory in 1928, seven years after Borel.
For Von Neumann, the inspiration for game theory was poker, a game he played occasionally and not terribly well. Von Neumann realized that poker was not guided by probability theory alone, as an unfortunate player who would use only probability theory would find out. Von Neumann wanted to formalize the idea of "bluffing," a strategy that is meant to deceive the other players and hide information from them.
In his 1928 article, "Theory of Parlor Games," Von Neumann first approached the discussion of game theory, and proved the famous Minimax theorem. From the outset, Von Neumann knew that game theory would prove invaluable to economists. He teamed up with Oskar Morgenstern, an Austrian economist at Princeton, to develop his theory.
I'm "All IN" on this hand.
1949 The American Museum of Atomic Energy opened for the public in an old WWII cafeteria in Oak Ridge, Tennessee. The site had been part of the US projects to develop atomic bombs by processing U235. A new facility was opened in 1975. *Lucio Gelmini
In 1958, Britain's first planetarium, the London Planetarium, opened in the west wing of Madame Tussaud's. It is one of the world's largest. The site used was that of the former Cinema and Restaurant added in 1929, that had been destroyed by a German bomb in 1940.*TIS
1953 Frances Crick writes a letter to his son. "Dear Michael, Jim Watson and I have probably made a most important discovery.” This was only two weeks after Crick solved the DNA puzzle and may well be the first written description of the code. The letter, was auctioned at Christie’s on April 10, 2013 for six million dollars. *NY Times Science
1953 Frances Crick writes a letter to his son. "Dear Michael, Jim Watson and I have probably made a most important discovery.” This was only two weeks after Crick solved the DNA puzzle and may well be the first written description of the code. The letter, was auctioned at Christie’s on April 10, 2013 for six million dollars. *NY Times Science
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| Crick letter *NBC |
2008 GRB 080319B was a gamma-ray burst (GRB) detected by the Swift satellite at 06:12 UTC on March 19, 2008. The burst set a new record for the farthest object that was observable with the naked eye: it had a peak visual apparent magnitude of 5.7 and remained visible to human eyes for approximately 30 seconds. The magnitude was brighter than 9.0 for approximately 60 seconds. If viewed from 1 AU away, it would have had a peak apparent magnitude of −67.57 (21 quadrillion times brighter than the Sun seen from Earth) *Wik
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| *artist's impression of gamma-ray burst GRB 080319B |
2019 One of the top prizes in mathematics has been given to a woman. The Norwegian Academy of Science and Letters announced it has awarded this year’s Abel Prize to Karen Uhlenbeck, an emeritus professor at the University of Texas at Austin. The award cites “the fundamental impact of her work on analysis, geometry and mathematical physics.” *NY Times
BIRTHS
1782 Baron Wilhelm von Biela (19 Mar 1782, 18 Feb 1856 at age 73) Austrian astronomer who was known for his measurement (1826) of a previously known comet as having an orbital period of 6.6 years. Subsequently, known as Biela's Comet, it was observed to break in two (1846), and in 1852 the fragments returned as widely separated twin comets that were not seen again. However, in 1872 and 1885, bright meteor showers (known as Andromedids, or Bielids... current Andromedids are only weakly represented by displays of less than three meteors per hour around November 14. ) were observed when the Earth crossed the path of the comet's known orbit. This observation provided the first concrete evidence for the idea that some meteors are composed of fragments of disintegrated comets.*TIS
1799 William Rutter Dawes (19 Mar 1799, 15 Feb 1868 at age 68) English amateur astronomer who set up a private observatory and made extensive measurements of binary stars and on 25 Nov 1850 discovered Saturn's inner Crepe Ring (independently of American William Bond). In 1864, he was the first to make an accurate map of Mars. He was called "Eagle-eyed Dawes" for the keenness of his sight with a telescope (though otherwise, he was very near-sighted). He devised a useful empirical formula by which the resolving power of a telescope - known as the Dawes limit - could be quickly determined. For a given telescope with an aperture of d cm, a double star of separation 11/d arcseconds or more can be resolved, that is, be visually recognized as two stars rather than one. *TIS
1862 Adolf Kneser (19 March 1862 in Grüssow, Mecklenburg, Germany - 24 Jan 1930 in Breslau, Germany (now Wrocław, Poland)) He is remembered most for work mainly in two areas. One of these areas is that of linear differential equations; in particular he worked on the Sturm-Liouville problem and integral equations in general. He wrote an important text on integral equations. The second main area of his work was the calculus of variations. He published Lehrbruch der Variationsrechnung (Textbook of the calculus of variations) (1900) and he gave the topic many of the terms in common use today including 'extremal' for a resolution curve, 'field' for a family of extremals, 'transversal' and 'strong' and 'weak' extremals *SAU
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| *Wik |
1885 Margaret Harwood (March 19, 1885 – February 6, 1979) was born in Littleton, Massachusetts, became the first woman – and for a long time the only woman – to serve as director of an independent astronomical observatory. She took charge of the Maria Mitchell Observatory on Nantucket Island in 1916, and remained in that post for forty-one years.
Miss Harwood had planned to study physics, chemistry and math when she entered Radcliffe College in 1903, but her choice of lodgings turned her to astronomy. She boarded with the family of Arthur Searle, a genial fixture at the Harvard College Observatory. Soon she was trailing him up Observatory Hill, learning to use the telescopes, earning the friendship and mentoring of other staff members, from Edward Pickering to Annie Jump Cannon and Henrietta Leavitt. By the time of Miss Harwood’s graduation, she was ready to step into a paid position as an assistant. The position didn’t pay much, however, and she supplemented her income of about $500 per year by teaching science in the mornings at a couple of local schools.
In 1912, the Maria Mitchell Association awarded Miss Harwood a new fellowship in astronomy worth $1,000. It came with a new opportunity: From June to December of that year, she took up residence in the old Mitchell homestead on Nantucket, where she curated a small museum and library, used the telescope in the next-door dome to further her own research on asteroids, and lectured on astronomy to the locals every Monday night.
She received an offer from Wellesley College to begin teaching astronomy there upon completion of her graduate studies. But the Maria Mitchell Association, keen to keep her and see her continue her own research, matched the Wellesley salary and made her director of the Nantucket observatory . She was only thirty years old.
In 1957, with considerable reluctance, Miss Harwood retired from her post at Nantucket. In 1961 she accepted the Annie Jump Cannon Prize, which had been established by its namesake in the 1930s, and first conferred on Cecilia Payne. The prize is still awarded today by the American Astronomical Society to a young woman at the start of her career, but it no longer comes with a custom-designed piece of astronomically themed jewelry . Instead, the winner is invited to lecture about her research at the Society’s annual meeting. No doubt Miss Harwood would approve.*LH
Custom-made pin in the shape of a galaxy, designed for the occasion of the award of the Annie Jump Cannon Prize to Margaret Harwood, 1961 (Schlesinger Library, Radcliffe Institute, Harvard Institute)
1900 Frederic Joliot-Curie (19 Mar 1900; 14 Aug 1958 at age 58) French physicist and physical chemist who became personal assistant to Marie Curie at the Radium Institute, Paris, and the following year married her daughter Irène (who was also an assistant at the institute). Later they collaborated on research, and shared the 1935 Nobel Prize in Chemistry "in recognition of their synthesis of new radioactive elements." For example, they discovered that aluminium atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. By 1939 he was investigating the fission of uranium atoms. After WW II he supervised the first atomic pile in France. He succeeded his wife as head of the Radium Institute upon her death in 1956. *TIS
Frédéric and Irène Joliot-Curie | Nobel Prize-Winning French
1910 Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American statistician and Shannon Award-winning information theorist. He was the father of former Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz.
While a part-time graduate student, Wolfowitz met Abraham Wald, with whom he collaborated in numerous joint papers in the field of mathematical statistics. This collaboration continued until Wald's death in an airplane crash in 1950. In 1951, Wolfowitz became a professor of mathematics at Cornell University, where he stayed until 1970. He died of a heart attack in Tampa, Florida, where he was a professor at the University of South Florida.
Wolfowitz's main contributions were in the fields of statistical decision theory, non-parametric statistics, sequential analysis, and information theory.*Wik
1910 Jerome Namias (19 Mar 1910, 10 Feb 1997 at age 86) American meteorological researcher most noted for having pioneered the development of extended weather forecasts and who also studied the Dust Bowl of the 1930s and the El Niño phenomenon. *TIS In 1971 he joined the Scripps Institution and established the first Experimental Climate Research Center. His prognosis of warm weather during the Arab oil embargo of 1973 greatly aided domestic policy response.*Wik
1927 Allen Newell (March 19, 1927 – July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND Corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology. He contributed to the Information Processing Language (1956) and two of the earliest AI programs, the Logic Theory Machine (1956) and the General Problem Solver (1957) (with Herbert A. Simon). He was awarded the ACM's A.M. Turing Award along with Herbert A. Simon in 1975 for their basic contributions to artificial intelligence and the psychology of human cognition *Wik
1951 Arthur T. Benjamin (March 19, 1961; ) is an American mathematician who specializes in combinatorics. Since 1989 he has been a Professor of Mathematics at Harvey Mudd College.
He is known for mental math capabilities and mathemagics performances. These have included shows at the Magic Castle and TED. He is also the first mathematician to have been featured on the Colbert Report.
The Mathematical Association of America gave him a regional award for distinguished teaching in 1999 and a national one in 2000. He was the Mathematical Association of America's George Pólya Lecturer for 2006-8. In 2012 he became a fellow of the American Mathematical Society.
Benjamin was one of the performers at the inaugural San Diego Science Festival on April 4, 2009. He also won the American Backgammon Tour in 1997. *Wik A video of his "mathmagic" is here
And his book, The Magic of Math: Solving for x and Figuring Out Why, is delightful,
DEATHS
1406 Ibn Khaldūn or Ibn Khaldoun Al-Ḥaḍrami, May 27, 1332 AD/732 AH – March 19, 1406 AD/808 AH) was a Muslim historiographer and historian who is often viewed as one of the fathers of modern historiography,sociology and economics.He is best known for his Muqaddimah (known as Prolegomenon in English), which was discovered, evaluated and fully appreciated first by 19th century European scholarship, although it has also had considerable influence on 17th-century Ottoman historians like Ḥajjī Khalīfa and Mustafa Naima who relied on his theories to analyze the growth and decline of the Ottoman Empire. Later in the 19th century, Western scholars recognized him as one of the greatest philosophers to come out of the Muslim world. *Wik
Ibn Khaldun Statue and Square, Mohandessin, Cairo
1862 John Edward Campbell (27 May 1862, Lisburn, Ireland – 1 October 1924, Oxford, Oxfordshire, England) is remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras. *SAU His 1903 book, Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups, popularized the ideas of Sophus Lie among British mathematicians.
He was elected a Fellow of the Royal Society in 1905, and served as President of the London Mathematical Society from 1918 to 1920. *Wik
1685 René François Walter de Sluse (2 July 1622 in Visé, Principality of Liège (now Belgium) - 19 March 1685 in Liège, Principality of Liège (now Belgium)) a French mathematician, intellectual and clergyman who wrote many books about mathematics and contributed to the development of mathematics.
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| Plague in Église Saint-Martin |
He studied at a university in Rome, and later moved to Liège. His position in the church prevented him from visiting other mathematicians, but he corresponded with the mathematicians and intellectuals of the day.
He studied calculus and his work discusses spirals, tangents, turning points and points of inflection.
There is a family of curves named after him called the Pearls of Sluze: the curves represented by the following equation with positive integer values of m, n and p:
yn = k(a - x)pxm *Wik
This group of curves was studied by de Sluze between 1657 and 1698. It was Blaise Pascal who named the curves after de Sluze.
1922 George Ballard Mathews, FRS (February 23, 1861 — March 19, 1922) was a London born mathematician who specialized in number theory.
After receiving his degree (as Senior Wrangler) from St John's College, Cambridge in 1883, he was elected a Fellow of St John's College. *Wik Mathews also wrote Algebraic equations (1907) which is a clear exposition of Galois theory, and Projective geometry (1914). This latter book develops the subject of projective geometry without using the concept of distance and it bases projective geometry on a minimal set of axioms. The book also treats von Staudt's theory of complex elements as defined by real involutions. The book contains a wealth of information concerning the projective geometry of conics and quadrics. *SAU
1930 Henry Faulds (1 Jun 1843, 19 Mar 1930 at age 86) Scottish physician who, from 1873, became a missionary in Japan, where he worked as a surgeon superintendent at a Tokyo hospital, taught at the local university, and founded the Tokyo Institute for the Blind. In the late 1870s, his attention was drawn to fingerprints of ancient potters remaining on their work that he helped unearth at an archaeological dig site in Japan. He commenced a study of fingerprints, and became convinced that each individual had a unique pattern. He corresponded on the subject with Charles Darwin, and published a paper about his ideas in Nature (28 Oct 1880). When he returned to Britain in 1886, he unsuccessfully offered his fingerprinting identification scheme for forensic uses to Scotland Yard. Undeserved confusion on priority for the discovery with Francis Galton and Sir William J. Herschel lasted until 1917. *TIS
1978 Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are closely related.*Wik A report of his bravery during WWI during which he lost his nose:
January 25, 1915, showed complete contempt for danger. Under an extremely violent bombardment, he succeeded despite his youth (22 years) to give a real example to his men. Struck by a bullet in the middle of his face causing a terrible injury, he could no longer speak but wrote on a ticket that he would not be evacuated. He only went to the ambulance when the attack had been driven back. It was the first time this officer had come under fire.When only 25 years of age, Julia published his 199 page masterpiece Mémoire sur l'iteration des fonctions rationelles which made him famous in the mathematics centres of his day. The beautiful paper, published in Journal de Math. Pure et Appl. 8 (1918), 47-245, concerned the iteration of a rational function f. Julia gave a precise description of the set J(f) of those z in C for which the nth iterate f n(z) stays bounded as n tends to infinity. (These are the Julia Sets popularized by Mandelbrot) *SAU
1984 Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an American applied mathematician, celebrated for his invention of dynamic programming in 1953, and important contributions in other fields of mathematics. A Bellman equation, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. Almost any problem which can be solved using optimal control theory can also be solved by analyzing the appropriate Bellman equation. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory. The "Curse of dimensionality", is a term coined by Bellman to describe the problem caused by the exponential increase in volume associated with adding extra dimensions to a (mathematical) space.*Wik
He is buried in the Cimetière de Neuilly-sur-Seine (Ancien),Hauts-de-Seine, Ile-de-France Region, France. (Just outside Paris)
1933 Chen Jingrun (Chinese: 陳景潤; 22 May 1933 – 19 March 1996), also known as Jing-Run Chen, was a Chinese mathematician who made significant contributions to number theory, including Chen's theorem and the Chen prime.
His work on the twin prime conjecture, Waring's problem, Goldbach's conjecture and Legendre's conjecture led to progress in analytic number theory. In a 1966 paper he proved what is now called Chen's theorem: every sufficiently large even number can be written as the sum of a prime and a semiprime (the product of two primes) – e.g., 100 = 23 + 7·11. Despite being persecuted during the Cultural Revolution, he expanded his proof in the 1970s.
After the end of the Cultural Revolution, Xu Chi wrote a biography of Chen entitled Goldbach's Conjecture). First published in People's Literature in January 1978, it was reprinted on the People's Daily a month later and became a national sensation. Chen became a household name in China and received a sackful of love letters from all over the country within two months.
Chen died of complications of pneumonia on March 19, 1996, at the age of 63 years
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2011 J(ames) Laurie Snell, (January 15th, 1925, Wheaton, Illinois; March 19, 2011, Hanover, New Hampshire) was an American mathematician.
A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995. Among his publications was the book "Introduction to Finite Mathematics", written with John George Kemeny and Gerald L. Thompson, first published in 1956 and in multiple editions since.
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating the price process. Snell has published the related theory 1952 in the paper Applications of martingale system theorems.*Wik
A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995. Among his publications was the book "Introduction to Finite Mathematics", written with John George Kemeny and Gerald L. Thompson, first published in 1956 and in multiple editions since.
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating the price process. Snell has published the related theory 1952 in the paper Applications of martingale system theorems.*Wik
Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell
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