Pat'sBlog

Saturday, 26 December 2015

On This Day in Math - December 26

A young man passes from our public schools to the universities, ignorant almost of the elements of every branch of useful knowledge.
~Charles Babbage

The 360th day of the year; Bryant Tuckerman found the Mersenne prime M19937 using an IBM360. *Prime Curios
360 is also the number of degrees in a full circle, and there is a (rather new) word for two angles that sum to 360 degrees. They are called "explementary" .

360 is a highly composite number, it has 24 divisors, more than any other number that is below twice its size.
It is the smallest number that is divisible by nine of the ten numbers 1-10 (not divisible by 7) What is next, students?

There are 360 possible rook moves on a 6x6 chess board.*Derek Orr

360 is centered on the 360th digit of pi (Also from Derek)[However they do occur once earlier centered at position 286.]

EVENTS
1837 Charles Babbage completed his “Calculating Engine” manuscript. *VFR

1843 John Graves write to William Rowan Hamilton that he has invented an eight-dimension normed division algebra he called "Octaves" Within a few months, Hamilton would realize that the octonions were not associative. This would lead to the first use of the term "associative" by Hamilton in 1844. (Except for matrices, which were not generally considered as "numbers", there were no common non-associative systems at that time) *Joan Baez Rankin Lecture of September 17, 2008 Glascow
The complete Volume Two of the Proceedings of the Royal Irish Academy were released in 1844, but the paper had been read on November 13, 1843; over a full month before Grave's letter. Hamilton created the phrase in explaining that although the Quaterninons maintained the distributive property, "yet the commutative character is lost," and then adds, "another important property of the old multiplication is preserved ... which may be called the associative character of the operation."
,

1864 The official seal of MIT was adopted on December 26, 1864. The craftsman at the anvil and the scholar with a book on the seal of the Massachusetts Institute of Technology embody the educational philosophy of William Barton Rogers and other incorporators of MIT as stated in their 1860 proposal Objects and Plan of an Institute of Technology. *MIT History

1898 Radium discovered by Pierre and Marie Curie. *VFR Actually, it seems this was the date of their announcement of the discovery(which must have occurred a few days earlier. They created the name radium for their element. This was their second discovery in the first year of her research on her thesis. They had also discovered Polonium earlier in the year.

In 1906, the world's first full-length feature film, the 70-min Story of the Kelly Gang was presented in the Town Hall at Melbourne, Australia, where it had been filmed at a cost of £450. It preceded D.W. Griffith's The Birth of a Nation by nine years. The subject of the Australian movie was Ned Kelly, a bandit who lived 1855 to 1880. The film toured through Australia for over 20 years, and abroad in New Zealand and Britain. Since some people, including politicians and police viewed the content of the film as glorifying the criminals, the movie was banned (1907) in Benalla and Wangaratta and also in Victoria (1912). Only fragments totalling about 10 minutes of the original nitrate film have survived to the present.*TIS

1951 Kurt Godel delivered the Gibbs Lecture, “Some Basic Theorems on the Foundations of Mathematics and their Philosophical Implications,” to the annual AMS meeting at Brown University. *VFR

1982 TIME Names a Non-Human “Man of the Year”
TIME magazine's editors selected the Personal Computer for “Machine of the Year,” in lieu of their well-known “Man of the Year” award. The computer beat out U.S. President Ronald Reagan, U.K. prime minister Margaret Thatcher and Prime Minister of Israel, Menachem Begin. The planet Earth became the second non-human recipient for the award in 1988. The awards have been given since 1927. The magazine's essay reported that in 1982, 80% of Americans expected that "in the fairly near future, home computers will be as commonplace as television sets or dishwashers.” In 1980, 724,000 personal computers were sold in the United States, according to Time. The following year, that number doubled to 1.4 million. *CHM

BIRTHS1532 Wilhelm Xylander (born Wilhelm Holtzman, graecized to Xylander) (December 26, 1532 – February 10, 1576) was a German classical scholar and humanist.
Xylander was the author of a number of important works. He translated the first six books of Euclid into German with notes, the Arithmetica of Diophantus, and the De quattuor mathematicis scientiis of Michael Psellus into Latin. *Wik

1780 Mary Fairfax Greig Somerville (26 Dec 1780 in Jedburgh, Roxburghshire, Scotland - 29 Nov 1872 in Naples, Italy) Somerville wrote many works which influenced Maxwell. Her discussion of a hypothetical planet perturbing Uranus led Adams to his investigation. Somerville College in Oxford was named after her.*SAU

1791 Charles Babbage born. *VFR (26 Dec 1791; 18 Oct 1871) English mathematician and pioneer of mechanical computation, which he pursued to eliminate inaccuracies in mathematical tables. By 1822, he had a small calculating machine able to compute squares. He produced prototypes of portions of a larger Difference Engine. (Georg and Edvard Schuetz later constructed the first working devices to the same design which were successful in limited applications.) In 1833 he began his programmable Analytical Machine, a forerunner of modern computers. His other inventions include the cowcatcher, dynamometer, standard railroad gauge, uniform postal rates, occulting lights for lighthouses, Greenwich time signals, heliograph opthalmoscope. He also had an interest in cyphers and lock-picking.*TIS

1861 Frederick Engle born in Germany. He became the closest student of the Norwegian mathe¬matician Sophus Lie. Engle was also the ﬁrst to translate Lobachevsky’s work into a Western language (German). *VFR

1900 Antoni Zygmund (26 Dec 1900; 30 May 1992) Polish-born mathematician who created a major analysis research centre at Chicago, and recognized in 1986 for this with the National Medal for Science. In 1940, he escaped with his wife and son from German controlled Poland to the USA. He did much work in harmonic analysis, a statistical method for determining the amplitude and period of certain harmonic or wave components in a set of data with the aid of Fourier series. Such technique can be applied in various fields of science and technology, including natural phenomena such as sea tides. He also did major work in Fourier analysis and its application to partial differential equations. Zygmund's book Trigonometric Series (1935) is a classic, definitive work on the subject*TIS

1903 Lancelot Stephen Bosanquet (26 Dec 1903 in St. Stephen's-by-Saltash, Cornwall, England - 10 Jan 1984 in Cambridge, Cambridgeshire, England) Bosanquet wrote many papers on the convergence and summability of Fourier series. He also wrote on the convergence and summability of Dirichlet series and studied specific kinds of summability such as summability factors for Cesàro means. His later work on integrals include two major papers on the Laplace-Stieltjes integral published in 1953 and 1961. Other topics he studied included inequalities, mean-value theorems, Tauberian theorems, and convexity theorems. *SAU

1937 John Horton Conway (born 26 December 1937, ) is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He has also contributed to many branches of recreational mathematics, notably the invention of the cellular automaton called the Game of Life.
Conway is currently Professor of Mathematics and John Von Neumann Professor in Applied and Computational Mathematics at Princeton University. He studied at Cambridge, where he started research under Harold Davenport. He received the Berwick Prize (1971),[1] was elected a Fellow of the Royal Society (1981),[2] was the first recipient of the Pólya Prize (LMS) (1987),[1] won the Nemmers Prize in Mathematics (1998) and received the Leroy P. Steele Prize for Mathematical Exposition (2000) of the American Mathematical Society. He has an Erdős number of one.*Wik Conway is known for his sense of humor, and the last proof in his "On Numbers and Games" is this:
Theorem 100; This is the last Theorem in this book.
The Proof is Obvious.

DEATHS
1624 Simon Marius (10 Jan 1573, 26 Dec 1624) (Also known as Simon Mayr) German astronomer, pupil of Tycho Brahe, one of the earliest users of the telescope and the first in print to make mention the Andromeda nebula (1612). He studied and named the four largest moons of Jupiter as then known: Io, Europa, Ganymede and Callisto (1609) after mythological figures closely involved in love with Jupiter. Although he may have made his discovery independently of Galileo, when Marius claimed to have discovered these satellites of Jupiter (1609), in a dispute over priority, it was Galileo who was credited by other astronomers. However, Marius was the first to prepare tables of the mean periodic motions of these moons. He also observed sunspots in 1611 *TIS You can find a nice blog about the conflict with Galileo by the Renaissance Mathematicus.

1931 Melvil Dewey (10 Dec 1851, 26 Dec 1931) American librarian who developed library science in the U.S., especially with his system of classification, the Dewey Decimal Classification (1876), for library cataloging. His system of classification (1876) uses numbers from 000 to 999 to cover the general fields of knowledge and designating more specific subjects by the use of decimal points. He was an activist in the spelling reform and metric system movements. Dewey invented the vertical office file, winning a gold medal at the 1893 World's Fair. It was essentially an enlarged version of a card catalogue, where paper documents hung vertically in long drawers. *TIS

2006 Martin David Kruskal (September 28, 1925 – December 26, 2006) was an American mathematician and physicist. He made fundamental contributions in many areas of mathematics and science, ranging from plasma physics to general relativity and from nonlinear analysis to asymptotic analysis. His single most celebrated contribution was the discovery and theory of solitons. His Ph.D. dissertation, written under the direction of Richard Courant and Bernard Friedman at New York University, was on the topic "The Bridge Theorem For Minimal Surfaces." He received his Ph.D. in 1952.
In the 1950s and early 1960s, he worked largely on plasma physics, developing many ideas that are now fundamental in the field. His theory of adiabatic invariants was important in fusion research. Important concepts of plasma physics that bear his name include the Kruskal–Shafranov instability and the Bernstein–Greene–Kruskal (BGK) modes. With I. B. Bernstein, E. A. Frieman, and R. M. Kulsrud, he developed the MHD (or magnetohydrodynamic) Energy Principle. His interests extended to plasma astrophysics as well as laboratory plasmas. Martin Kruskal's work in plasma physics is considered by some to be his most outstanding.
In 1960, Kruskal discovered the full classical spacetime structure of the simplest type of black hole in General Relativity. A spherically symmetric black hole can be described by the Schwarzschild solution, which was discovered in the early days of General Relativity. However, in its original form, this solution only describes the region exterior to the horizon of the black hole. Kruskal (in parallel with George Szekeres) discovered the maximal analytic continuation of the Schwarzschild solution, which he exhibited elegantly using what are now called Kruskal–Szekeres coordinates.
This led Kruskal to the astonishing discovery that the interior of the black hole looks like a "wormhole" connecting two identical, asymptotically flat universes. This was the first real example of a wormhole solution in General Relativity. The wormhole collapses to a singularity before any observer or signal can travel from one universe to the other. This is now believed to be the general fate of wormholes in General Relativity.
Martin Kruskal was married to Laura Kruskal, his wife of 56 years. Laura is well known as a lecturer and writer about origami and originator of many new models.[3] Martin, who had a great love of games, puzzles, and word play of all kinds, also invented several quite unusual origami models including an envelope for sending secret messages (anyone who unfolded the envelope to read the message would have great difficulty refolding it to conceal the deed).
His Mother, Lillian Rose Vorhaus Kruskal Oppenheimer was an American origami pioneer. She popularized origami in the West starting in the 1950s, and is credited with popularizing the Japanese term origami in English-speaking circles, which gradually supplanted the literal translation paper folding that had been used earlier. In the 1960s she co-wrote several popular books on origami with Shari Lewis.*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

Friday, 25 December 2015

On This Day in Math - December 25

God Bless Us, Everyone

Me, and Tiny Tim

The 359th day of the year; 359 is a Sophie Germain prime. If you start with n=89 and iterate 2n+1 you will get a string of primes that includes 359. (How many in all?)
It is also the smallest Sophie Germain prime whose reversal, 953 is also a Sophie Germain prime
and Sadly, the last day of the year that is prime.

EVENTS
1843 Sir Henry Cole British industrial designer, museum director and writer who produced the first commercial Christmas card. In 1843, wishing to save much handwriting of seasonal correspondence, Cole introduced the world's first commercial Christmas card. He commissioned artist John Callcott Horsley to make the artwork for 1000 hand-coloured lithographs. (Individuals' homemade Christmas cards had existed earlier.) (See Image at top)

1656 Huygens (who was a bachelor) spent Christmas Day making the ﬁrst model of a pendulum clock. *VFR(And then he was visited by three spirits.... oops, wrong story)

In 1741, the Centigrade temperature scale was devised by astronomer Anders Celsius (1701-44) and incorporated into a Delisle thermometer at Uppsala in Sweden. Celsius divided the fixed-point range of the Fahrenheit scale (the freezing and boiling temperatures of water) into 100 equal divisions, but curiously set the freezing point at 100 and the boiling point at 0. This reverse scaling was changed to match the sense of the other temperature scales after Celsius's death.*TIS

1758 Halley’s comet ﬁrst sighted after he predicted its return. After Newton explained planetary motion, he suggested that comets could have elongated elliptical orbits. Halley’s comet has eccentricity 0.9675. [UMAP Journal, 4(1983), p. 162] *VFR
In 1758, the predicted return of Halley's comet was first sighted by German farmer and amateur astronomer, Johann Georg Palitzsch, as a faint object in Pisces. Edmund Halley had predicted in 1705 the return of the comet to the Earth's vicinity every 75.5 years. For the first time the scientific prediction had been proven. Halley himself had died 16 years before this new event. Palitzsch also observed the 6 Jun 1761 transit of Venus, when he saw a black band linking Venus and the Sun near the beginning and end of the transit ("black drop effect") and correctly interpreted this as evidence that Venus possessed an atmosphere. He also measured the period of the variation of the brightness of the star Algol. *TIS
The BAYEUX TAPESTRY (Tapisserie de la Reine Mathilde) includes a clear picture of Halley's Comet, as shown on the stamp below.

and here is a Blog regarding the return in 1758.

In 1780, Luigi Galvani recorded, "The electric fluid should be considered a means to the nervo-muscular force." He reached this conclusion from work in his laboratory in Bologna, Italy, after a series of experiments and his accidental discovery that muscles are operated by electrical stimulation of nerves. He worked diligently along these lines, but waited for eleven years before he published the results and an ingenious and simple theory. His theory was that of a nervous electric fluid, secreted by the brain, conducted by the nerves, and stored in the muscles. Though his ideas were abandoned by scientists on account of later discoveries, his work opened the way to new research in the physiology of muscle and nerve and pioneered the subject of electrophysiology. *TIS

In 1999, space shuttle Discovery's astronauts finished their maintenance work on the Hubble Space Telescope, installing correcting optics to repair problems due to a design flaw in the mirror. The first images the Hubble Telescope took after its original launch were disappointingly fuzzy, but after this repair mission the instrument returned crisp images of a clarity never before possible from terrestrial observatories *TIS

BIRTHS
1642 Isaac Newton born on Julian Calendar. (5 January 1643 New style) *VFR
Born 25 Dec 1642; died 20 Mar 1727. English physicist and mathematician, who made seminal discoveries in several areas of science, and was the leading scientist of his era. His study of optics included using a prism to show white light could be split into a spectrum of colours. The statement of his three laws of motion are fundamental in the study of mechanics. He was the first to describe the moon as falling (in a circle around the earth) under the same influence of gravity as a falling apple, embodied in his law of universal gravitation. As a mathematician, he devised infinitesimal calculus to make the calculations needed in his studies, which he published in Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy, 1687)*TIS

1763 Claude Chappe (25 Dec 1763; 23 Jan 1805) French engineer who invented the semaphore visual telegraph. He began experimenting in 1790, trying various types of telegraph. An early trial used telescopes, synchronised pendulum clocks and a large white board, painted black on the back, with which he succeeded in sending a message a few sentences long across a 16km (10mi) distance. To simplify construction, yet still easily visible to read from far away, he changed to using his semaphore telegraph in 1793. Smaller indicators were pivoted at each end of large horizontal member. The two indicators could each be rotated to stand in any of eight equally spaced positions. By setting them at different orientations, a set of corresponding codes was used to send a message.*TIS

1900 Antoni Szczepan Zygmund (25 Dec 1900 in Warsaw, Russian Empire (now Poland)
- 30 May 1992 in Chicago, Illinois, USA) Zygmund's work in harmonic analysis has application in the theory of waves and vibrations. He also did major work in Fourier analysis and its application to partial differential equations.*SAU

1905 Gottfried Maria Hugo Köthe (born 25 December 1905 in Graz; died 30 April 1989 in Frankfurt) was an Austrian mathematician working in abstract algebra and functional analysis.*SAU Köthe's best known work has been in the theory of topological vector spaces. In 1960, volume 1 of his seminal monograph Topologische lineare Räume was published (the second edition was translated into English in 1969). It was not until 1979 that volume 2 appeared, this time written in English. He also made contributions to the theory of lattices. *Wik

DEATHS
1921 Piers Bohl (October 23, 1865 – December 25, 1921) was a Latvian mathematician, who worked in differential equations, topology and quasi-periodic functions.
He was born in 1865 in Walk, Livonia, in the family of a poor Baltic German merchant. In 1884, after graduating from a German school in Viljandi, he entered the faculty of physics and mathematics at the University of Tartu. In 1893 Bohl was awarded his Master's degree. This was for an investigation of quasi-periodic functions. The notion of quasi-periodic functions was generalised still further by Harald Bohr when he introduced almost-periodic functions. *Wik

1929 Percy Alexander MacMahon (b. 26 September 1854, Sliema, Malta – 25 December 1929, Bognor Regis, England) was a mathematician, especially noted in connection with the partitions of numbers and enumerative combinatorics. MacMahon was elected a Fellow of the Royal Society in 1890. He received the Royal Society Royal Medal in 1900, the Sylvester Medal in 1919, and the Morgan Medal by the London Mathematical Society in 1923. MacMahon was the President of the London Mathematical Society from 1894 to 1896.
MacMahon is best known for his study of symmetric functions and enumeration of plane partitions; see MacMahon Master theorem. His two volume Combinatory analysis, published in 1915/16, is the first major book in enumerative combinatorics. MacMahon also did pioneering work in recreational mathematics and patented several successful puzzles.*WIK

1930 Eugen Goldstein (5 Sep 1850, 25 Dec 1930) German physicist who discovered and named canal rays (1886) which emerge through holes in the anodes of low-pressure electrical discharge tubes (later shown to be positively charged particles). Earlier, he coined the term "cathode ray" (1876) emitted from a cathode. He was the first to see that they could cast a shadow, and were emitted at right angles to the surface. He also investigated the wavelengths of light emitted by metals and oxides when canal rays impinge on them. When the Berlin Urania, opened in 1889 it had five scientific departments and a "science theatre", it was Goldstein who had recommended the "hall of physics in which the visitor could experiment on his own". Students of his that continued his work included Wien and Stark. *TIS

1941 Theodor Molien or Fedor Eduardovich Molin (September 10, 1861 - December 25, 1941) was a Baltic-German mathematician. He was born in Riga, Latvia, which at that time was a part of Russian Empire. Molien studied associative algebras and polynomial invariants of finite groups.*Wik

1944 Wilhelm Kutta was a German engineer who is best known for his work on the numerical solution of differential equations (the Runge-Kutta method).*SAU Kutta was born in Pitschen, Upper Silesia (today Byczyna, Poland). He attended the University of Breslau from 1885 to 1890, and continued his studies in Munich until 1894, where he became the assistant of Walther Franz Anton von Dyck. From 1898, he spent half a year at the University of Cambridge.[1] From 1899 to 1909 he worked again as an assistant of von Dyck in Munich; from 1909 to 1910 he was adjunct professor at the Friedrich Schiller University Jena. He was professor at the RWTH Aachen from 1910 to 1912. Kutta became professor at the University of Stuttgart in 1912, where he stayed until his retirement in 1935.
In 1901, he co-developed the Runge-Kutta method, used to solve ordinary differential equations numerically. He is also remembered for the Zhukovsky-Kutta aerofoil, the Kutta-Zhukovsky theorem and the Kutta condition in aerodynamics. Kutta died in Fürstenfeldbruck, Germany in 1944. *Wik

2000 Willard Van Orman Quine (June 25, 1908 – December 25, 2000) (known to intimates as "Van")[1] was an American philosopher and logician in the analytic tradition. From 1930 until his death 70 years later, Quine was continuously affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of mathematics, and finally as a professor emeritus who published or revised several books in retirement. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978. A recent poll conducted among philosophers named Quine one of the five most important philosophers of the past two centuries.[2] He won the first Schock Prize in Logic and Philosophy in 1993, for "his systematical and penetrating discussions of how learning of language and communication are based on socially available evidence and of the consequences of this for theories on knowledge and linguistic meaning.*Wik

Thursday, 24 December 2015

On This Day in Math - December 24

Earthrise: See 1968 below

The 358th day of the year; 358 is twice a prime, and the sum of six consecutive primes.
The sum of the first 358 prime numbers is itself a prime number.

EVENTS
1754 Euler writes to Muller in St Petersburg and describes d'Alembert as "the most argumentative man in the world," and calls him, "hated by everyone in Paris." *Thomas L. Hankins, Jean d'Alembert: science and the Englightenment; pg 58

1819 Bernard Bolzano was dismissed from his theological chair at the University of Prague and put under police supervision for his unorthodox religious views. In mathematics he helped remove the scandal of inﬁnitesimals from the calculus. *VFR

1849 Guass writes to the Astronomer Johann Franz Encke in response to Encke's remarks about the Frequency of Primes.

"Most Honored Friend!
. . .The kind communication of your remarks on the frequency of prime numbers
was interesting to me in more than one respect. You have reminded me of
my own pursuit of the same subject, whose first beginnings occurred a very long
time ago, in 1792 or 1793, when I had procured for myself Lambert’s supplement
to the table of logarithms. Before I had occupied myself with the finer
investigations of higher arithmetic, one of my first projects was to direct my
attention to the decreasing frequency of prime numbers, to which end I counted
them up in several chiliads (sets of a thousand) and recorded the results on one of the affixed white sheets. I soon recognized, that under all variations of this frequency, on average, it is nearly inversely proportional to the logarithm..."

Guass never published his results. The first published version of the Prime Number Theorem was by Legendre in 1798. *John Derbyshire, Prime Obsession

1899 the Physico-Mathematic Society of Kazan (Russia) celebrated a Jubilee in honor of the twenty-fifth year of professional and scientific service of its President, Professor A. Vasiliev. It is also the fifteenth year of his presidency. Professor Vasiliev has been an extraordinarily important figure in Russian science. Outside of Russia he has chiefly
been known for his remarkable discourse on Lobachevski. *The American Mathematical Monthly, Vol. 7, No. 1 (Jan., 1900), p. 30

1906 First Long Range transmisson of voice: Reginald Aubrey Fessenden was a Canadian inventor and engineer with 300 patents. He broadcast the first program of voice and music. In 1893, Fessenden moved to Pittsburgh as the head of electrical engineering at the university, Fessenden read of Marconi's work and began experimenting himself. Marconi could only transmit Morse code. But Fessenden's goal was to transmit the human voice and music. He invented the "continuous wave": sound superimposed onto a radio wave for transmission. A radio receiver extracts the signal so the listener with the original sound. Fessenden made the first long-range transmissions of voice on Christmas Eve 1906 from a station at Brant Rock, Massachusetts, heard hundreds of miles out in the Atlantic.*TIS He used a 42 kHz radio frequency Alexanderson alternator which produced about 1kW of power. Although Fessenden's work made voice radio possible, it would take 10 years and the First World War before it became commonplace. Throughout this period, radio was still seen primarily as point-to-point communication between transmitting stations--a sort of wireless telephone. *CHM

1912 Irving Fisher (1867-1947), a Yale professor, patented an archiving system with index cards. On 1 Jul 1925, Fisher's own firm, the Index Visible Company, merged with its principal competitor to form Kardex Rand Co., later Remington Rand, still later Sperry Rand. Fisher earned about $$1 million$ for the invention, which grew to the princely sum of $$9 million$ before being lost in the stock market crash of 1929. Fisher is widely regarded as the greatest economist America has produced, who made much use of mathematics in his work.*TIS

1968 On Christmas Eve, the Apollo 8 astronauts saw the entirety of Earth for the first time. Turing their cameras to the Earth they took the first three pictures of the whole earth from space. The one above, by William Anders, has been called "the most influential environmental photograph ever taken." *Wik, NASA

In 2004, the Huygens probe began a 22-day descent towards Saturn's largest moon, Titan. It had been launched as part of the Cassini spacecraft in 1997, and together they entered Saturn's orbit in June 2004. As the paths of the spacecraft and Titan converged, Cassini ejected the Huygens probe, sending it on a 22-day coast toward the cloud-covered moon. It landed 14 Jan 2005, and sent back photgraphs of the moon's surface. Cassini will remain in orbit around Saturn until at least July 2008. The Cassini-Huygens mission to study Saturn and its 33 known moons resulted from an unprecedented cooperative effort between the NASA of the United States, the European Space Agency and Italy's space program, at a cost of $3.3 billion. *TIS

BIRTHS
1740 Anders Johan Lexell (December 24, 1740 – December 11, 1784 (Julian calendar: November 30)) was a Swedish-born Russian astronomer, mathematician, and physicist who spent most of his life in Russia where he is known as Andrei Ivanovich Leksel.
Lexell made important discoveries in polygonometry and celestial mechanics; the latter led to a comet named in his honor. La Grande Encyclopédie states that he was the prominent mathematician of his time who contributed to the spherical trigonometry with new and interesting solutions, which he took as a basis for his research of comet and planet motion. His name was given to one of the theorems about spherical triangles.
Lexell was one of the most prolific members of the Russian Academy of Sciences at that time, having published 66 papers in 16 years of his work there. A statement attributed to Leonhard Euler expresses high approval of Lexell's works: "Besides Lexell, such a paper could only be written by D'Alambert or me". Daniel Bernoulli also praised his work, writing in a letter to Johann Euler "I like Lexell's works, they are profound and interesting, and the value of them is increased even more because of his modesty, which adorns great men".
Lexell did not have a family and kept up a close friendship with Leonhard Euler and his family. He witnessed Euler's death at his house and succeeded him to the chair of the mathematics department at the Russian Academy of Sciences, but died the following year. The asteroid 2004 Lexell is named in his honour, as is the lunar crater Lexell.*Wik

1818 James Prescott Joule (24 Dec 1818; 11 Oct 1889) English physicist who established that the various forms of energy - mechanical, electrical, and heat - are basically the same and can be changed, one into another. Thus he formed the basis of the law of conservation of energy, the first law of thermodynamics. He discovered (1840) the relationship between electric current, resistance, and the amount of heat produced. In 1849 he devised the kinetic theory of gases, and a year later announced the mechanical equivalent of heat. Later, with William Thomson (Lord Kelvin), he discovered the Joule-Thomson effect. The SI unit of energy or work , the joule (symbol J), is named after him. It is defined as the work done when a force of 1 newton moves a distance of 1 metre in the direction of the force.*TIS

1822 Charles Hermite (24 Dec 1822; 14 Jan 1901) French mathematician whose work in the theory of functions includes the application of elliptic functions to provide the first solution to the general equation of the fifth degree, the quintic equation. In 1873 he published the first proof that e is a transcendental number. Hermite is known also for a number of mathematical entities that bear his name, Hermite polynomials, Hermite's differential equation, Hermite's formula of interpolation and Hermitian matrices. Poincaré is the best known of Hermite's students.*TIS

1838 Thorvald Nicolai Thiele (24 December 1838 – 26 September 1910) was a Danish astronomer, actuary and mathematician, most notable for his work in statistics, interpolation and the three-body problem. He was the first to propose a mathematical theory of Brownian motion. Thiele introduced the cumulants and (in Danish) the likelihood function; these contributions were not credited to Thiele by Ronald A. Fisher, who nevertheless named Thiele to his (short) list of the greatest statisticians of all time on the strength of Thiele's other contributions.
Thiele also was a founder and Mathematical Director of the Hafnia Insurance Company and led the founding of the Danish Society of Actuaries. It was through his insurance work that he came into contact with fellow mathematician Jørgen Pedersen Gram. Asteroid 843 Nicolaia is named in his honor. *Wik

1868 Emanuel Lasker (24 Dec 1868 in Berlinchen, Prussia (now Barlinek, Poland) - 11 Jan 1941 in New York, USA) Lasker became World Chess Champion in 1894 and held the championship until 1921. In mathematics he introduced the notion of a primary ideal. *SAU

1904 Sir William Hunter McCrea FRS (13 December 1904, Dublin – 25 April 1999) was an English astronomer and mathematician. He went to Trinity College, Cambridge in 1923 where he studied Mathematics, later gaining a PhD in 1929 under Ralph H. Fowler. He was later appointed a lecturer of Mathematics at the University of Edinburgh in 1929. He also served as reader and assistant professor at Imperial College London. In 1936 he became head of the mathematics department at the Queen's University of Belfast. After serving in the war, he joined the mathematics department at Royal Holloway College in 1944 (the McCrea Building on Royal Holloway's campus is named after him). In 1965, McCrea created the astronomy centre of the physics department at the University of Sussex.
In 1928, he studied Albrecht Unsöld's hypothesis, and discovered that three quarters of the Sun is made of Hydrogen, and about one quarter is Helium, with 1% being other elements. Previous to this many people thought the Sun consisted mostly of Iron. After this, people realized most stars consist of Hydrogen.
McCrea was president of the Royal Astronomical Society from 1961-3 and president of Section A of the British Association for the Advancement of Science from 1965-6. He was knighted in 1985. He won the Gold Medal of the Royal Astronomical Society in 1976. McCrea died on April 25, 1999 in Lewes. *Wik

1910 William Hayward Pickering (24 Dec 1910; 15 Mar 2004) Engineer and physicist, head of the team that developed Explorer 1, the first U.S. satellite. He collaborated with Neher and Robert Millikan on cosmic ray experiments in the 1930s, taught electronics in the 1930s, and was at Caltech during the war. He spent the rest of his career with the Jet Propusion Laboratory, becoming its Director (1954) with responsibility for the U.S. unmanned exploration of the planets and the solar system. Among these were the Mariner spacecraft to Venus and Mercury, and the Viking mission to Mars. The Voyager spacecraft yielded stunning photographs of the planets Jupiter and Saturn.*TIS

DEATHS
(How sad to be one of these people who died on Christmas Eve)
1872 William John Macquorn Rankine (5 Jul 1820, 24 Dec 1872) Scottish engineer and physicist and one of the founders of the science of thermodynamics, particularly in reference to steam-engine theory. As the chair (1855) of civil engineering and mechanics at Glasgow, he developed methods to solve the force distribution in frame structures. Rankine also wrote on fatigue in the metal of railway axles, on Earth pressures in soil mechanics and the stability of walls. He was elected a Fellow of the Royal Society in 1853. Among his most important works are Manual of Applied Mechanics (1858), Manual of the Steam Engine and Other Prime Movers (1859) and On the Thermodynamic Theory of Waves of Finite Longitudinal Disturbance. *TIS (Many students are not aware there is a absolute temperature scale called the Rankine, named for him)

1882 Johann Benedict Listing (25 July 1808 in Frankfurt am Main, Germany - 24 Dec 1882 in Göttingen, Germany)wrote one of the earliest texts on Topology. he studied the figure of the earth in minute detail; he made observations in meteorology, terrestrial magnetism, and spectroscopy; he wrote on the quantitative determination of sugar in the urine of diabetics; he promoted the nascent optical industry in Germany and better street lighting in Göttingen; he travelled to the world exhibitions in London 1851, Vienna 1873 and London 1876 as an observer for his government; he assisted in geodetic surveys; ... he invented a good many terms [other than topology], some of which have became current: "entropic phenomenona", "nodal points", "homocentric light", "telescopic system", " geoid" ...he coined "one micron" for the millionth of a metre ...*SAU

1927 William Henry Dines (5 Aug 1855, 24 Dec 1927) was an English meteorologist (like his father) and inventor of related measurement instruments such as the Dines pressure tube anemometer (the first instrument to measure both the velocity and direction of wind, 1901), a very lightweight meteorograph, and a radiometer (1920). He joined the Royal Meteorological Society study of the cause of the disastrous Tay Bridge collapse of 1879. His measurements of upper air conditions, first with kites and later by balloon ascents (1907), brought an understanding of cyclones from dynamic processes in the lower stratosphere rather than thermal effects nearer to the ground.*TIS

1962 Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.*Wik

1994 Alfred Leon Foster (13 July 1904 in New York City, New York, USA - 24 Dec 1994 in Berkeley, California, USA) Foster went on to define the concept of a primal algebra generalising a Boolean algebra within the theory of varieties of universal algebras. In 1953 showed that the variety generated by a primal algebra has the same essential structure as the variety of Boolean algebras. He continued devoting his efforts to the structure theory of algebras that are generalizations of Boolean algebras and, more than ten years down the line in 1966, he published Families of algebras with unique (sub-)direct factorization. Equational characterization of factorization in Mathematische Annalen.*SAU

2000 Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He is the son of William Henry Young and Grace Chisholm Young, both prominent mathematicians.
The concept of Young measure is named after him. *Wik

Wednesday, 23 December 2015

On This Day in Math - December 23

The mathematician may be compared to a designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago; to this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight.
~Tobias Danzig

The 357th day of the year; there are 357 odd numbers in the first 46 rows of Pascal's Arithmetic triangle.
s
357 is made up of three consecutive prime digits, and is the product of three distinct primes, 3 x 7 x 17=357

EVENTS

1493 The German version of the Nuremberg Chronicle - in German 'Schedelsche Weltchronik' - was published. It is one of the best-documented early printed books - an incunabulum - and one of the first to successfully integrate illustrations and text. Moreover, it was the most extensively illustrated book of the 15th century. See more detail and some of the beautiful graphics at *Yovisto

In 1672, astronomer Giovanni Cassini discovered Saturn's moon Rhea, the fifth major satellite of Saturn, which may be one of the most heavily cratered satellites in the solar system. Its surface appears to be saturated with craters, but long, bright linear features can be seen on the trailing hemisphere and linear ridges can be seen in the leading hemisphere. These ancient features may record changes in Rhea's shape due to internal heating or cooling. Rhea is 950 miles (1500 km) in diameter. Its largest crater is 190 miles (300 km) in diameter. Cassini also discovered three more of Saturn's major moons -- Iapetus, Tethys, and Dione. In 1675, he discovered that Saturn's rings are split largely into two parts by a narrow gap - known since as the "Cassini Division." *TS

1690 Flamsteed observes Uranus, but doesn’t recognize it as undiscovered planet. *VFR

1750, Benjamin Franklin was severely shocked while electrocuting a turkey.*TIS

1751 Jacobi called this the birthday of elliptic functions because on this day a work by the Italian mathematician Giulio Carlo Fagnano, which had been sent to the Berlin Academy, was handed to Euler for review. The study of this work led Euler to his important investigations on elliptic integrals and to the discovery of the addition theorem. [Cajori, Historical Introduction to Mathematical Literature, p. 213) *VFR Fagnano had discovered a way to find the length of a lemniscate.

1763 Price read Bayes’s essay to the Royal Society. *VFR Bayes never published what would eventually become his most famous accomplishment; his notes were edited and published after his death by Richard Price. In his later years he took a deep interest in probability. Stephen Stigler feels that he became interested in the subject while reviewing a work written in 1755 by Thomas Simpson,but George Alfred Barnard thinks he learned mathematics and probability from a book by de Moivre *Wik

1788 First use of "catenary", rather than the longer, more formal Latin "catenaria", may have been in a letter from Thomas Jefferson to Thomas Paine. Paine had written to Jefferson regarding the design of Iron Bridges. Jefferson's response was:

You hesitate between the catenary, and portion of a circle. I have lately received from Italy a treatise on the equilibrium of arches by the Abbe 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.'

The earliest citation for catenary in the OED2 is from the above letter. *Jeff Miller

1907 William Thompson, Lord Kelvin; died of a severe chill on 17 December 1907.
The Royal Society asked the Dean of Westminster if Kelvin could be buried in the Abbey and he agreed. The funeral was on 23 December and he lies to the south of Sir Isaac Newton's grave in the nave. On the previous night the coffin, covered by a purple pall, had rested in St Faith's chapel. The simple stone reads: WILLIAM THOMSON LORD KELVIN 1824-1907.
In 1913 a stained glass window, designed by J.Ninian Comper, was erected near the grave. This contains large figures of King Henry V and Abbot William Colchester and below is an inscription "In memory of Baron Kelvin of Largs. Engineer, Natural Philosopher. B.1824.D.1907". His coat of arms and those of Glasgow University are shown. The window was the gift of engineers from Great Britain and America. *Wik

1947 Bardeen and Brattain demonstrate the transistor to the Bell Labs brass
It was the point-contact transistor, made from strips of gold foil on a plastic triangle, pushed down into contact with a slab of germanium. To measure the amplification they hooked up a microphone to one end of the device and a loudspeaker to the other. One by one, the men picked up the microphone and whispered hello; the loudspeaker at the other end of the circuit shouted HELLO!
Later, realizing that another major breakthrough in electronics had occurred in Bell’s lab, Shockley wrote Hearing speech amplified by the transistor was in tradition of Alexander Graham Bell’s famous ‘Mr. Watson, come here, I want you.’*CHM (The name transistor came from its electrical property known as trans-resistance.)

1949 J. R. Arnold and W. F. Libby publish "Age determinations by radiocarbon content: checks with samples of known age", the results of their experiments on using Carbon 14 for dating ancient organic materials in Science Magazine. The experiments were done on samples of wood of known age. For example, two samples taken from the tombs of two Egyptian kings, Zoser and Sneferu, independently dated to 2625 BC plus or minus 75 years, were dated by radiocarbon measurement to an average of 2800 BC plus or minus 250 years. *Wik

In 1953, Dr. Robert Oppenheimer was notified that his security clearance had been suspended. (He had directed the Manhattan Project that produced the atomic bombs used during WW II). There were allegations questioning his trustworthiness for association with Communists. By telegram dated 29 Jan 1954, he requested a hearing. On 4 Mar 1954, he submitted his answer to the original notification. Within two weeks, the Commisssion informed him who would conduct the hearing, to be led by Gordon Gray. The hearing before the Gray Board began 12 Apr 1954. It returned a result on 29 Jun 1954 that by a vote of 4 to1, it had made a decision against reinstating Dr. J. Robert Oppenheimer's access to classified information.*TIS

1955 The term ALPHAMETIC was coined in 1955 by J. A. H. Hunter (Schwartzman). In the Dec. 23, 1955, Toronto Globe & Mail Hunter wrote, "These alphametics seem set to take the place of crosswords as a new craze... Don't forget that each letter stands for a particular figure" *Earliest Known Uses of Some of the Words of Mathematics
An alphametic is a peculiar type of mathematical puzzle, in which a set of words is written down in the form of an ordinary "long-hand" addition sum, and it is required that the letters of the alphabet be replaced with decimal digits so that the result is a valid arithmetic sum. For an example one can do no better than the first modern alphametic, published by the great puzzlist H.E. Dudeney in the July 1924 issue of Strand Magazine:

SEND
MORE
-----
MONEY

whose (unique) solution is:

9567
1085
-----
10652
*Alphametic Page BTW alph + a = metic is a self referential name since it is, itself, and alphametic.

In 1968, American astronauts on Apollo 8 became the first men to orbit the Moon. The three-man crew was Frank Borman (Commander), James A. Lovell, Jr. (Command Module Pilot) and William Anders (Lunar Module Pilot). Not only was this the first manned flight to and from the Moon, but Apollo 8 served to validate many of the technical procedures necessary to support upcoming lunar missions. During ten lunar orbits, the astronauts took star sightings to pinpoint landmarks, surveyed landing sites, took both still and motion pictures and made two television transmissions to Earth. It was also the world's first manned flight to escape the influence of Earth's gravity. Launched on 21 Dec 1968, the mission lasted 6 days 3 hours until recovery on 27 Dec 1968. *TIS

Apollo 8 crew. From left: Borman, Anders, Lovell. NASA.

1987 Egypt issued a stamp honoring the mathematician Ali Mustafa Mousharafa (1898–1950). [Scott #1147]. *VFR Dr. Ali Moustafa Mosharafa Pasha was an Egyptian theoretical physicist. He was professor of applied mathematics in the Faculty of Science at Cairo University, and also served as its first dean. *Wik

BIRTHS
1872 Georgii Pfeiffer did important work on partial differential equations.*SAU

1909 John Hamilton Curtiss is born on December 23, 1909. He obtained an MS degree in statistics from Northwestern University in 1930, and a PhD from Harvard in 1935. He obtained an MS degree in statistics from Northwestern University in 1930, and a PhD from Harvard in 1935. He had taught at Cornell University (1935-1943) and had served in U.S. Navy (1943-1946). In 1946 Curtiss joined National Bureau of Standards, where in 1947 he became a chief of the Applied Mathematical Division (AMD), the first centralized national computing center dedicated to accelerate the progress of USA in the computing industry. AMD's expertise proved the necessity of development of the UNIVAC, the SEAC, and the SWAC computers. At the same time Curtiss played the crucial role in the organization of ACM, then Eastern Association of Computing Machinery, and in 1947 he became the first ACM president.
Curtiss remained at NBS until 1953. From 1954 to 1959 he was an executive director of the American Mathematical Society. In 1959 he became a professor of mathematics at the University of Miami, where he remained until his death in 1977. While no one can recall Curtiss at the console of a computer, he always said that "I was involved in the salt mines of computing." *CHM

1936 Peter L. Hammer (December 23, 1936 - December 27, 2006) was an American mathematician native to Romania. He contributed to the fields of operations research and applied discrete mathematics through the study of pseudo-Boolean functions and their connections to graph theory and data mining.*Wk

1938 Robert E(lliot) Kahn (23 Dec 1938, ) American computer scientist who co-created the packet-switching protocols that enable computers to exchange information on the Internet. In the late 1960s Kahn realized that a packet-switching network could effectively transmit large amounts of data between computers. Along with fellow computer scientists Vinton Cerf, Lawrence Roberts, Paul Baran, and Leonard Kleinrock, Kahn built the ARPANET, the first network to successfully link computers around the country. Kahn and Cerf also developed the Transmission Control Protocol (TCP) and the Internet Protocol (IP), which together enable communication between different types of computers and networks; TCP/IP is the standard still in use today. *TIS

1943 Mikhail Leonidovich Gromov (23 December 1943 - ), is a French–Russian mathematician known for important contributions in many different areas of mathematics. He is considered a geometer in a very broad sense of the word. In 2009 he was awarded the Abel Prize "for his revolutionary contributions to geometry." *Wik

DEATHS
1722 Pierre Varignon (Caen 1654 – December 23, 1722 Paris) was a French mathematician. He was educated at the Jesuit College and the University in Caen, where he received his M.A. in 1682. He took Holy Orders the following year.
Varignon gained his first exposure to mathematics by reading Euclid and then Descartes' La Géométrie. He became professor of mathematics at the Collège Mazarin in Paris in 1688 and was elected to the Académie Royale des Sciences in the same year. In 1704 he held the departmental chair at Collège Mazarin and also became professor of mathematics at the Collège Royal. He was elected to the Berlin Academy in 1713 and to the Royal Society in 1718. Many of his works were published in Paris in 1725, three years after his death. His lectures at Mazarin were published in Elemens de mathematique in 1731.
Varignon was a friend of Newton, Leibniz, and the Bernoulli family. Varignon's principal contributions were to graphic statics and mechanics. Except for l'Hôpital, Varignon was the earliest and strongest French advocate of infinitesimal calculus, and exposed the errors in Michel Rolle's critique thereof. He recognized the importance of a test for the convergence of series, but analytical difficulties prevented his success. Nevertheless, he simplified the proofs of many propositions in mechanics, adapted Leibniz's calculus to the inertial mechanics of Newton's Principia, and treated mechanics in terms of the composition of forces in Projet d'une nouvelle mécanique in 1687. Among Varignon's other works was a 1699 publication concerning the application of differential calculus to fluid flow and to water clocks. In 1690 he created a mechanical explanation of gravitation. In 1702 he applied calculus to spring-driven clocks. *Wik
(Varignon's theorem is a statement in Euclidean geometry by Pierre Varignon that was first published in 1731. It deals with the construction of a particular parallelogram from an arbitrary quadrangle.

The midpoints of the sides of an arbitrary quadrangle form a parallelogram. If the quadrangle is convex or reentrant, i.e. not a crossing quadrangle, then the area of the parallelogram is half as big as the area of the quadrangle.

If one introduces the concept of oriented areas for n-gons, then the area equality above holds for crossed quadrangles as well.
The Varignon parallelogram exists even for a skew quadrilateral, and is planar whether or not the quadrilateral is planar. *Wik )

1834 Thomas Robert Malthus (13 Feb 1766; 23 Dec 1834 at age 68) English economist and demographer who can be regarded as a pioneer sociologist. He was one of the first to systematically analyze human society when he published his theories in An Essay on the Principle of Population. Malthus predicted population would always outrun the food supply and that would result in famine, disease or war to reduce the number of people. As Malthus observed the Industrial Revolution was causing a rapid increase in population, he indicated keeping improved social conditions would require imposing strict limits on reproduction. Reading the book inspired Charles Darwin to reflect upon the survival of the fittest individuals in the process of natural selection in evolving populations of any organism. Alfred Russell Wallace likewise acknowledged his theory was stimulated by the book by Malthus. *TIS

1890 Edward Sang,(30 Jan 1805 in Kirkcaldy, Fife, Scotland - 23 Dec 1890) A native of Fife, Sang wrote extensively on mathematical, mechanical, optical and actuarial topics. *SAU

1907 Pierre (-Jules-César) Janssen (22 Feb 1824, 23 Dec 1907) was a French astronomer who in 1868 devised a method for observing solar prominences without an eclipse (an idea reached independently by Englishman Joseph Norman Lockyer). Janssen observed the total Sun eclipse in India (1868). Using a spectroscope, he proved that the solar prominences are gaseous, and identified the chromosphere as a gaseous envelope of the Sun. He noted an unknown yellow spectral line in the Sun in 1868, and told Lockyer (who subsequently recognized it as a new element he named helium, from Greek "helios" for sun). Janssen was the first to note the granular appearance of the Sun, regularly photographed it, and published a substantial solar atlas with 6000 photographs (1904). *TIS

1973 Gerard Peter Kuiper (7 Dec 1905, 23 Dec 1973) Dutch-born American astronomer, who discovered Miranda, a moon of Uranus, and Nereid, a moon of Neptune. The Kuiper Belt is so-named after his original suggestion of its existence outside the orbit of Neptune before it was confirmed as a belt of small bodies. He measured the diameter of Pluto. In the Martian atmosphere Kuiper detected carbon dioxide, but the absence of oxygen (1947). In the 1960s, Kuiper pioneered airborne infrared observing using a Convair 990 aircraft and served as chief scientist for the Ranger spacecraft crash-landing probes of the moon. By analyzing Ranger photographs, he identified landing sites on the lunar surface most suitable for safe manned landings. *TIS

1989 Richard Rado FRS(28 April 1906 – 23 December 1989) was a Jewish German mathematician. He earned two Ph.D.s: in 1933 from the University of Berlin, and in 1935 from the University of Cambridge. He was interviewed in Berlin by Lord Cherwell for a scholarship given by the chemist Sir Robert Mond which provided financial support to study at Cambridge. After he was awarded the scholarship, Rado and his wife left for the UK in 1933. He made contributions in combinatorics and graph theory. He wrote 18 papers with Paul Erdős. In 1964, he discovered the Rado graph (The Rado graph contains all finite and countably infinite graphs as induced subgraphs..)
In 1972, he was awarded the Senior Berwick Prize*Wik

1992 Robert Eugene Marshak (October 11, 1916 – December 23, 1992) was an American physicist dedicated to learning, research, and education.
Marshak was born in the Bronx, New York City. His parents were immigrants to New York from Minsk. He was educated at Columbia University.
Marshak received his PhD from Cornell University in 1939. Along with his thesis advisor, Hans Bethe, he discovered many of the fusion aspects involved in star formation. This helped him on his work for the Manhattan Project, in Los Alamos, during World War II.
In 1947, at the Shelter Island Conference, Marshak presented his two-meson hypothesis about the pi-meson, which were discovered shortly thereafter.[1]
In 1957, he and George Sudarshan proposed a V-A ("vector" minus "axial vector") Lagrangian for weak interactions, which was later independently discovered by Richard Feynman and Murray Gell-Mann. His biography below, is explicit about it "Perhaps Marshak's most significant scientific contribution was the proposal of the V-A Theory of Weak Interactions (the fourth force in nature) in collaboration with his student George Sudarshan. Unfortunately, the pair published the theory only in a conference proceedings for a meeting in Italy. Six months later, a different derivation of the same concept was published by Feynman and Gell-Mann in a mainstream scientific journal. Marshak had talked with Feynman about the general problem in California some time before. Though the V-A Concept was considered to be one of the most important contributions to theoretical physics, a Nobel Prize was never awarded for it." Sudarshan himself later commented in a TV interview in 2006 that Murray Gell-Mann got the idea from him, in an informal coffee time!
He was Chairman of the Department of Physics at the University of Rochester for fourteen years (1956 to 1970)
He was the President of the City College of New York from 1970-1979.
Marshak died by accidental drowning in Cancún, Mexico in 1992. *Wik

2001 Donald Clayton Spencer (April 25, 1912 – December 23, 2001) was an American mathematician, known for major work on deformation theory of structures arising in differential geometry, and on several complex variables from the point of view of partial differential equations. He was born in Boulder, Colorado, and educated at the University of Colorado and MIT.
He wrote a Ph.D. in diophantine approximation under J. E. Littlewood at the University of Cambridge, completed in 1939. He had positions at MIT and Stanford before his appointment in 1950 at Princeton University. There he was involved in a major series of collaborative works with Kunihiko Kodaira on the deformation of complex structures, which had a profound influence on the theory of complex manifolds and algebraic geometry, and the conception of moduli spaces.
He later worked on pseudogroups and their deformation theory, based on a fresh approach to overdetermined systems of PDEs (bypassing the Cartan-Kähler ideas based on differential forms by making an intensive use of jets). Formulated at the level of various chain complexes, this gives rise to what is now called Spencer cohomology, a subtle and difficult theory both of formal and of analytical structure. This is a kind of Koszul complex theory, taken up by numerous mathematicians during the 1960s. In particular a theory for Lie equations formulated by Malgrange emerged, giving a very broad formulation of the notion of integrability.
After his death, a mountain peak outside of Silverton, Colorado was named in his honor. *Wik