Monday, 23 December 2024

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. (How many evens?)

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

There are 21 year dates for which the sum of the divisors is a square number. 357 is the 20th of them. 1+3+7+17+21+51+119+357=576=242

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.   *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. 
By 1690 Flamsteed's growing catalogue of "fixed stars" included the rather innocuously titled 34 Tauri, a faint object on the cusp of human eyesight in the constellation of Taurus.
34 Tauri would again be observed by Flamsteed in 1712 and 1715 and by one of Flamsteed's successors as Astronomer Royal, James Bradley, in 1748, 1750 and 1753.
The trouble was that no one realised they were looking at the same thing; the 'fixed' star had wandered across the heavens, the distinct calling card of a planet (from the Greek for 'wanderer'). 
It took the great resolving power of William Herschel's newly built 6.2 inch reflecting telescope to see 34 Tauri, which by 1781 had wandered into the constellation of Gemini, as a disc rather than a point-like star. In fact, Herschel's telescope was better than any at the disposal of Nevil Maskelyne, the latest Astronomer Royal.

Replica in the William Herschel Museum, Bath, of a telescope similar to that with which Herschel discovered Uranus





 1750, Benjamin Franklin was severely shocked while electrocuting a turkey.*TIS  (although I heard he described the meat as unusually tender)
The audience for this accident reported that they had seen a great flash and heard a loud crack, but Franklin didn’t notice this, having been shocked senseless. He did record that “the first thing I took notice of was a violent, quick shaking of my body, which gradually remitting, my sense as gradually returned.” Franklin felt some numbness for a short while afterwards, and experienced some soreness for a few days, but otherwise, he suffered only from embarrassment at his mistake. He made an effort to warn others against making a similar mistake when conducting such dangerous experiments.
Franklin wrote about this event and his many other experiments in his letters, and in 1751 published a book, Experiments and Observations on Electricity, which became very popular.*APS News



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.
This seems also to have been in his own estimation his most important work, since he had the figure of the lemniscate with the inscription "Multifariam divisa atque dimensa Deo veritatis gloria" engraved on the title-page of his Produzioni Matematiche,





1763 Price read Thomas 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 Price 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.)  The next day Brattain noted the important event into his notebook.

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

*Science




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 Commission 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, an alphametic.  
For more on Some History notes about alphametics puzzles (Send+More = Money) and more




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.
He did both his undergraduate and graduate studies at the University of Bucharest, earning a diploma in 1958 and a doctorate in 1965 under the supervision of Grigore Moisil. For a while in the 1960s he published under the name of Petru L. Ivănescu. In 1967, he and his wife (Anca Ivănescu) escaped Romania and defected to Israel. Hammer taught at the Technion from 1967 to 1969, then moved to Canada at McGill University in Montreal from 1969 to 1972, at the University of Waterloo from 1972 to 1983, and finally at Rutgers University in New Brunswick, New Jersey for the remainder of his career. He was killed in a car accident on December 27, 2006.

Hammer founded the Rutgers University Center for Operations Research, and created and edited the journals Discrete Mathematics, Discrete Applied Mathematics, Discrete Optimization, Annals of Discrete Mathematics, Annals of Operations Research, and SIAM Monographs on Discrete Mathematics and Applications.*Wik




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 )  A skew quadrilateral is one in which all four vertices are not coplanar.

*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



1805 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

Sang was a Scottish mathematician and civil engineer, best known for having computed large tables of logarithms, with the help of two of his daughters  [Flora and Jane]. These tables went beyond the tables of Henry Briggs, Adriaan Vlacq, and Gaspard de Prony.
He attended the Subscription School in Kirkcaldy and from there went on to study at the University of Edinburgh.
In the 1830s he is listed as a teacher of mathematics living at 32 St Andrew Square in Edinburgh.
He was elected a Fellow of the Royal Society of Edinburgh in May 1836. In 1884 he was awarded their Makdougall-Brisbane Prize. He served as their Vice President 1883 to 1885.
In 1841 he took the role of Professor of Mechanical Science at Manchester New College. In 1854 he briefly served as Professor of Mechanical Science in Constantinople. He returned to Edinburgh in 1854 to again teach mathematics.
He was elected a Fellow of the Royal Scottish Society of the Arts in 1828, and was its president from 1857 to 1858.
In 1884 he was elected an Honorary Fellow of the Franklin Institute in Philadelphia.
Sang died at his home, 31 Mayfield Road, Edinburgh Newington on 23 December 1890. *Wik
The list of his writing citations on Wikipedia is so vast that they divide them into fife year bundles, many with active links to the works.  My introduction to Sang is in relation to my search on the history of near equilateral triangles,




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 ErdÅ‘s. 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

Marshak in 1939 with a glass of radiosodium he has been drinking from during a radioactive tracer experiment





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




2016 John Aitchison (22 July 1926 – 23 December 2016) was a Scottish statistician.

John Aitchison studied at the University of Edinburgh after being uncomfortable explaining to his headmaster that he didn’t plan to attend university. He graduated in 1947 with an MA in mathematics.

After two years wherein he did actuarial work, he also attended Trinity College, Cambridge. He had a scholarship to do so, and graduated in 1951 with a BA focused on statistics. The year after he graduated, he joined the Department of Applied Economics at Cambridge as a statistician. He continued his work at Cambridge until 1956, when he was offered the position of Lecturer of Statistics at the University of Glasgow. During his time at Glasgow, he wrote The Lognormal Distribution, With Special Reference to its Uses in Economics (1957) with J A C Brown (who he met at Cambridge).

However, he left Glasgow in 1962, when the University of Liverpool offered him the positions of Senior Lecturer and head of Mathematical Statistics. In 1964, he was promoted to Reader.

From 1966 to 1976 he was Titular Professor of Statistics and Mitchell Lecturer in Statistics at the University of Glasgow. He was made a Fellow of the Royal Society of Edinburgh in 1968. He began writing student level books, Solving Problems in Statistics (Volume 1 in 1968, Volume 2 in 1972)  and Choice Against Chance: An Introduction to Statistical Decision Theory (1970).

In 1976 he joined the University of Hong Kong as a Chaired Professor of Statistics. He resigned from the University of Glasgow the year after and founded the Hong Kong Statistical Society. He was the President of the Society during 1977 to 1979.

In 1986 he published the book The Statistical Analysis of Compositional Data, an important resource on the analysis of compositional data.

On his retirement from the University of Hong Kong in 1989, he joined the University of Virginia as Professor and Chairman of the Division of Statistics, which he retired from in 1994. After this, he returned to the University of Glasgow as an Honorary Senior Research Fellow in the Department of Statistics.



2018  Elias Menachem Stein (January 13, 1931 – December 23, 2018) was an American mathematician who was a leading figure in the field of harmonic analysis. He was the Albert Baldwin Dod Professor of Mathematics, Emeritus, at Princeton University, where he was a faculty member from 1963 until his death in 2018.

Stein was born in Antwerp Belgium, to Elkan Stein and Chana Goldman, Ashkenazi Jews from Belgium. After the German invasion in 1940, the Stein family fled to the United States, first arriving in New York City. He graduated from Stuyvesant High School in 1949, where he was classmates with future Fields Medalist Paul Cohen, before moving on to the University of Chicago for college. In 1955, Stein earned a Ph.D. from the University of Chicago under the direction of Antoni Zygmund. He began teaching at MIT in 1955, moved to the University of Chicago in 1958 as an assistant professor, and in 1963 became a full professor at Princeton.

Stein worked primarily in the field of harmonic analysis, and made contributions in both extending and clarifying Calderón–Zygmund theory. These include Stein interpolation (a variable-parameter version of complex interpolation), the Stein maximal principle (showing that under many circumstances, almost everywhere convergence is equivalent to the boundedness of a maximal function), Stein complementary series representations, Nikishin–Pisier–Stein factorization in operator theory, the Tomas–Stein restriction theorem in Fourier analysis, the Kunze–Stein phenomenon in convolution on semisimple groups, the Cotlar–Stein lemma concerning the sum of almost orthogonal operators, and the Fefferman–Stein theory of the Hardy space. 

He wrote numerous books on harmonic analysis , which are often cited as the standard references on the subject. His Princeton Lectures in Analysis series were penned for his sequence of undergraduate courses on analysis at Princeton. Stein was also noted as having trained a high number of graduate students. According to the Mathematics Genealogy Project, Stein had at least 52 graduate students—including the Fields medalists Charles Fefferman and Terence Tao—some of whom went on to shape modern Fourier analysis.

His honors included the Steele Prize (1984 and 2002), the Schock Prize in Mathematics (1993), the Wolf Prize in Mathematics (1999), and the National Medal of Science (2001). In addition, he had fellowships to National Science Foundation, Sloan Foundation, Guggenheim Foundation, and National Academy of Sciences. Stein was elected as a member of the American Academy of Arts and Sciences in 1982. In 2005, Stein was awarded the Stefan Bergman prize in recognition of his contributions in real, complex, and harmonic analysis. In 2012 he became a fellow of the American Mathematical Society.




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


 

Sunday, 22 December 2024

On This Day in Math - December 22

  

*Wik

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


The 356th day of the year; There are 356 ways to partition the number 36 into distinct parts without a unit.

356 is the last day of the year that will be a self-number, (there is no number n such that n+ digit sum of n = 356)

356 = 22 x 89. Numbers that are the product of a prime and the square of a prime are sometimes called Einstein numbers, after E = m c2



EVENTS

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

1666 Seven mathematicians and seven physicists met at the king’s Library to inaugurate the French Academy of sciences. They would not receive a formal decree of protection from Louis XIV until 1699. For three centuries women were not allowed as members of the Academy. The first female full member was Yvonne Choquet-Bruhat in 1979. *VFR The society was an outgrowth of an informal community of scientists who coordinated their research efforts through the efforts of Marin Mersenne, a monk at the Minim monastery, who had exchanged 10,000 letters with them. *TIS
Mersenne was a  French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for Mersenne prime numbers, those written in the form Mn = 2n − 1 for some integer n. He also developed Mersenne's laws, which describe the harmonics of a vibrating string (such as may be found on guitars and pianos), and his seminal work on music theory, Harmonie universelle, for which he is referred to as the "father of acoustics". Mersenne, an ordained Catholic priest, had many contacts in the scientific world and has been called "the center of the world of science and mathematics during the first half of the 1600s and, because of his ability to make connections between people and ideas, "the post-box of Europe" He was also a member of the Minim religious order and wrote and lectured on theology and philosophy. *Wik



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



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












1831 The first use of Sir Francis Beaufort's scale of wind force in an official log was by Captain Robert Fitzroy on the first day of the voyage of exploration of the HMS Beagle that included a young naturalist named Charles Darwin. *Isaac's Storm, Erik Larson
 The scale starts with 0 and goes to a force of 12. The Beaufort scale is still used today to estimate wind strengths.

A ship in a force 12 ("hurricane-force") storm at sea, the highest rated on the Beaufort scale



1859 On a warm Saturday in late March of 1859, a small country doctor just 70 miles west of Paris
Dr. Lescarbault's Observatory *Wik
retreated to his barn observatory to check on a hunch about the inconsistencies of the orbit of Mercury, and on that eventful day, the dedicated amateur found a small planet, or asteroid which he carefully measured to be inside the orbit of Mercury. After careful measurements, and rechecking, he closed his books and ...... did nothing. For months, he continued to observe to see if he could improve, or repeat, his observations, but only seventy miles from the center of the Astronomical Universe, Where Le Verrier, the man who had discovered Neptune with his pen, held audience.It was not until Dec 22, that he put pen to paper to inform the astronomical world of his discovery. He decided to write after he read a journal article in "Cosmos" by the great man himself, that Dr. Lescarbault felt bold enough to entrust a local Inspector of Roads and Bridges with a letter to the Great Le Verrier informing him of his discovery. After a brief interrogation in the rural home and examination of his work, Le Verrier pronounced the work good, and within a week took the humble Doctor's observations and produced an orbit for the new planet, another example of Le Verrier's magic of producing celestial objects from his mathematical pen. Within a few months, in early 1860, the press had a name for his new creation, Vulcan explained the mystery of Mercury's Perihelion Precession in seeming defiance of Newton's laws. *Thomas Levenson, The Hunt for Vulcan
1966 L(uitzen) E(gbertus) J(an) Brouwer (27 Feb 1881, 2 Dec 1966) was a Dutch mathematician who founded mathematical Intuitionism (a doctrine that views the nature of mathematics as mental constructions governed by self-evident laws). He founded modern topology by establishing, for example, the topological invariance of dimension and the fixpoint theorem. (Topology is the study of the most basic properties of geometric surfaces and configurations.) The Brouwer fixed point theorem is named in his honor. He proved the simplicial approximation theorem in the foundations of algebraic topology, which justifies the reduction to combinatorial terms, after sufficient subdivision of simplicial complexes, the treatment of general continuous mappings. *TIS
Regarded as one of the greatest mathematicians of the 20th century, he is known as the founder of modern topology, particularly for establishing his fixed-point theorem and the topological invariance of dimension. *Wik



1866 L E Becker wrote to Darwin to ask if he would “be so very good as to send us a paper to be read at our first meeting”. “Of course we are not so unreasonable as to desire that you should write anything specially for us” Becker said, “but I think it possible you may have by you a copy of some paper such as that on the Linum which you have communicated to the learned societies but which is unknown and inaccessible to us unless through your kindness.”
Darwin responded by sending not one but three papers to be read at the ladies’ inaugural meeting. Whether Darwin realized that he was providing materials for a feminist organization is unclear, although Becker’s use of headed paper and the enclosure in her letter to Darwin of the society’s first pamphlet certainly made no secret of her political affiliations.
Regardless, what is interesting is that despite what he said in the public context about women’s intellectual in-capabilities and designated social role, in private his thoughts and actions were very different. Darwin was happy to work in collaboration with many women like Becker. He encouraged women’s scientific interests wherever possible, frequently sharing observations, samples and reading materials with women across the world. In some rare instances he was even happy to acknowledge that a woman’s scientific skill and knowledge might be superior to his own! *Darwin and Gender, the blog)
Lydia Ernestine Becker (24 February 1827 – 18 July 1890) was a leader in the early British suffrage movement, as well as an amateur scientist with interests in biology and astronomy. She established Manchester as a centre for the suffrage movement and with Richard Pankhurst she arranged for the first woman to vote in a British election and a court case was unsuccessfully brought to exploit the precedent. Becker is also remembered for founding and publishing the Women's Suffrage Journal between 1870 and 1890.



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




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




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



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





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



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

"To mathematicians, Grigori Perelman's proof of the Poincaré conjecture qualifies at least as the Breakthrough of the Decade. But it has taken them a good part of that decade to convince themselves that it was for real. In 2006, nearly 4 years after the Russian mathematician released the first of three papers outlining the proof, researchers finally reached a consensus that Perelman had solved one of the subject's most venerable problems. But the solution touched off a storm of controversy and drama that threatened to overshadow the brilliant work."




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

On this day in 2012, the first National Mathematics Day was celebrated in India. It is celebrated every year on Ramanujan's birthday.



BIRTHS

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




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



1819 Pierre Ossian Bonnet (22 December 1819, Montpellier – 22 June 1892, Paris) was a French mathematician. He made some important contributions to the differential geometry of surfaces, including the Gauss–Bonnet theorem.
Bonnet was elected to the Academy of Sciences in 1862 to replace Biot. He defeated Bour for this position. From 1868 Bonnet assisted Chasles at the Ecole Polytechnique, and three years later he became a director of studies there. In addition to this post he also taught at the Ecole Normale Supérieure.

In 1878 Bonnet succeeded Le Verrier to the chair at the Sorbonne, then in 1883 he succeeded Liouville as a member of the Bureau des Longitudes.

Bonnet did important work on differential geometry, a topic that was also being investigated in France by Serret, Frenet, Bertrand and Puiseux. Here Bonnet made major contributions to the concept of curvature. In particular, he published a formula relating the surface integral of the Gauss curvature to the Euler characteristic of the surface and the line integral of the geodesic curvature of its boundary; this result is now known as the Gauss–Bonnet theorem. Gauss was known to have previously discovered a special case of this fundamental result, but had never published it. 
In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology.

In the simplest application, the case of a triangle on a plane, the sum of its angles is 180 degrees. The Gauss–Bonnet theorem extends this to more complicated shapes and curved surfaces, connecting the local and global geometries.  *Wik




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

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



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





1887 Srinivasa Ramanujan (22 Dec 1887; 26 Apr 1920) Indian mathematician known for his work on hypergeometric series and continued fractions. In number theory, he discovered properties of the partition function. Although self-taught, he was one of India's greatest mathematical geniuses. He worked on elliptic functions, continued fractions, and infinite series. His remarkable familiarity with numbers, was shown by the following incident. While Ramanujan was in hospital in England, his Cambridge professor, G. H. Hardy, visited and remarked that he had taken taxi number 1729, a singularly unexceptional number. Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=1^3+12^3=9^3+10^3. *TIS Ramanujan's recognition of 1729 could be partly due to his studying examples of numbers such that a^3+b^3=c^3+1.  His papers had several examples of them.




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




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

1911 Grote Reber (22 Dec 1911; 20 Dec 2002) U.S. amateur astronomer and radio engineer who self-financed and built the first radio telescope. He pioneered the new field of radio astronomy, and was the first to systematically study the sky by observing non-visible radiation. After reading about Jansky's discovery (1932) of natural radio emissions from space, Reber constructed a 9-meter dish antenna in his back yard and built three different detectors before finding 160 MHz signals (1939). In 1940 and 1944 he published articles titled Cosmic Static in the Astrophysical Journal. He was the first to express received radio signals in terms of flux density and brightness, first to find evidence that galactic radiation is non-thermal, and first to produce radio maps of the sky (1941).*TIS




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



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





DEATHS

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

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




1693 Elisabetha Koopman (17 Jan 1647 in Danzig, now GdaÅ„sk, Poland - 22 Dec 1693 in Danzig, now GdaÅ„sk, Poland) was the wife of the Polish astronomer Johannes Hevelius and helped him with his observations.*SAU
It was a fascination for astronomy which led Elisabetha, when still only a child, to approach Johannes Hevelius, an astronomer of international repute who had a complex of three houses in Danzig which contained the best observatory in the world. The marriage of the seventeen-year-old to fifty-two-year-old Hevelius in 1663  allowed her also to pursue her own interest in astronomy by helping him manage his observatory.
Johannes and Elisabetha Hevelius observing the sky with a brass sextant (1673).



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



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

In Volume II of his Mathematicals series, Howard Eves tells the following tale of Poncelet impacting the education of French school children:
"Poncelet, .. accompanied Napoleon on his fareful 1812 invasion of Russia. ... Poncelet was captured and taken to Saratov on the Volga, living there among simple people.  Poncelet became impressed with the excellence of the Russian abacus as a device for teaching children..  Upon his return to France, he introduced the abacus into all the schools in the city of Metz, from where it spread all over France."


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

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



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



1994 John Arthur Todd FRS (23 August 1908 – 22 December 1994) was a British geometer. He was born in Liverpool, and went to Trinity College of the University of Cambridge in 1925. He did research under H.F. Baker, and in 1931 took a position at the University of Manchester. He became a lecturer at Cambridge in 1937. He remained at Cambridge for the rest of his working life.

The Todd class in the theory of the higher-dimensional Riemann–Roch theorem is an example of a characteristic class (or, more accurately, a reciprocal of one) that was discovered by Todd in work published in 1937. It used the methods of the Italian school of algebraic geometry. The Todd–Coxeter process for coset enumeration is a major method of computational algebra, and dates from a collaboration with H.S.M. Coxeter in 1936. In 1953 he and Coxeter discovered the Coxeter–Todd lattice. In 1954 he and G. C. Shephard classified the finite complex reflection groups.
In March 1948 he was elected a Fellow of the Royal Society. *Wik



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



2018 Jean Bourgain(28 Feb 1954 -  22 Dec, 2018)Belgian mathematician who was awarded the Fields Medal in 1994 for his work in analysis. His achievements in several fields included the problem of determining how large a section of a Banach space of finite dimension n can be found that resembles a Hilbert subspace; a proof of Luis Antonio Santaló's inequality; a new approach to some problems in ergodic theory; results in harmonic analysis and classical operators; and nonlinear partial differential equations. Bourgain's work was noteworthy for the versatility it displayed in applying ideas from wide-ranging mathematical disciplines to the solution of diverse problems. *TIS
*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