Tuesday 19 March 2024

On This Day in Math - March 19

  

Pearls of Sluze, *Mathworld Wolfram


There is no reason why the history and philosophy of science should not be taught in such a way as to bring home to all pupils the grandeur of science and the scope of its discoveries.
~Prince Louis-Victor de Broglie


The 78th day of the year; 78 is the smallest number that can be written as the sum of 4 distinct squares in 3 ways.  *What's Special About This Number

In his pamphlet, "The Thousand Yard Model," Guy Ottewell creates a sacale model universe with the sun as a bowling ball.  78 feet away, the Earth is represented by a peppercorn.

In his doctoral thesis in the early 60's, Ron Graham proved that 78, and every number greater than 78 can be partitioned into distinct numbers so that the sum of their reciprocals is one. 78=2+6+8+10+12+40, and the reciprocals of all these distinct integers add up to one. There are at least two smaller numbers for which this is true. Can you find them?

78 is the sum of the first twelve integers, and thus a triangular number.

90 = 21+22+23+24, 78= 25+26 + 27, but 21^2 + 22^2 + 23^2 + 24^2 = 25^2 + 26^2 + 27^2 = 2030


The cube of 78 is equal to the sum of three distinct cubes, 783 = 393 + 523 + 653
(Historically, it seems Ramanujan was inspired by a much smaller such triplet 63 = 33 + 43 + 53

77 and 78 form the fourth Ruth-Aaron pair, named for the number of home runs hit by Babe Ruth, 714, and the number when Aaron broke the record, 715 (he hit more afterward).  They are consecutive numbers that have the same sums of their prime factors (77 = 7*11, 78 = 2*3*13, and 7+11 = 2+3+13).



EVENTS

In 1474, the Venetian Patent Law, the first of its kind in the world, declared that “each person who will make in this city any new and ingenious contrivance, not made heretofore in our dominion, as soon as it is reduced to perfection... It being forbidden to any other in any territory and place of ours to make any other contrivance in the form and resemblance thereof, without the consent and licence of the author up to ten years.” The law was intended to attract inventors and investors to Venice and stimulate new economic activities. *TIS

*Mark Jardine,
1681 Last observation of C/1680 V1, also called the Great Comet of 1680, Kirch's Comet, and Newton's Comet. It has the distinction of being the first comet discovered by telescope. Discovered by Gottfried Kirch on 14 November 1680, New Style, it became one of the brightest comets of the 17th century--reputedly visible even in daytime--and was noted for its spectacularly long tail. Passing only 0.4 AUs from Earth on 30 November, it sped around an incredibly close perihelion of .006 AU (898,000 km) on 18 December 1680, reaching its peak brightness on 29 December as it rushed outward again. It was last observed on 19 March 1681. As of December 2010 the comet was about 252.1 A.U. from the Sun. While the Kirch Comet of 1680-1681 was discovered and subsequently named for Gottfried Kirch , credit must also be given to the Jesuit, Eusebio Kino, who charted the comet’s course. During his delayed departure for Mexico, Kino began his observations of the comet in Cadíz in late 1680. Upon his arrival in Mexico City, he published his Exposisión astronómica de el [sic] cometa (Mexico City, 1681) in which he presented his findings. Kino’s Exposisión astronómica is among one of the earliest scientific treatises published by a European in the New World. Aside from its brilliance, it is probably most noted for being used by Isaac Newton to test and verify Kepler's laws. *Wik

1706 Advertisement in English Tabloid for William Jones's Synopsis Palmariorum Matheseos, or A New Introduction to the Mathematics. This is the book in which Jones introduces the symbol pi for the ratio of the circumference to diameter of a circle.
*Review of the State of the English Nation (Cumulation) (London, England), Tuesday, March 19, 1706; Issue 34.

1752 Following the death of her father on March 19, 1752, a new phase of Maria Agnesi’s life began that lasted until her death. She restricted her study to theology and gave her time, effort, and money to devotional and charitable activities. Although continuing to live with her family, she kept a separate apartment, where she cared for a few poor, sick people. From 1759 she lived in a rented house with four of her poor people; and when money was needed for her charitable activity, she sold her gifts from the Empress Maria Theresa to a rich Englishman. Besides caring for the sick and indigent, she often taught catechism to working-class people. *Hubert Kennedy, Eight Mathematical Biographies, Pg 8
 
*Selected witch of Agnesi curves



1791 Prior to 1784, when Jefferson arrived in France, most if not all of his drawings were made in ink. In Paris, Jefferson began to use pencil for drawing, and adopted the use of coordinate, or graph, paper. He treasured the coordinate paper that he brought back to the United States with him and used it sparingly over the course of many years. He gave a few sheets to his good friend David Rittenhouse, the astronomer and inventor:

"I send for your acceptance some sheets of drawing-paper, which being laid off in squares representing feet or what you please, saves the necessity of using the rule and dividers in all rectangular draughts and those whose angles have their sines and cosines in the proportion of any integral numbers. Using a black lead pencil the lines are very visible, and easily effaced with Indian rubber to be used for any other draught."
A few precious sheets of the paper survive today. *Monticello.org
Jefferson was widely interested in Science. For those who wish to know more about his scientific interest, I can recommend this book





1791 Report made to the Paris Academy of Sciences advocating the metric system, including the decimal subdivision of the circle. The committee consisted of J. C. Borda, J. Lagrange, P. S. Laplace, G. Monge, and de Condorcet. [Cajori, History of Mathematics 266] See April 14, 1790. *VFR
A metric system of angles was brought in, with 400 degrees in a full turn (100 degrees in a right angle). Now the earth would rotate 40 degrees in an hour and, since the metre had been designed so that one quarter meridian was 10 million metres, each degree of latitude would be 100 kilometres long. It was certainly a rational system but its introduction would require all watches, all clocks, all trigonometric tables, all charts etc. to be changed. Condorcet proposed that teams of out of work wig makers should be used to recalculate new mathematical tables with the new units. Why, one might ask, were the wig makers out of work? Well they had been employed by the aristocrats who, following the Revolution, no longer required their services! *SAU
The resolution found some traction in angle measures."In 1857, Mathematical Dictionary and Cyclopedia of Mathematical Science has: "The French have proposed to divide the right angle into 100 equal parts, called grades, but the suggestion has not been extensively adopted." In 1987 Mathographics by Robert Dixon has: “360° = 400 gradians = 2π radians.” And for those who have, or had, one, "The Texas Instruments TI-89 Titanium calculator has three modes, radians, degrees, and gradians."
*Jeff Miller "Angle: Units in which angle values are interpreted and displayed: RADIAN, DEGREE or GRADIAN*  (* not available on the TI-92 family).  *TI Knowledge Base web page




1797 The date of the entry in Gauss’s scientific diary showing that he had already discovered the double periodicity of certain elliptic functions. *VFR Gauss was investigating the lemniscate.  Two days later he would show how to divide the lemniscate into five equal parts by ruler and compass.  This means he must have had some sense of complex multiplication of elliptic functions.  Abel would generalize this in 1826.  
Lemniscate of Bernoulli


1892 E. Hastings Moore, of Northwestern University, was elected professor of mathematics by the Board of Trustees of the new University of Chicago. *T. W. Goodspeed, The Story of the University of Chicago

1915  The first image of Pluto was taken by astronomer Thomas Gill  at Lowell Observatory in 1915  using a nine-inch telescope borrowed from Swarthmore College. Percival undertook a passionate search for what he called “Planet X.” He took photographs of the sky where Planet X was predicted to be lurking, but failed to recognize Pluto because it was much fainter than expected. Percival died suddenly in 1916, not knowing he had in fact taken an image of Pluto. Only with the lens of history can we look back and recognize those photographs as containing some of the first images of Pluto.  The calculations for the place to search for the undiscovered planet were directed by Elizabeth Williams, the head human computer, performing mathematical calculations on where Lowell should search for an unknown object and its size based on the differences in the orbits of Neptune and Uranus. Her calculations led to predictions for the location of the unknown planet. Lowell died unexpectedly in 1916 and the search was discontinued.  In 1930 the search would resume, leading to the recognition of Pluto as a planet.  Williams and her husband were then dismissed from their positions at the observatory by Percival Lowell's widow, Constance, because it was considered inappropriate to employ a married woman. 



1918 "An Act to preserve daylight and provide standard time for the United States" was enacted on March 19, 1918. It both established standard time zones and set summer DST to begin on March 31, 1918. *WebExhibits 

1937 John von Neumann gave a popular lecture at Princeton on the game of poker. Game Theory became one of his substantial contributions to mathematics. [A. Hodges, Alan Turing. The Enigma, p. 550]The Book that inspired the movie.
In 1921, Emile Borel, a French mathematician, published several papers on the theory of games. He used poker as an example and addressed the problem of bluffing and second-guessing the opponent in a game of imperfect information. Borel envisioned game theory as being used in economic and military applications. Borel's ultimate goal was to determine whether a "best" strategy for a given game exists and to find that strategy. While Borel could be arguably called as the first mathematician to envision an organized system for playing games, he did not develop his ideas very far. For that reason, most historians give the credit for developing and popularizing game theory to John Von Neumann, who published his first paper on game theory in 1928, seven years after Borel.
For Von Neumann, the inspiration for game theory was poker, a game he played occasionally and not terribly well. Von Neumann realized that poker was not guided by probability theory alone, as an unfortunate player who would use only probability theory would find out. Von Neumann wanted to formalize the idea of "bluffing," a strategy that is meant to deceive the other players and hide information from them.

In his 1928 article, "Theory of Parlor Games," Von Neumann first approached the discussion of game theory, and proved the famous Minimax theorem. From the outset, Von Neumann knew that game theory would prove invaluable to economists. He teamed up with Oskar Morgenstern, an Austrian economist at Princeton, to develop his theory.
I'm "All IN" on this hand.



1949 The American Museum of Atomic Energy opened for the public in an old WWII  cafeteria in Oak Ridge, Tennessee.  The site had been part of the US projects to develop atomic bombs by processing U235.  A new facility was opened in 1975.  *Lucio Gelmini  
In 1958, Britain's first planetarium, the London Planetarium, opened in the west wing of Madame Tussaud's. It is one of the world's largest. The site used was that of the former Cinema and Restaurant added in 1929, that had been destroyed by a German bomb in 1940.*TIS

1953 Frances Crick writes a letter to his son. "Dear Michael, Jim Watson and I have probably made a most important discovery.” This was only two weeks after Crick solved the DNA puzzle and may well be the first written description of the code. The letter, was auctioned at Christie’s on April 10, 2013 for six million dollars.   *NY Times Science
Crick letter *NBC


2008  GRB 080319B was a gamma-ray burst (GRB) detected by the Swift satellite at 06:12 UTC on March 19, 2008. The burst set a new record for the farthest object that was observable with the naked eye: it had a peak visual apparent magnitude of 5.7 and remained visible to human eyes for approximately 30 seconds. The magnitude was brighter than 9.0 for approximately 60 seconds. If viewed from 1 AU away, it would have had a peak apparent magnitude of −67.57 (21 quadrillion times brighter than the Sun seen from Earth)  *Wik 
*artist's impression of gamma-ray
 burst GRB 080319B



2019 One of the top prizes in mathematics has been given to a woman. The Norwegian Academy of Science and Letters announced it has awarded this year’s Abel Prize to Karen Uhlenbeck, an emeritus professor at the University of Texas at Austin. The award cites “the fundamental impact of her work on analysis, geometry and mathematical physics.” *NY Times




BIRTHS

1782 Baron Wilhelm von Biela (19 Mar 1782, 18 Feb 1856 at age 73) Austrian astronomer who was known for his measurement (1826) of a previously known comet as having an orbital period of 6.6 years. Subsequently, known as Biela's Comet, it was observed to break in two (1846), and in 1852 the fragments returned as widely separated twin comets that were not seen again. However, in 1872 and 1885, bright meteor showers (known as Andromedids, or Bielids... current Andromedids are only weakly represented by displays of less than three meteors per hour around November 14. ) were observed when the Earth crossed the path of the comet's known orbit. This observation provided the first concrete evidence for the idea that some meteors are composed of fragments of disintegrated comets.*TIS




1799 William Rutter Dawes (19 Mar 1799, 15 Feb 1868 at age 68) English amateur astronomer who set up a private observatory and made extensive measurements of binary stars and on 25 Nov 1850 discovered Saturn's inner Crepe Ring (independently of American William Bond). In 1864, he was the first to make an accurate map of Mars. He was called "Eagle-eyed Dawes" for the keenness of his sight with a telescope (though otherwise, he was very near-sighted). He devised a useful empirical formula by which the resolving power of a telescope - known as the Dawes limit - could be quickly determined. For a given telescope with an aperture of d cm, a double star of separation 11/d arcseconds or more can be resolved, that is, be visually recognized as two stars rather than one. *TIS




1862 Adolf Kneser (19 March 1862 in Grüssow, Mecklenburg, Germany - 24 Jan 1930 in Breslau, Germany (now Wrocław, Poland)) He is remembered most for work mainly in two areas. One of these areas is that of linear differential equations; in particular he worked on the Sturm-Liouville problem and integral equations in general. He wrote an important text on integral equations. The second main area of his work was the calculus of variations. He published Lehrbruch der Variationsrechnung (Textbook of the calculus of variations) (1900) and he gave the topic many of the terms in common use today including 'extremal' for a resolution curve, 'field' for a family of extremals, 'transversal' and 'strong' and 'weak' extremals *SAU
*Wik



1985 Margaret Harwood (March 19, 1885 – February 6, 1979) was born in Littleton, Massachusetts, became the first woman – and for a long time the only woman – to serve as director of an independent astronomical observatory. She took charge of the Maria Mitchell Observatory on Nantucket Island in 1916, and remained in that post for forty-one years.
Miss Harwood had planned to study physics, chemistry and math when she entered Radcliffe College in 1903, but her choice of lodgings turned her to astronomy. She boarded with the family of Arthur Searle, a genial fixture at the Harvard College Observatory. Soon she was trailing him up Observatory Hill, learning to use the telescopes, earning the friendship and mentoring of other staff members, from Edward Pickering to Annie Jump Cannon and Henrietta Leavitt. By the time of Miss Harwood’s graduation, she was ready to step into a paid position as an assistant. The position didn’t pay much, however, and she supplemented her income of about $500 per year by teaching science in the mornings at a couple of local schools.
In 1912, the Maria Mitchell Association awarded Miss Harwood a new fellowship in astronomy worth $1,000. It came with a new opportunity: From June to December of that year, she took up residence in the old Mitchell homestead on Nantucket, where she curated a small museum and library, used the telescope in the next-door dome to further her own research on asteroids, and lectured on astronomy to the locals every Monday night.
She received an offer from Wellesley College to begin teaching astronomy there upon completion of her graduate studies. But the Maria Mitchell Association, keen to keep her and see her continue her own research, matched the Wellesley salary and made her director of the Nantucket observatory . She was only thirty years old.
In 1957, with considerable reluctance, Miss Harwood retired from her post at Nantucket. In 1961 she accepted the Annie Jump Cannon Prize, which had been established by its namesake in the 1930s, and first conferred on Cecilia Payne. The prize is still awarded today by the American Astronomical Society to a young woman at the start of her career, but it no longer comes with a custom-designed piece of astronomically themed jewelry . Instead, the winner is invited to lecture about her research at the Society’s annual meeting. No doubt Miss Harwood would approve.*LH
Custom-made pin in the shape of a galaxy, designed for the occasion of the award of the Annie Jump Cannon Prize to Margaret Harwood, 1961 (Schlesinger Library, Radcliffe Institute, Harvard Institute)






1900 Frederic Joliot-Curie (19 Mar 1900; 14 Aug 1958 at age 58) French physicist and physical chemist who became personal assistant to Marie Curie at the Radium Institute, Paris, and the following year married her daughter Irène (who was also an assistant at the institute). Later they collaborated on research, and shared the 1935 Nobel Prize in Chemistry "in recognition of their synthesis of new radioactive elements." For example, they discovered that aluminium atoms exposed to alpha rays transmuted to radioactive phosphorus atoms. By 1939 he was investigating the fission of uranium atoms. After WW II he supervised the first atomic pile in France. He succeeded his wife as head of the Radium Institute upon her death in 1956. *TIS
Frédéric and Irène Joliot-Curie | Nobel Prize-Winning French




1910 Jacob Wolfowitz (March 19, 1910 – July 16, 1981) was a Polish-born American statistician and Shannon Award-winning information theorist. He was the father of former Deputy Secretary of Defense and World Bank Group President Paul Wolfowitz.
While a part-time graduate student, Wolfowitz met Abraham Wald, with whom he collaborated in numerous joint papers in the field of mathematical statistics. This collaboration continued until Wald's death in an airplane crash in 1950. In 1951, Wolfowitz became a professor of mathematics at Cornell University, where he stayed until 1970. He died of a heart attack in Tampa, Florida, where he was a professor at the University of South Florida.
Wolfowitz's main contributions were in the fields of statistical decision theory, non-parametric statistics, sequential analysis, and information theory.*Wik



1910 Jerome Namias (19 Mar 1910, 10 Feb 1997 at age 86) American meteorological researcher most noted for having pioneered the development of extended weather forecasts and who also studied the Dust Bowl of the 1930s and the El Niño phenomenon. *TIS In 1971 he joined the Scripps Institution and established the first Experimental Climate Research Center. His prognosis of warm weather during the Arab oil embargo of 1973 greatly aided domestic policy response.*Wik

1927 Allen Newell (March 19, 1927 – July 19, 1992) was a researcher in computer science and cognitive psychology at the RAND Corporation and at Carnegie Mellon University’s School of Computer Science, Tepper School of Business, and Department of Psychology. He contributed to the Information Processing Language (1956) and two of the earliest AI programs, the Logic Theory Machine (1956) and the General Problem Solver (1957) (with Herbert A. Simon). He was awarded the ACM's A.M. Turing Award along with Herbert A. Simon in 1975 for their basic contributions to artificial intelligence and the psychology of human cognition *Wik



1951 Arthur T. Benjamin (March 19, 1961; ) is an American mathematician who specializes in combinatorics. Since 1989 he has been a Professor of Mathematics at Harvey Mudd College.
He is known for mental math capabilities and mathemagics performances. These have included shows at the Magic Castle and TED. He is also the first mathematician to have been featured on the Colbert Report.
The Mathematical Association of America gave him a regional award for distinguished teaching in 1999 and a national one in 2000. He was the Mathematical Association of America's George Pólya Lecturer for 2006-8. In 2012 he became a fellow of the American Mathematical Society.
Benjamin was one of the performers at the inaugural San Diego Science Festival on April 4, 2009. He also won the American Backgammon Tour in 1997. *Wik A video of his "mathmagic" is here 
And his book, The Magic of Math: Solving for x and Figuring Out Why, is delightful,





DEATHS

1406 Ibn Khaldūn or Ibn Khaldoun  Al-Ḥaḍrami, May 27, 1332 AD/732 AH – March 19, 1406 AD/808 AH) was a Muslim historiographer and historian who is often viewed as one of the fathers of modern historiography,sociology and economics.
He is best known for his Muqaddimah (known as Prolegomenon in English), which was discovered, evaluated and fully appreciated first by 19th century European scholarship, although it has also had considerable influence on 17th-century Ottoman historians like Ḥajjī Khalīfa and Mustafa Naima who relied on his theories to analyze the growth and decline of the Ottoman Empire. Later in the 19th century, Western scholars recognized him as one of the greatest philosophers to come out of the Muslim world. *Wik
Ibn Khaldun Statue and Square, Mohandessin, Cairo




1862 John Edward Campbell (27 May 1862, Lisburn, Ireland – 1 October 1924, Oxford, Oxfordshire, England) is remembered for the Campbell-Baker-Hausdorff theorem which gives a formula for multiplication of exponentials in Lie algebras. *SAU His 1903 book, Introductory Treatise on Lie's Theory of Finite Continuous Transformation Groups, popularized the ideas of Sophus Lie among British mathematicians.
He was elected a Fellow of the Royal Society in 1905, and served as President of the London Mathematical Society from 1918 to 1920. *Wik

1685 René François Walter de Sluse (2 July 1622 in Visé, Principality of Liège (now Belgium) - 19 March 1685 in Liège, Principality of Liège (now Belgium)) a French mathematician, intellectual and clergyman who wrote many books about mathematics and contributed to the development of mathematics.
Plague in Église Saint-Martin

He studied at a university in Rome, and later moved to Liège. His position in the church prevented him from visiting other mathematicians, but he corresponded with the mathematicians and intellectuals of the day.
He studied calculus and his work discusses spirals, tangents, turning points and points of inflection.
There is a family of curves named after him called the Pearls of Sluze: the curves represented by the following equation with positive integer values of m, n and p:
yn = k(a - x)pxm *Wik
This group of curves was studied by de Sluze between 1657 and 1698. It was Blaise Pascal who named the curves after de Sluze.

1922 George Ballard Mathews, FRS (February 23, 1861 — March 19, 1922) was a London born mathematician who specialized in number theory.
After receiving his degree (as Senior Wrangler) from St John's College, Cambridge in 1883, he was elected a Fellow of St John's College. *Wik  Mathews also wrote Algebraic equations (1907) which is a clear exposition of Galois theory, and Projective geometry (1914). This latter book develops the subject of projective geometry without using the concept of distance and it bases projective geometry on a minimal set of axioms. The book also treats von Staudt's theory of complex elements as defined by real involutions. The book contains a wealth of information concerning the projective geometry of conics and quadrics. *SAU

1930 Henry Faulds (1 Jun 1843, 19 Mar 1930 at age 86) Scottish physician who, from 1873, became a missionary in Japan, where he worked as a surgeon superintendent at a Tokyo hospital, taught at the local university, and founded the Tokyo Institute for the Blind. In the late 1870s, his attention was drawn to fingerprints of ancient potters remaining on their work that he helped unearth at an archaeological dig site in Japan. He commenced a study of fingerprints, and became convinced that each individual had a unique pattern. He corresponded on the subject with Charles Darwin, and published a paper about his ideas in Nature (28 Oct 1880). When he returned to Britain in 1886, he unsuccessfully offered his fingerprinting identification scheme for forensic uses to Scotland Yard. Undeserved confusion on priority for the discovery with Francis Galton and Sir William J. Herschel lasted until 1917. *TIS



1978 Gaston Maurice Julia (February 3, 1893 – March 19, 1978) was a French mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are closely related.*Wik A report of his bravery during WWI during which he lost his nose:
January 25, 1915, showed complete contempt for danger. Under an extremely violent bombardment, he succeeded despite his youth (22 years) to give a real example to his men. Struck by a bullet in the middle of his face causing a terrible injury, he could no longer speak but wrote on a ticket that he would not be evacuated. He only went to the ambulance when the attack had been driven back. It was the first time this officer had come under fire.
When only 25 years of age, Julia published his 199 page masterpiece Mémoire sur l'iteration des fonctions rationelles which made him famous in the mathematics centres of his day. The beautiful paper, published in Journal de Math. Pure et Appl. 8 (1918), 47-245, concerned the iteration of a rational function f. Julia gave a precise description of the set J(f) of those z in C for which the nth iterate f n(z) stays bounded as n tends to infinity. (These are the Julia Sets popularized by Mandelbrot) *SAU




1984 Richard Ernest Bellman (August 26, 1920 – March 19, 1984) was an American applied mathematician, celebrated for his invention of dynamic programming in 1953, and important contributions in other fields of mathematics. A Bellman equation, also known as a dynamic programming equation, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming. Almost any problem which can be solved using optimal control theory can also be solved by analyzing the appropriate Bellman equation. The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory. The "Curse of dimensionality", is a term coined by Bellman to describe the problem caused by the exponential increase in volume associated with adding extra dimensions to a (mathematical) space.*Wik




1987 Louis Victor Pierre Raymond duc de Broglie (15 Aug 1892,19 Mar 1987 at age 94) was a French physicist best known for his research on quantum theory and for his discovery of the wave nature of electrons. De Broglie was of the French aristocracy - hence the title "duc" (Prince). In 1923, as part of his Ph.D. thesis, he argued that since light could be seen to behave under some conditions as particles (photoelectric effect) and other times as waves (diffraction), we should consider that matter has the same ambiguity of possessing both particle and wave properties. For this, he was awarded the 1929 Nobel Prize for Physics. *TIS
He is buried in the Cimetière de Neuilly-sur-Seine (Ancien),Hauts-de-Seine, Ile-de-France Region, France. (Just outside Paris)

2011 J(ames) Laurie Snell, (January 15th, 1925, Wheaton, Illinois; March 19, 2011, Hanover, New Hampshire) was an American mathematician.
A graduate of the University of Illinois, he taught at Dartmouth College until retiring in 1995. Among his publications was the book "Introduction to Finite Mathematics", written with John George Kemeny and Gerald L. Thompson, first published in 1956 and in multiple editions since.
The Snell envelope, used in stochastics and mathematical finance, is the smallest supermartingale dominating the price process. Snell has published the related theory 1952 in the paper Applications of martingale system theorems.*Wik








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


Monday 18 March 2024

The Also-ran and the King

 The Also-ran and the King



Combing through Greg Ross wonderful Futility Closet I found a nice post he called "Also-Ran".  

I'll give you his article and then fill in the missing details...

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Arthur Conan Doyle tells us little about James Moriarty, the criminal mastermind in the Sherlock Holmes stories. But he does mention one intriguing accomplishment in The Valley of Fear:

Is he not the celebrated author of The Dynamics of an Asteroid, a book which ascends to such rarefied heights of pure mathematics that it is said that there was no man in the scientific press capable of criticizing it?

Mathematicians Alain Goriely and Simon P. Norton have both pointed out that in 1887 King Oscar II of Sweden offered a bounty for the solution to the n-body problem in celestial mechanics. Doyle’s story was set in 1888, so it’s possible that Moriarty had intended his book as his entry in this contest.

If he did, he was disappointed — the prize went to Henri Poincaré.

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Ok, I thought, but wait.... I didn't think the n-body solution was actually solved, so I did the obvious thing, I queried Quora.  Quora says, "There are no solutions to the n-body question.. " quickly followed by such things as, "If you stand on one leg and squint your eyes" ... Ok, they don't say that bit exactly, but lots of talk about assumptions that might make it "sort of"accurate if you stand on one leg... but I covered that.   

So I started to research the actual  contest described in his post.  Turns out the idea did not suddenly appear to the king of Sweden one day.  His 60th birthday they were celebrating, just to plant this thing in calendar tile, was January 21, 1889.  And it wasn't exactly the King's idea from the start. The usually quite accurate Wikipedia tells it this way, " "Oscar was also particularly interested in mathematics. In 1889 he set up a contest, on the occasion of his 60th birthday, for "an important discovery in the realm of higher mathematical analysis". In truth the contest was to be decided and awarded on the Kings Birthday on, yep, January 21, 1889.  That doesn't leave much time to solve, write up and deliver your solution to an unsolved problem."  In fact the idea was thought up years before with not a whisper at first to the Good King Oscar II.  


The whole contest was the brainchild of Magnus Gustaf "Gösta" Mittag-Leffler, who had founded in 1882,  the most important mathematical periodical ever, Acta Mathematica, and would be its editor for 40 years.  One of Mittag-Leffler’s inventive ideas in promoting Acta Mathematica was to turn to King Oscar II of Sweden and Norway, both for financial support of the project and as the first enlisted subscriber. In 1884 another grand idea from Mittag-Leffler had matured. Again involving King Oscar, he now wanted to arrange an international prize competition in mathematics honouring   the 60th birthday of the king. It seems that Mittag-Leffler first revealed his plan to Kovalevskaya. We find a short reference in a letter to her from 4 May 1884. 


The special features of this competition was the international and ambitious appeal, and the connection not to an academy or  institution, but to the journal Acta Mathematica, where the winning entry finally was to be published. The prize consisted of a gold medal and 2,500 Swedish kronor. (Note the prize amount, it becomes important later.) The memoirs should be submitted before 1 June 1888 (nearly three years after the original announcement and six months before the King's birthday), with anonymity maintained through a motto on an enclosed sealed envelope containing the name of the author. (Even in the beginning the three judges, "Mittag-Leffler himself, acting as administrative and coordinative liaison with his mentors and friends Karl Weierstrass in Berlin and Charles Hermite in Paris. They were not only the two dominant mathematicians of the older generation, but there was also a special sympathy between them. This would be a prize awarded not for past contributions, but for a solution to an unsolved problem specified by the committee. In order to attract the best mathematicians from different branches of mathematical analysis they agreed on four questions."   (So there were choices and the n-body problem was just one of them. )* Institut Mittag-Leffler

Institut Mittag-Leffler

The committee knew very well that Poincaré had the capacity to attack any of the four questions. In correspondence with Mittag-Leffler he made clear his intention to grapple with Question 1, the n-body problem. In May 1888, after hard work and many doubts, he submitted his memoir Sur le problème des trois corps et les équations de la dynamique. As for the anonymity, well …, accompanying the memoir were two letter notes, one to the prize jury and one to Mittag-Leffler.

A list of all the twelve manuscripts received by June 1888 was published in Volume 11 of Acta with their identifying epigraphs. It turned out that five of the authors had attempted the prestigious n-body problem, one had tried Question 3 (???), while six treated a subject of their own, which remained a secondary option. Only four of the authors have been identified: in addition to Poincaré also Paul Appell, Guy de Longchamps and Jean Escary.

Finally after almost 300 handwritten pages (including the appendices) his (Poincaré ) new concept of integral invariants and the subsequent geometrical arguments led to a claim of stability for this system.

Mittag-Leffler made his final presentation to the king on 20 January 1889, the day before the monarch’s 60th birthday, only the brief summary from Weierstrass was enclosed in the general report. For the winning entry Henri Poincaré received the sum of 2,500 kronor together with a gold medal. Paul Appell was also rewarded with a gold medal in addition to the honourable mention. For various reasons the prize ceremony didn’t take place on the king’s birthday, but the announcement was made public that day. Instead Poincaré received his prize from the hands of the Swedish ambassador in Paris later in March. Mittag-Leffler also informed the French Academy of Sciences of the news.



One of Mittag-Leffler’s inventive ideas in promoting Acta Mathematica was to turn to King Oscar II of Sweden and Norway, both for financial support of the project and as the first enlisted subscriber. In 1884 another grand idea from Mittag-Leffler had matured. Again involving King Oscar, he now wanted to arrange an international prize competition in mathematics honouring   the 60th birthday of the king. It seems that Mittag-Leffler first revealed his plan to Kovalevskaya. We find a short reference in a letter to her from 4 May 1884. 

The prize consisted of a gold medal and 2,500 Swedish kronor. (As a comparison, Mittag-Leffler’s annual salary as professor was 7,000 kronor.) The memoirs should be submitted before 1 June 1888 (almost three years after the announcement), with anonymity maintained through a motto on an enclosed sealed envelope containing the name of the author.

A list of all the twelve manuscripts received by June 1888 was published in Volume 11 of Acta with their identifying epigraphs. It turned out that five of the authors had attempted the prestigious Question 1, the n-body problem;  one had tried Question 3, while six treated a subject of their own, which remained a secondary option. Only four of the authors have been identified: in addition to Poincaré also Paul Appell, Guy de Longchamps and Jean Escary.

Finally after almost 300 handwritten pages (including the appendices) his (Poincaré ) new concept of integral invariants and the subsequent geometrical arguments led to a claim of stability for this system.

Although no entry had actually solved any of the questions, Mittag-Leffler and his jury were soon of the preliminary opinion that Poincaré was in a class of his own, that Appell should be awarded a second honorary prize, and that no other entries needed much further examination.

Mittag-Leffler made his final presentation to the king on 20 January 1889, the day before the monarch’s 60th birthday, only the brief summary from Weierstrass was enclosed in the general report. For the winning entry Henri Poincaré received the sum of 2,500 kronor together with a gold medal. Paul Appell was also rewarded with a gold medal in addition to the honourable mention. For various reasons the prize ceremony didn’t take place on the king’s birthday, but the announcement was made public that day. Instead Poincaré received his prize from the hands of the Swedish ambassador in Paris later in March. Mittag-Leffler also informed the French Academy of Sciences of the news.

Amid suspicions of a flaw in the work by assistant and gifted former student Edvard Phragmén, who became an active editor in Stockholm while Mittag-Leffler traveled Europe, the printing was held up.

Finally, in July 1889, Mittag-Leffler decided that it was time to take action and print Poincaré’s dissertation, with all its added appendices. This went on until mid November, when the next volume of Acta was due to appear. Phragmén  went on with the editorial work, and from the summer he was the only one who still raised objections to conclusions in the memoir that he didn’t understand, first to Mittag-Leffler and Weierstrass, and then directly in contact with Poincaré. The queries forced Poincaré more and more to confront his arguments in detail.On the last day of November 1889, an ominous telegram reached Mittag-Leffler. Poincaré briefly told him to stop the presses. He had found an error. An explanation was expected by letter the next day. After a sleepless night Mittag-Leffler could then read that the error was graver than Poincaré had first thought. “It is not true that the asymptotic surfaces are  closed”, he wrote.

Poincaré was asked to pay for the first printing, which he accepted. The expenses amounted to over 3,500 kronor, i.e. 1,000 more than the prize money he had received!

After intense work in December, and over Christmas and New Year, Poincaré was ready to submit a substantially revised memoir on 5 January 1890. He had altered some of the implicit assumptions which had turned out to be precipitate. Instead of stability for the restricted three-body problem, he had come to the inevitable conclusion that chaotic motion could occur, as we would now call the phenomenon.

The printing resumed in late April 1890, but Poincaré’s final memoir of 290 pages only appeared in December 1890, in Volume 13 of Acta, together with Appell’s contribution and Hermite’s report. 

Henri Poincaré and Gösta Mittag-Leffler



A remarkable epilogue to King Oscar’s prize competition occurred when the Finnish mathematician and astronomer Karl Sundman actually found a complete solution to Question 1 in the general case of three bodies. In articles between 1907 and 1912 he gave a proof of the convergence of an infinite series solution to the three-body problem for almost all initial values, using well-known results. Although the methods used are relatively simple, the very slow convergence renders the series solutions unusable for practical purposes, and they provide no qualitative insight into the motion of the bodies. Even though Sundman’s achievement was praised and received attention in the decade to follow, it soon faded into oblivion. In 1991 Qiudong Wang managed to generalize Sundman’s solution to the general n-body case. 

Extensive parts of this post have been clipped and/or paraphrased from a much longer article at Mittag-Leffler Institute  *PB











On This Day in Math - March 18

 

Steiner eircumellipse *wolfram  alpha


Scientific discovery consists in the interpretation for our own convenience of a system of existence which has been made with no eye to our convenience at all.
~Norbert Wiener


The 77th day of the year; 77 is the only number less than 100 with a multiplicative persistence of 4. Can you find the next? (Multiply all the digits of a number n, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative persistence, and the final digit obtained is called the multiplicative digital root of n.) There is not another year day that will have a multiplicative persistence greater than four. [7x7=49, 4x9=36, 3x6=18, 1x8=8]

772 is the smallest square number that can be the sum of consecutive squares greater than 1, \(sum_{k=18}^{28}k^2 = 77^2\)


Every integer greater than 77 is the sum of integers whose reciprocals sum to 1 @AlgebraFact. I take this to mean that 77 can not be the sum of such numbers, and 78 can. What are the digits that sum to 78 whose reciprocals sum to one? ***

The concatenation of all palindromes from one up to 77 is prime.

77 is equal to the sum of three consecutive squares, \(4^2 + 5^2 + 6^2= 77\) and also the sum of the first 8 primes. *Prime Curios

77 and 78 form the fourth Ruth-Aaron pair, named for the number of home runs hit by Babe Ruth, 714, and the number when Aaron broke the record, 715 (he hit more afterward).  They are consecutive numbers that have the same sums of their prime factors (77 = 7*11, 78 = 2*3*13, and 7+11 = 2+3+13).


***





EVENTS


1658  The younger Franz von Schooten, in a letter to John Wallis, challenged Fermat to prove or disprove the existence of  Perfect numbers other than the type of Euclid. At this time there was much discussion of whether or not other forms of perfect numbers existed that did not meet Euclid's format. In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Euclid stated that if the sum of the powers of two from zero to some n are a prime number p, then \( 2^n*P \) is perfect), although this method applies only to even perfect numbers. In a 1638 letter to Mersenne, Descartes proposed that every even perfect number is of Euclid's form, and stated that he saw no reason why an odd perfect number could not exist (Dickson 2005, p. 12). Descartes was therefore among the first to consider the existence of odd perfect numbers; prior to Descartes, many authors had implicitly assumed (without proof) that the perfect numbers generated by Euclid's construction comprised all possible perfect numbers (Dickson 2005, pp. 6-12). In 1657, Frenicle repeated Descartes' belief that every even perfect number is of Euclid's form and that there was no reason odd perfect number could not exist. Like Frenicle, Euler also considered odd perfect numbers.

To this day, it is not known if any odd perfect numbers exist, although numbers up to 10^(1500) have been checked without success, making the existence of odd perfect numbers appear unlikely (Ochem and Rao 2012). 
*Wolfram Mathworld



1649 Christopher Wren received his BA degree from Oxford. He was elected a Fellow of All Souls, Oxford, two years later and lived in the College until 1657. At Oxford Wren carried out many scientific experiments. He worked on anatomy, making drawings of the human brain for Willis's Cerebri anatome and he devised a blood transfusion method which he demonstrated by transfusing blood from one dog to another.
Wren's crypt at St. Pauls.. " 'Lector, si monumentum requiris, circumspice. ' Translated from the original Latin, this means, 'Reader if you wish to see his memorial, look around you. "




1940 The first bombe, an electro-mechanical device used to try to decode German Enigma codes, was named "Victory". It was installed in "Hut 1" at Bletchley Park on 18 March 1940 (14 March is sometimes given). It was based on Turing's original design and so lacked a diagonal board.  Successful messages from late April were de coded in May and June of the same year.  The first US Navy machines were competed and tested on 3 May of 1943.
*Wik



1965  Alexei Arkhipovich Leonov became the first person to conduct a spacewalk, exiting the capsule during the Voskhod 2 mission for 12 minutes and 9 seconds. He was also selected to be the first Soviet person to land on the Moon although the project was cancelled.  Leonov[a] (30 May 1934 – 11 October 2019) was a Soviet and Russian cosmonaut, Air Force major general, writer, and artist.*Wik
*Leonov's 1967 painting Near the Moon 



1973 Comet Kohoutek, formally designated C/1973 E1, 1973 XII, and 1973f, was first discovered on this date while examining photographic plates taken on 7 March 1973 by Czech astronomer Luboš Kohoutek. It attained perihelion on 28 December that same year. Will not be back for a really, really long time.

1986  The New York Times reports that a 17-year-old student in New Jersey had tracked the launch of the new Soviet space station, Mir, before the Soviet government formally announced it. With a group of friends, Phillip Naranjo tracked transmissions between space vessels and control centers on Earth. Just before the Russians announced Mir on February 20, the teens had picked up some Cyrillic code.




In 1987, the discovery of "high-temperature" superconductivity was announced to thousands of scientists at a packed meeting of the American Physical Society in New York City. The phenomenon, discovered 1911, was at first known to occur at only 4 degrees above absolute zero, when all electrical resistance in a metal sample disappeared. In 1986, researchers discovered a ceramic material that was a superconductor at a temperature of more than 30 degrees above absolute zero. When published in September of that year, that news stirred the wider scientific community into action. By the time of the APS meeting, further discoveries had been made. The scene of excitement at the meeting was dubbed the "Woodstock of Physics." *TIS

Many questions remain about high temperature superconductivity, and many of the expected applications have not appeared, speakers pointed out. At the time nothing seemed impossible; more great developments were expected to be just around the corner. But while engineers have made a number of minor improvements in high Tc materials, there have been no major breakthrough in the past 20 years. No one has made a room temperature superconductor, and it is not known whether such a material is possible. *APS

In 2020, the headline in Science  read:  "After decades, room temperature superconductivity achieved

But the hydrogen-based material requires high pressure"


1990 The Mathematische Gesellschaft, the world’s oldest existing mathematical society (founded 1690) began a seven day meeting in Hamburg to celebrate its third centenary. *VFR




2010 It was announced that Grigori Yakovlevich Perelman had met the criteria to receive the first Clay Millennium Prize for resolution of the Poincaré conjecture. On 1 July 2010, he turned down the prize of one million dollars, saying that he considers his contribution to proving the Poincaré conjecture to be no greater than that of Richard Hamilton, who introduced the theory of Ricci flow with the aim of attacking the geometrization conjecture. *Wik




2011 The Pluto-bound New Horizons spacecraft flew past Uranus’ orbit at about 6 p.m. EDT, 1.8 billion miles from Earth. New Horizons is now well over halfway through its journey to Pluto. Motoring along at 57,9000 km/hr (36,000 mph), it will travel more than 4.8 billion km (3 billion miles) to fly past Pluto and its moons Nix, Hydra and Charon in July 2015.The next planetary milestone for New Horizons will be the orbit of Neptune, which it crosses on Aug. 25, 2014, exactly 25 years after Voyager 2 made its historic exploration of that giant planet. *Universe Today (Hat tip to David Dickinson@Astroguyz



2012 The Sunday following March 15 is "Buzzard Sunday" at the Hinckley Reservation (Near Cleveland, Ohio) a family fun day celebrating the buzzards (a common name for the "turkey vulture,"). Every year on March 15 since 1957, the city of Hinckley Ohio has eagerly awaited the return of the buzzards at "Buzzards' Roost" at the Hinckley Reservation, part of the Cleveland Metroparks. *about.com         So in 2020 you'll have to wait until the 22nd for the official Buzzard Sunday!



BIRTHS

1550  Johannes Petreius, a German printer, died in Nuremberg on Mar. 18, 1550; his day and year of birth are unknown. Petreius was the foremost publisher of scientific books in the sixteenth century. The most famous book to emerge from his press was De revolutionibus orbium coelestium (1543) by Nicholas Copernicus (see fifth image above), but Petreius also printed books by such important authors as Regiomontanus (fourth image above), Girolamo Cardano, Johannes Schöner, Peter Apian, Witelo, and Ptolemy of Alexandria. When Georg Joachim Rheticus went to visit Copernicus in 1539, he brought several books with him, as presents, including the Petreius editions of Apian’s instrument book (second image above) and Witelo’s book on optics (third image above). The suspicion is that Rheticus was trying to show Copernicus what a fine printer Petreius was, so that Copernicus might choose Petreius as publisher for his own book. And that is exactly how things turned out. A detail from the Regiomontanus book shows the typical Petreius imprint, embellished by a fine example of Petreius' ability to print complicated astronomical diagrams .

The Linda Hall Library has one of the finest Petreius collections in the United States, with twenty-five Petreius imprints in our holdings. We used to be able to add a Petreius printing to the collection every few years, but Petreius books now command such a high price that further acquisitions seem unlikely. But we are pleased with what we have. *LH




1602 Jacques de Billy (18 March 1602 in Compiègne, France - 14 Jan 1679 in Dijon, France) was a French Jesuit. Billy corresponded with Fermat and produced a number of results in number theory which have been named after him. Billy had collected many problems from Fermat's letters and, after the death of his father, Fermat's son appended de Billy's collection under the title Doctrinae analyticae inventum novum (New discovery in the art of analysis) as an annex to his edition of the Arithmetica of Diophantus (1670). *SAU . At the College de Dijon he taught privately Jacques Ozanam, in whom he instilled a love of the calculus. *VFR




1640 Philippe de La Hire (or Lahire or Phillipe de La Hire) (March 18, 1640 – April 21, 1718) was a French mathematician and astronomer. According to Bernard le Bovier de Fontenelle he was an "academy unto himself". La Hire wrote on graphical methods, 1673; on conic sections, 1685; a treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708. His works on conic sections and epicycloids were founded on the teaching of Desargues, of whom he was his favourite pupil. He also translated the essay of Manuel Moschopulus on magic squares, and collected many of the theorems on them which were previously known; this was published in 1705. He also published a set of astronomical tables in 1702. La Hire's work also extended to descriptive zoology, the study of respiration, and physiological optics.
Two of his sons were also notable for their scientific achievements: Gabriel-Philippe de La Hire (1677–1719), mathematician, and Jean-Nicolas de La Hire (1685–1727), botanist.
The mountain Mons La Hire on the Moon is named for him. *Wik He was also the first to find the arc length of the cardioid in 1708.






1690 Christian Goldbach (18 Mar 1690, 20 Nov 1764) Russian mathematician whose contributions to number theory include Goldbach's conjecture, formulated in a letter to Leonhard Euler dated 7 Jul 1742. Stated in modern terms it proposes that: "Every even natural number greater than 2 is equal to the sum of two prime numbers." It has been checked by computer for vast numbers - up to at least 4 x 1014 - but still remains unproved. Goldbach made another conjecture that every odd number is the sum of three primes, on which Vinogradov made progress in 1937. (It has been checked by computer for vast numbers, but remains unproved.) Goldbach also studied infinite sums, the theory of curves and the theory of equations. *TIS




1796 Jakob Steiner (18 Mar 1796; 1 Apr 1863 at age 67) Swiss mathematician who was one of the greatest, contributors to projective geometry. He discovered the Steiner surface which has a double infinity of conic sections on it. The Steiner theorem states that the two pencils by which a conic is projected from two of its points are projectively related. He is also known for the Poncelet-Steiner theorem which shows that only one given circle and a straight edge are required for Euclidean constructions. His work included conic sections and surfaces, the theory of second-degree surfaces and centre-of-gravity problems. He developed the principle of symmetrization (1840-41). In 1848 he ws the first to define various polar curves with respect to a given curve, and introduced the “Steiner Curves.” *TIS




1839 Joseph Émile Barbier (18 March 1839 in St Hilaire-Cottes, Pas-de-Calais, France - 28 Jan 1889 in St Genest, Loire, France)
He was offered a post at the Paris Observatory by Le Verrier and Barbier left Nice to begin work as an assistant astronomer. For a few years he applied his undoubted genius to problems of astronomy. He proved a skilled observer, a talented calculator and he used his brilliant ideas to devise a new type of thermometer. He made many contributions to astronomy while at the observatory but his talents in mathematics were also to the fore and he looked at problems in a wide range of mathematical topics in addition to his astronomy work.
As time went by, however, Barbier's behaviour became more and more peculiar. He was clearly becoming unstable and exhibited the fine line between genius and mental problems which are relatively common. He left the Paris Observatory in 1865 after only a few years of working there. He tried to join a religious order but then severed all contacts with his friends and associates. Nothing more was heard of him for the next fifteen years until he was discovered by Bertrand in an asylum in Charenton-St-Maurice in 1880.
Bertrand discovered that although Barbier was clearly unstable mentally, he was still able to make superb original contributions to mathematics. He encouraged Barbier to return to scientific writing and, although he never recovered his sanity, he wrote many excellent and original mathematical papers. Bertrand, as Secretary to the Académie des Sciences, was able to find a small source of income for Barbier from a foundation which was associated with the Académie. Barbier, although mentally unstable, was a gentle person and it was seen that, with his small income, it was possible for him to live in the community. This was arranged and Barbier spent his last few years in much more pleasant surroundings.
Barbier's early work, while at the Observatory, consists of over twenty memoirs and reports. These cover topics such as spherical geometry and spherical trigonometry. We mentioned above his work with devising a new type of thermometer and Barbier wrote on this as well as on other aspects of instruments. He also wrote on probability and calculus.
After he was encouraged to undertake research in mathematics again by Bertrand, Barbier wrote over ten articles between the years 1882 and 1887. These were entirely on mathematical topics and he made worthwhile contributions to the study of polyhedra, integral calculus and number theory. He is remembered for Barbier's theorem, nicely explained here by Alex Bogomolny.*SAU

These Reuleaux polygons have constant width, and all have the same width; therefore by Barbier's theorem they also have equal perimeters.




1870 Agnes Sime Baxter (Hill) (18 March 1870 – 9 March 1917) was a Canadian-born mathematician. She studied at Dalhousie University, receiving her BA in 1891, and her MA in 1892. She received her Ph.D. from Cornell University in 1895; her dissertation was “On Abelian integrals, a resume of Neumann’s ‘Abelsche Integrele’ with comments and applications." *Wik




1891 Walter Andrew Shewhart (March 18, 1891 - March 11, 1967) was an American physicist, engineer and statistician, sometimes known as the father of statistical quality control.
W. Edwards Deming said of him, "As a statistician, he was, like so many of the rest of us, self-taught, on a good background of physics and mathematics. "
His more conventional work led him to formulate the statistical idea of tolerance intervals and to propose his data presentation rules, which are listed below:

Data have no meaning apart from their context.
Data contain both signal and noise. To be able to extract information, one must separate the signal from the noise within the data.
Walter Shewhart visited India in 1947-48 under the sponsorship of P. C. Mahalanobis of the Indian Statistical Institute. Shewhart toured the country, held conferences and stimulated interest in statistical quality control among Indian industrialists
*SAU




1911 Walter Ledermann (18 March 1911 in Berlin, Germany - 22 May 2009 in London, England) graduated from Berlin but was forced to leave Germany in 1933 to avoid Nazi persecution. He came to St Andrews and studied under Turnbull. He worked at Dundee and St Andrews until after World War II when he moved to Manchester and then to the University of Sussex. He is especially known for his work in homology, group theory and number theory. *SAU




1928 Lennart Axel Edvard Carleson (18 March 1928 in Stockholm, Sweden - ) is a Swedish mathematician who solved one of the most important problems in the theory of Fourier series. He was director of the Mittag-Leffler Institute, Stockholm, from 1968 to 1984, during which time he built the Institute from a small base into one of the leading mathematical research institutes in the world.*SAU





DEATHS

1871 Augustus de Morgan  (born 27 Jun 1806, 18 Mar 1871 at age 64) Born in Madura (now Madurai), India, son of a colonel in the Indian Army. He is best known for his work in Formal Logic. “De Morgan’s Laws”, are contained in his first book (1847), although they were known to Peter of Spain in the fourteenth century. *VFR
In formal logicDe Morgan's laws are rules relating the logical operators "and" and "or" in terms of each other via negation. With two operands A and B:

\overline{A \cdot B} = \overline A + \overline B
\overline{A + B} = \overline {A} \cdot \overline {B}

In another form:

NOT (P AND Q) = (NOT P) OR (NOT Q)
NOT (P OR Q) = (NOT P) AND (NOT Q)

The rules can be expressed in English as:

"The negation of a conjunction is the disjunction of the negations." and
"The negation of a disjunction is the conjunction of the negations."

*Wik
When he defined and introduced the term "mathematical induction" (1838), he gave the process a rigorous basis and clarity that it had previously lacked. He originated the use of the slash to represent fractions, as in 1/5 or 3/7. In Trigonometry and Double Algebra (1849) he gave a geometric interpretation of complex numbers. *TIS  A nice blog about De Morgan's life and relationships is at The Renaissance Mathematicus.
Teachers might give students the opportunity to find the date of his birth using De Morgan's own clues; “I was x years old in the year x2” *VFR





1907 Pierre-Eugène-Marcellin Berthelot (27 Oct 1827, 18 Mar 1907 at age 79) was a French chemist and science historian and government official whose creative thought and work significantly influenced the development of chemistry in the late 19th century. He helped to found the study of thermochemistry, introduced a standard method for determining the latent heat of steam, measured hundreds of heats of reactions and coined the words exothermic and endothermic. Berthelot systematically synthesized organic compounds, including some not found in nature. His syntheses of many fundamental organic compounds helped to destroy the classical division between organic and inorganic compounds. *TIS




1964 Norbert Wiener (26 Nov 1894; 18 Mar 1964) U.S. mathematician, who established the science of cybernetics, a term he coined, which is concerned with the common factors of control and communication in living organisms, automatic machines, and organizations. He attained international renown by formulating some of the most important contributions to mathematics in the 20th century. His work on generalised harmonic analysis and Tauberian theorems won the Bôcher Prize in 1933 when he received the prize from the American Mathematical Society for his memoir Tauberian theorems published in Annals of Mathematics in the previous year. His extraordinarily wide range of interests included stochastic processes, quantum theory and during WW II he worked on gunfire control. *TIS Cybernetics, published in 1948, was a major influence on later research into artificial intelligence. In the book, Wiener drew on World War II experiments with anti-aircraft systems that anticipated the course of enemy planes by interpreting radar images. Wiener also did extensive analysis of brain waves and explored the similarities between the human brain and a modern computing machine capable of memory association, choice, and decision making.*CHM (Wiener is somewhat revered as the ultimate absent-minded professor. An anecdote I used to share with my classes, almost certainly exaggerated, went something like this: Wiener had moved to a new address, and his wife knowing of his forgetfulness wrote a note with his new address and put it in his coat pocket. During the day struck by a mathematical muse he whipped out the piece of paper and scribbled notes on the back, then realizing his idea had been wrong, he tossed the piece of paper away and went about his day. In the afternoon he returned to his old house out of habit and coming up to the empty house remembered that he had moved, but not where. As he started to leave a young girl walked up and he stopped here. "Young lady, I am the famous mathematician Wiener. Do you know where I live?" The lass replied, "Yes, father, I'll show you the way home."... )
Wiener is buried in Vittum Hill Cemetery in Sandwich, Carroll County, New Hampshire, USA
reader Tom ‏@umacf24 told me that "Before this guy, 'kyber' was an obscure Greek word for 'steering.' " (seems very appropriate root) Thanks Tom.



1989 Sir Harold Jeffreys (22 Apr 1891, 18 Mar 1989 at age 97)English astronomer, geophysicist and mathematician who had diverse scientific interests. In astronomy he proposed models for the structures of the outer planets, and studied the origin of the solar system. He calculated the surface temperatures of gas at less than -100°C, contradicting then accepted views of red-hot temperatures, but Jeffreys was shown to be correct when direct observations were made. In geophysics he researched the circulation of the atmosphere and earthquakes. Analyzing earthquake waves (1926), he became the first to claim that the core of the Earth is molten fluid. Jeffreys also contributed to the general theory of dynamics, aerodynamics, relativity theory and plant ecology.*TIS




2001 Dirk Polder (August 23, 1919, The Hague — March 18, 2001, Iran) was a Dutch physicist who, together with Hendrik Casimir, first predicted the existence of what today is known as the Casimir-Polder force, sometimes also referred to as the Casimir effect or Casimir force. He also worked on the similar topic of radiative heat transfer at nanoscale. *Wik


2013 Mary Ellen Rudin (born December 7, 1924, Hillsboro, Texas - March 18, 2013, Madison, Wisconsin) was an American mathematician.
Born Mary Ellen Estill, she attended the University of Texas, completing her B.A. in 1944 and her Ph.D. in 1949, under Robert Lee Moore. In 1953, she married the mathematician Walter Rudin. Following her mentor Moore, her research centers on point-set topology. She was appointed as Professor of Mathematics at the University of Wisconsin in 1971, and is currently a Professor Emerita there. She served as vice-president of the American Mathematical Society, 1980–1981. In 1984 she was selected to be a Noether Lecturer. She is an honorary member of the Hungarian Academy of Sciences (1995).
Rudin is best known in topology for her constructions of counterexamples to well-known conjectures. Most famously, she was the first to construct a Dowker space, thus disproving a conjecture of Dowker's that had stood, and helped drive topological research, for more than twenty years. She also proved the first Morita conjecture and a restricted version of the second. Her latest major result is a proof of Nikiel's conjecture. Rudin's Erdős number is 1.
"Reading the articles of Mary Ellen Rudin, studying them until there is no mystery takes hours and hours; but those hours are rewarded, the student obtains power to which few have access. They are not hard to read, they are just hard mathematics, that's all." (Steve Watson)
She lived in Madison, Wisconsin, in the Rudin House, a home designed by architect Frank Lloyd Wright, and died at the age of 88. *SAU




2015 Bernice (Trimble) Steadman (July 9, 1925, Rudyard, Michigan – March 18, 2015, Traverse City, Michigan) was an American aviator and businesswoman. She was one of thirteen women chosen to take the same tests as the astronauts of the Mercury 7 during the early 1960's. The group later became known as the Mercury 13. However, Steadman and the other twelve women in the program were denied the opportunity to become astronauts due to their gender.[Steadman, a professional pilot, later co-founded the International Women's Air & Space Museum in Ohio during the 1980's.  

Bernice Steadman died at her home in Traverse City, Michigan, on March 18, 2015, at the age of 89 following a lengthy battle with Alzheimer's disease. *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 & Campbel