On This Day in Math - June 21

 

I had this rare privilege of being able 
to pursue in my adult life, 

what had been my childhood dream.

~Andrew Wiles

The 172nd day of the year; seventeen 2's followed by two 17's is prime.*Prime Curios
222222222222222221717 is prime

172 = pi(1+7+2) * p_n{(1*7*2)} . It is the only known number (up to 10^8) with this property.
pi(n) is the number of primes less than or equal to n, and p_n is the nth prime.

172/4 = 43, so 44^2 - 42^2 = 172

172/4 = 43, so 44^2 - 42^2  = 172

172 is the sum of Euler's Totient function (the number of smaller numbers for each n, which are coprime to n) over the first 23 integers

172 is the number of pieces a circle can be divided into with 18 straight cuts. It is sometimes called the Lazy Caterer's sequence, and is given by the relation \(p = \frac{n^2+n+2}{2}\)
Since I haven't mentioned this anywhere else yet, these numbers appear in Floyd's Triangle, a programing exercise for beginning programmers which has the Lazy Caterer sequence going veritcally down the altitude of a triangle of numbers, and the triangular numbers on the hypotenuse
1
2, 3
4, 5, 6
7, 8, 9, 10
11.....

*Wik

Floyd's Triangle is the creation of Robert W Floyd, an outstanding computer scientist with many awards, so instead of all those, I tell you he was a roommate of Carl Sagan in college. *Wik

172 is a repdigit in base 6(444), and also in base 42 (44)

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EVENTS

1667 Louis XIV, The Sun King of France, attends the ceremony of inauguration of the Observatoire de Paris, the oldest working observatory in the world. *Amir D. Aczel, Pendulum, pg 66

The Paris Observatory (French: Observatoire de Paris;  a research institution of the Paris Sciences et Lettres University, is the foremost astronomical observatory of France, and one of the largest astronomical centers in the world. Its historic building is on the Left Bank of the Seine in central Paris, but most of the staff work on a satellite campus in Meudon, a suburb southwest of Paris.

The Paris Observatory at the beginning of the eighteenth century, with the wooden "Marly Tower" on the right, a remnant of the Machine de Marly moved to the grounds by Giovanni Cassini, for the mounting of long-tubed telescopes and even longer tubeless aerial telescopes.

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1669 Christopher Wren gives first proof that the hyperboloid of one sheet (Wren uses the term Hyperbolic Cylindroid.) is doubly ruled in the Philosophical Transactions of the Royal Society. The only three doubly ruled surfaces are the plane, the hyperboloid of one sheet, and the hyperbolic paraboloid. Wren includes an image of the hyperboloid of one sheet that may be the earliest ever in print. In a footnote in Boyer's History of History of Analytic Geometry he notes that there is a figure in Kepler's Stereometria which looks like it might be this shape. (It is interesting that in his work on the geometry of a barrel, Kepler gives an approximation formula for the volume of a barrel that is exact for the hyperboloid of one sheet.)
The invention of the telescope and efforts to reduce distortion in the lenses led to suggestions of hyperbolic lenses, and Wren's paper pointed out "an application thereof for grinding hyperbolical glasses." Newton had applied the knowledge that the hyperboloid of one sheet was doubly ruled in his notes in 1666 when he demonstrated how to turn the shape on a lathe holding the cutting tool obliquely to the axis of rotation.
The image of Newton's method below is from a paper by Professor Rickey on the net.

*Wik, *VFR,

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1798 Henry Cavendish reads a paper to the Royal Society of London describing experiments to measure the density of the earth, and hence its weight, with results that it is 5.48 times the density of water. (the figures seem to include at least one calculating error) *Philosophical Transactions, 1798, Part II, pgs 469-526

Cavendish  was an English experimental and theoretical chemist and physicist. He is noted for his discovery of hydrogen, which he termed "inflammable air". He described the density of inflammable air, which formed water on combustion, in a 1766 paper, On Factitious Airs. Antoine Lavoisier later reproduced Cavendish's experiment and gave the element its name. *Wik

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1808 on 30 June, Humphry Davy announced he had separated the element boron. However, working independently, French chemist, Joseph Louis Gay-Lussac had announced* the same accomplishment nine days earlier, on 21 Jun 1808*TIS

*Davy statue in his hometown, Penzance... (but he wasn't a Pirate).

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1838 The earliest stereoscopes, "both with reflecting mirrors and with refracting prisms", were invented by Sir Charles Wheatstone and constructed for him by optician R. Murray in 1832. Herbert Mayo  shortly described Wheatstone's discovery in his book Outlines of Human Physiology (1833) and claimed that Wheatstone was about to publish an essay about it. It was only one of many projects of Wheatstone's and he first presented his findings on 21 June 1838 to the Royal College of London. 

In this presentation he used a pair of mirrors at 45 degree angles to the user's eyes, each reflecting a picture located off to the side. It demonstrated the importance of binocular depth perception by showing that when two pictures simulating left-eye and right-eye views of the same object are presented so that each eye sees only the image designed for it, but apparently in the same location, the brain will fuse the two and accept them as a view of one solid three-dimensional object. Wheatstone's stereoscope was introduced in the year before the first practical photographic processes became available, so initially drawings were used. The mirror type of stereoscope has the advantage that the two pictures can be very large if desired.

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In 1886, the foundation stone of the Tower Bridge in London, England was laid (over a time capsule) by the Prince of Wales. The need to cross the River Thames at this point had become increasingly urgent for many years, and finally the necessary Act was passed in 1885. The bridge, designed by Mr. Wolfe Barry, CB, was completed at a cost of about £1,000,000. To permit the passage of tall ships between the towers, two bascule spans, each of 100-ft length, are raised. The side spans to the towers are of the more familiar suspension type. Pedestrians can traverse a high-level footway nearly at the top of the towers, even when the bridge is raised. It was officially opened 30 Jun 1894, by the Prince of Wales, later Edward VII, on behalf of Queen *TIS

*wik

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In 1893, the first Ferris wheel premiered at Chicago's Colombian Exposition, America's third world's fair. It was invented by George Washington Ferris, a Pittsburgh bridge builder, for the purpose of creating an attraction like the Eiffel Tower in Paris. Each of the 36 cars carried 60 passengers, making a full passenger load of 150 tons. Ferris didn't use rigid spokes: instead, he used a web of taut cables, like a bicycle wheel. Supported by two 140 foot steel towers, its 45 foot axle was the largest single piece of forged steel at the time in the world. The highest point of the wheel was 264 feet. The wheel and cars weighed 2100 tons, with another 2200 tons of associated levers and machinery. Ferris died just four years later, at the age of only 38. *TIS

"Pleasure wheels", whose passengers rode in chairs suspended from large wooden rings turned by strong men, may have originated in 17th-century Bulgaria. *Wik

The Original Ferris Wheel *Wik

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1929 Kazimierz Kuratowski (1896–1980) at a meeting of the Warsaw Section of the Polish Mathemat­ical Society, announced that a graph is planar iff it does not contain a subgraph homeomorphic to either K–5, the complete graph on 5 points, or K–3–3, the complete bipartite graph on two sets of three points. See HM 12, 258, for a discussion of the early history of this theorem which is now the most cited result in graph theory. *VFR (See June 18) 

 "A finite graph is planar if and only if it does not contain a subgraph that is a subdivision of K₅ (the complete graph on five vertices) or K_3,3 (complete bipartite graph on six vertices, three of which connect to each of the other three)." *Wik 
 (in more simple, but less exact terms,  "it can be drawn in such a way that no edges cross each other."  The well-known recreational problem of connecting three houses to three utilities is not possible to draw because it is K_3,3 (below).  The utility problem posits three houses and three utility companies--say, gas, electric, and water--and asks if each utility can be connected to each house without having any of the gas/water/electric lines/pipes pass over any other. (1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917)

(1913 Dudeney: first publication of Gas, Water and Electricity Problem. according to David Singmaster, Gardner says 1917)   [Since Kuratowski was 15 years old at this time, it could not have been a proof of the houses and utilities problem then, however it could have been proven by the Gem of Euler, (V - E + F = 2).  My version is here.  *PB ]

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1948 the first stored-program computer, the Small-Scale Experimental Machine, SSEM, ran its first program. Written by Professor Tom Kilburn, it took 52 minutes to run. The tiny experimental computer had no keyboard or printer, but it successfully tested a memory system developed at Manchester University in England. The system, based on a cathode-ray tube, could store programs. Previous electronic computers had to be rewired to execute each new problem. The Manchester computer proved theories set forth by John von Neumann in a report that proposed modifications to ENIAC, the electronic computer built at the University of Pennsylvania in the mid-1940s. The report also proposed the use of binary instead of digital numbers. *TIS

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1963 A brief note about the introduction of the Friden 6010 Computyper business computer system in the June, 21, 1963 edition of Electronics magazine. The 6010 was a small-scale desk-sized computing system with plug-board and tab-rack controlled programming/sequencing, as well as magnetic core memory for storage registers, and an electronic math unit for performing fixed point addition, subtraction, multiplication and division. The primary input to the machine was eight-channel punched paper tape or ledger cards, with human input through the keyboard of the included Friden Flexowriter. Output could be typewritten via the Flexowriter, or to punched tape or ledger cards via the Flexowriter's eight-channel tape punch. Later, various peripheral devices were added to the system's options including magnetic tape, and even a removable platter disk drive system.

It is one of the earliest all-electronic desktop calculators, and is generally regarded as the first solid-state transistorized electronic calculator, although there is evidence that Sharp (Compet 10) and IME (IME 84) actually introduced their first electronic calculator just days before Friden did.

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1976 Kenneth Appel and Wolfgang Haken announced that with the aid of a computer that they had proved the four color problem. Because of the use of the computer the solution was not quickly accepted by all, but today most mathematicians accept the proof as correct. However, no simple proof is known as yet. *VFR  

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In 1963 Donald B. Gillies had found three new primes. When the primes were confirmed the UIUC Math dept (which has a postal branch) used this cancellation stamp on all mail from roughly 1964 - 1976. When Appel and Haken proved the four color theorem ("Four Colors Suffice") a new stamp was created. Trivia question : how far away from Gillies did Appel live in Urbana Illinois ??
Answer : He lived 3 houses away. *Wik

*Wik courtesy of Chris Caldwell

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1993   Andrew Wiles  begins the three days of lectures leading to a solution of Taniyama-Shimura conjecture, and completing the proof of Fermat’s last theorem.. See (June 23)

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2023  On non-leap years (until 2039), this day marks the summer solstice in the northern hemisphere and the winter solstice in the southern hemisphere, and this is the day of the year with the longest hours of daylight in the northern hemisphere and the shortest in the southern hemisphere.  On Leap years it happens a day earlier.*Wik

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BIRTHS

1710 James Short (June 10 {June 21 NS), 1710, Edinburgh, Scot. -  June 14, 1768, London, Eng) British optician and astronomer who produced the first truly

parabolic and elliptic (hence nearly distortionless) mirrors for reflecting telescopes. During his working life of over 35 years, Short made about 1,360 instruments - not only for customers in Britain but also for export: one is still preserved in Leningrad, another at Uppsala and several in America. Short was principal British collator and computer of the Transit of Venus observations made throughout the world on 6th June 1761. His instruments travelled on Endeavour with Captain Cook to observe the next Transit of Venus on 3rd June 1769, but Short died before this event took place.

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 1781 Siméon-Denis Poisson ( 21 June 1781 – 25 April 1840) French mathematician known for his work on definite integrals, advances in Fourier series, electromagnetic theory, and probability. The Poisson distribution (1837) describes the probability that a random event will occur in a time or space interval under the conditions that the probability of the event occurring is very small, but the number of trials is very large so that the event actually occurs a few times. His works included applications to electricity and magnetism, and astronomy. He is also known for the Poisson's integral, Poisson's equation in potential theory, Poisson brackets in differential equations, Poisson's ratio in elasticity, and Poisson's constant in electricity.*TIS   Libri wrote of him: “His only passion has been science: he lived and is dead for it.” *VFR

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1857 Hugh Frank Newall, FRS FRAS (21 June 1857 – 22 February 1944) was a British astrophysicist. Newall held the first chair of astrophysics at Cambridge University (1909-1928). After teaching at Wellington College, he went to Cambridge to be an assistant to J. J. Thomson. He changed his interests from being senior demonstrator in experimental physics to astronomy when he facilitated the university's acquisition of the 25-inch Newall Telescope after the death of his father, Robert Stirling Newall, in 1889. His father, an engineer in manufacturing wire ropes and submarine telegraph cables, had the telescope built for private use at his Gateshead home. Hugh paid the moving expenses. When built, it was the largest in the world, and remained so for many years. He designed spectrographs and studied the solar corona, became director of the Solar Physics Observatory (1913) and led many eclipse expeditions. *TiS

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1863 Maximilian Franz Joseph Cornelius Wolf ( 21 June 1863 – 3 October 1932) was a German astronomer who founded and directed the Königstuhl Observatory. He used wide-field photography to study the Milky Way and used statistical treatment of star counts to prove the existence of clouds of dark matter. He was among the first astronomers to show that the spiral nebulae have absorption spectra typical of stars and thus differ from gaseous nebulae. His most important contribution was the introduction of photography to discover hundreds of asteroids, the first of which he named Brucia in honor of the donor of his 16-inch double telescope, Catherine Wolfe Bruce.*TIS

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1870 Clara Helene Immerwahr (21 June 1870 – 2 May 1915) was a German chemist. She was the first German woman to be awarded a doctorate in chemistry from the University of Breslau, and is credited with being a pacifist as well as a "heroine of the women's rights movement". From 1901 until her suicide in 1915, she was married to the Nobel Prize-winning chemist Fritz Haber.

Due to societal expectations that a married woman's place was in the home, her ability to conduct research was limited. She instead contributed to her husband's work with minimal recognition, translating some of his papers into English. On 1 June 1902 she gave birth to Hermann Haber (1902–1946), the only child of that marriage.

Confiding in Abegg, Immerwahr expressed her deep dissatisfaction with this subservient role:

It has always been my attitude that a life has only been worth living if one has made full use of all one's abilities and tried to live out every kind of experience human life has to offer. It was under that impulse, among other things, that I decided to get married at that time... The life I got from it was very brief...and the main reasons for that was Fritz's oppressive way of putting himself first in our home and marriage, so that a less ruthlessly self-assertive personality was simply destroyed.

*Wik

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1876 Willem Hendrik Keesom  (21 June 1876, Texel – 3 March 1956, Leiden)  Dutch physicist  who was a pioneer in cryogenics and was the first to solidify helium under pressure (1926). He was a research assistant for Kamerlingh Onnes working on the liquefaction of helium, and several years later, subsequently succeeded him (1923) as director of the Physics Laboratory at Leiden. In work done with M. Wolfke, after studying discontinuities in several properties of helium at very low temperatures (1927) they suggested that it may be due to a phase change. They called the helium above the transitional helium I and the helium below the transition helium II. In 1932, he produced a temperature just two degrees above absolute zero (-272° C or -457.6° F). In 1942 he wrote the book Helium.*TiS

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1916  Herbert Friedman (June 21, 1916 – September 9, 2000) American astronomer who made seminal contributions to the study of solar radiation. He joined the Naval Research Laboratory in 1940 and developed defense-related radiation detection devices during WW II. In 1949, he obtained the first scientific proof that X rays emanate from the sun. When he directed the firing into space of a V-2 rocket carrying a detecting instrument. Through rocket astronomy, he also produced the first ultraviolet map of celestial bodies, and gathered information for the theory that stars are being continuously formed, on space radiation affecting Earth and on the nature of gases in space. He also made fundamental advances in the application of x rays to material analysis.*TiS

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1918 Tibor Szele (21 June 1918 – 5 April 1955) worked in group theory. *VFR  Hungarian mathematician, working in combinatorics and abstract algebra. After graduating at the Debrecen University, he became a researcher at the Szeged University in 1946, then he went back to Debrecen University in 1948 where he became full professor in 1952. He worked especially in the theory of Abelian groups and ring theory. He generalized Hajós's theorem. He founded the Hungarian school of algebra. *Wik

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1954 David Ríos Insua (born June 21, 1964 in Madrid) is a Spanish mathematician, and son and disciple of Sixto Ríos, father of Spanish Statistics. He is currently also the youngest Fellow of the Spanish Royal Academy of Sciences (de la Real Academia de Ciencias Exactas, Físicas y Naturales, RAC), which he joined in 2008. He received a PhD in Computational Sciences at the University of Leeds. He is Full Professor of the Statistics and Operations Research Department at Rey Juan Carlos University (URJC), and he has been Vice-dean of New Technologies and International Relationships at URJC (2002–2009). He has worked in fields such as Bayesian inference in neuronal networks, MCMC methods in decision analysis, Bayesian robustness or adversarial risk analysis. He has also worked in applied areas such as Electronic Democracy, reservoirs management, counterterrorism model and many others. He is married and has two daughters. Wik

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1964 Haim Nessyahu was born in Tel Aviv, on June 21st, 1964, the only son to Judith and Mordechay. His long journey of studying began at home, where his intellectual and almost antipodal mother and father created a very fertile ground for learning and nourished his zest for learning, questioning and thinking.

His formal education began in 1970 in “Gavrieli” school, in Tel-Aviv. Then, in 1973, Haim joined a newly formed class of gifted children, the first of its kind in Israel. Haim stayed with this class throughout the years in “Gretz” primary school and high-school “Ironi Dalet”. In that class, Haim met most of his lifetime friends that accompanied him and his family until his last day and beyond.

In 1982, Haim joined the military academic reserve, in the framework of which he studied towards a B.Sc. degree in mathematics and computer science at Tel Aviv University. He graduated in 1984, Summa Cum Laude. During the following five-year military service in the Intelligence Force, Haim completed his Masters in applied mathematics under the supervision of Professor Eitan Tadmor and began working on his doctoral thesis.

After resigning from the army, in 1989, he joined Professor Tadmor at NASA Langley Research Center, in Hampton Virginia, as a graduate fellow, where he continued his mathematical research. From there, Haim went on a six-month backpacking trip to South America, after which he returned to Tel Aviv University as an Instructor. He completed his doctoral dissertation in 1994 and was accepted for a post-doctoral position as Assistant Professor of Computational and Applied Mathematics at the University of Los Angeles (UCLA).

Before departing to Los Angeles, Haim and Dafna, his partner, went on a trip to the Far East.

At dawn of April 26th, on their way down from the Annapurna Mountain in Nepal, Haim suffered a heart failure and passed away.

Haim's parents decided to commemorate their son's memory by establishing The Nessyahu Award. The award is given for outstanding achievements in a mathematical Ph.D. dissertation. *Israel Mathematical Union

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DEATHS

1820 Alexis Thérèse Petit (2 October 1791, Vesoul, Haute-Saône – 21 June 1820, Paris) was a French physicist.

Petit is known for his work on the efficiencies of air- and steam-engines, published in 1818 (Mémoire sur l’emploi du principe des forces vives dans le calcul des machines). His well-known discussions with the French physicist Sadi Carnot, founder of thermodynamics, may have stimulated Carnot in his reflexions on heat engines and thermodynamic efficiency. The Dulong–Petit law (1819) is named after him and his collaborator Pierre Louis Dulong.

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1874 Anders Jonas Ångström (  13 August 1814 – 21 June 1874) was a Swedish physicist whose pioneering use of spectroscopy is recognised in the name of the angstrom, a unit of length equal to 10^-10 metre. In 1853, he studied the spectrum of hydrogen for which Balmer derived a formula. He announced in 1862 that analysis of the solar spectrum showed that hydrogen is present in the Sun's atmosphere. In 1867 he was the first to examine the spectrum of aurora borealis (northern lights). He published his extensive research on the solar spectrum in Recherches sur le spectre solaire (1868), with detailed measurements of more than 1000 spectral lines. He also published works on thermal theory and carried out geomagnetical measurements in different places around Sweden.*TIS

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1913  Gaston Tarry (27 September 1843 – 21 June 1913) was a French combinatorialist whose best-known work is a method for solving mazes.*SAU  He also was able to confirm Leonhard Euler's conjecture that no 6×6 Graeco-Latin square was possible. 
In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint sets A and B of n integers each, such that:

for each integer power  i from 1 to a given k.
For example, a solution with n = 6 and k = 5 is the two sets { 0, 5, 6, 16, 17, 22 } and { 1, 2, 10, 12, 20, 21 }, because:

0¹ + 5¹ + 6¹ + 16¹ + 17¹ + 22¹ = 1¹ + 2¹ + 10¹ + 12¹ + 20¹ + 21¹

0² + 5² + 6² + 16² + 17² + 22² = 1² + 2² + 10² + 12² + 20² + 21²

0³ + 5³ + 6³ + 16³ + 17³ + 22³ = 1³ + 2³ + 10³ + 12³ + 20³ + 21³

0⁴ + 5⁴ + 6⁴ + 16⁴ + 17⁴ + 22⁴ = 1⁴ + 2⁴ + 10⁴ + 12⁴ + 20⁴ + 21⁴

0⁵ + 5⁵ + 6⁵ + 16⁵ + 17⁵ + 22⁵ = 1⁵ + 2⁵ + 10⁵ + 12⁵ + 20⁵ + 21⁵.

This problem was named after Eugène Prouhet, who studied it in the early 1850s, and Gaston Tarry and Escott, who studied it in the early 1910s.

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1940 Wolfgang Döblin, known in France as Vincent Doblin, (17 March 1915 – 21 June 1940) was a German-French mathematician. Wolfgang was the son of the Jewish-German novelist, Alfred Döblin. His family escaped from Nazi Germany to France where he became a citizen. Studying probability theory at the Institute Henri Poincaré under Fréchet, he quickly made a name for himself as a gifted theorist. He became a doctor at age 23. Drafted in November 1938, after refusing to be exempted of military service, he had to stay in the active Army when World War II broke out in 1939, and was quartered at Givet, in the Ardennes, as a telephone operator. There, he wrote down his latest work on the Chapman-Kolmogorov equation, and sent this as a "pli cacheté" (sealed envelope) to the French Academy of Sciences. His company, sent to the sector of the Saare on the ligne Maginot in April 1940, was caught in the German attack in the Ardennes in May, withdrew to the Vosges, and capitulated on June 22, 1940. On June 21, Doeblin had committed suicide in Housseras (a small village near to Epinal), at the moment where German troops came in sight of the place. In his last moments, he burned his mathematical notes.
The sealed envelope was opened in 2000, revealing that Döblin was ahead of his time in the development of the theory of Markov processes. In recognition of his results, Itō's lemma is now referred to as the Itō–Doeblin Theorem.
His life was recently the subject of a movie by Agnes Handwerk and Harrie Willems, A Mathematician Rediscovered. *Wik

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1948 Sir D'Arcy Wentworth Thompson CB FRS FRSE (2 May 1860 – 21 June 1948)  graduated from Cambridge University in Zoology. He was a appointed Professor of Biology at Dundee and later Professor of Natural History at St Andrews. He combined skills in a way that made him unique. He was a Greek scholar, a naturalist and a mathematician. He was the first biomathematician. He became an honorary member of the EMS in 1933. *SAU

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1957 Johannes Stark ( 15 April 1874 – 21 June 1957) was a German physicist who was awarded the Nobel Prize in Physics in 1919 "for his discovery of the Doppler effect in canal rays and the splitting of spectral lines in electric fields". This phenomenon is known as the Stark effect.

Stark received his Ph.D. in physics from the University of Munich in 1897 under the supervision of Eugen von Lommel, and served as Lommel's assistant until his appointment as a lecturer at the University of Göttingen in 1900. He was an extraordinary professor at Leibniz University Hannover from 1906 until he became a professor at RWTH Aachen University in 1909. In 1917, he became professor at the University of Greifswald, and he also worked at the University of Würzburg from 1920 to 1922.

A supporter of Adolf Hitler from 1924, Stark was one of the main figures, along with fellow Nobel laureate Philipp Lenard, in the anti-Semitic Deutsche Physik movement, which sought to remove Jewish scientists from German physics. He was appointed head of the German Research Foundation in 1933 and was president of the Reich Physical-Technical Institute from 1933 to 1939. In 1947 he was found guilty as a "Major Offender" by a denazification court. *Wik

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1999 Edwin Hewitt (January 20, 1920, Everett, Washington – June 21, 1999) was an American mathematician known for his work in abstract harmonic analysis and for his discovery, in collaboration with Leonard Jimmie Savage, of the Hewitt–Savage zero–one law. [The Hewitt–Savage zero–one law is a theorem in probability theory, similar to Kolmogorov's zero–one law and the Borel–Cantelli lemma, that specifies that a certain type of event will either almost surely happen or almost surely not happen.]

He received his Ph.D. in 1942 from Harvard University, and served on the faculty of mathematics at the University of Washington from 1954.

Hewitt pioneered the construction of the hyperreals by means of an ultrapower construction (Hewitt, 1948).

Hewitt wrote the 1975 English translation of A. A. Kirillov's 1972 Russian monograph Elements of the Theory of Representations (Элементы Теории Представлений), and co-authored Abstract Harmonic Analysis with Kenneth A. Ross (1st edn., 1st vol. in 1963; 1st edn., 2nd vol. in 1970), an extensive work in two volumes.  *Wik

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2007 John Todd (May 16, 1911 – June 21, 2007) was a Northern Irish mathematician most of whose career was spent in England and the USA; he was a pioneer in the field of numerical analysis.

He was born in Carnacally, County Down, Ireland, and grew up near Belfast. He attended Methodist College Belfast after winning a scholarship. In his final year at the College he only studied maths as a result of his desire to become an engineer. He received his BSc degree from Queen's University in 1931, and went to St. John's College at Cambridge University, studying for 2 years with J. E. Littlewood, who advised him against getting a doctorate and just to do research.

He taught at Queen's University Belfast 1933-1937, and was an invited speaker at the 1936 ICM in Oslo on "Transfinite Superpositions of Absolutely Continuous Functions"

He worked at King's College in London for the years 1937–1939 (and again 1945–1947), where he met Olga Taussky, a matrix and number theorist (she had also been an invited speaker in Oslo). They were married in 1938. Todd returned to Belfast to teach at Methodist College Belfast 1940-1941. As part of the war effort, he had worked for the British Admiralty 1941-1945. One of Todd's greatest achievements was the preservation of the Mathematical Research Institute of Oberwolfach in Germany at the end of the war.

In 1945 the Todds emigrated to the United States and worked for the National Bureau of Standards. In 1957 they joined the faculty of California Institute of Technology in Pasadena, California.

Todd retired from the faculty, and in May, 2001 was honored by a symposium at Caltech in honor of his 90th birthday. He was called Jack Todd by all who knew him. He died at his home in Pasadena, California on June 21, 2007. *Wik

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2017 Jean-Pierre Kahane (11 December 1926 – 21 June 2017) was a French mathematician with contributions to harmonic analysis.

Kahane attended the École normale supérieure and obtained the agrégation of mathematics in 1949. He then worked for the CNRS from 1949 to 1954, first as an intern and then as a research assistant. He defended his PhD in 1954; his advisor was Szolem Mandelbrojt.

He was assistant professor, then professor of mathematics in Montpellier from 1954 to 1961. Since then, he has been professor until his retirement in 1994, then professor emeritus at the Université de Paris-Sud in Orsay.

He was a Plenary Speaker at the International Congress of Mathematicians in 1962 in Stockholm and an Invited Speaker at the 1986 ICM meeting in Berkeley, California. He was elected corresponding member of the French Academy of Sciences in 1982 and full member in 1998. He was president of the Société mathématique de France, the French Mathematical Society from 1971 to 1973. In 2000 Kahane received an honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden In 2002 he was elevated to the rank of commander in the order of the Légion d'Honneur. In 2012 he became a fellow of the American Mathematical Society

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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 

On This Day in Math - September 7

   

If there is a problem you can't solve, 

then there is an easier problem you can solve: find it.

~George Polya, How to Solve It

The 250th day of the year; 250 is the smallest number expressible as the
sum of two positive cubes, which is also expressible as the sum of two (unique)
positive squares in more than one way. ( on Feb. 16, 1745 Euler wrote to Goldbach and shows that numbers represented in two different ways as a sum of two squares must be composite; hence 250 is composite. )
5³+ 5 ³ = 250
15²+ 5 ² = 250 ; 13 ² + 9² = 250

and 250 = (3!)³ + (2!)^⁵ + (1!)⁷+ (0!)⁹ *Derek Orr

250 is the smallest multidigit number where the sum of the squares of its prime factors is the same as the sum of the squares of its digits. *Prime Curios


250 is the 49th prime - 1. Its square is also one less than a prime

Strange that I would learn this from a Brit, but "Length of a baseball pitch, pitcher to batter (18.44 m) is 250 x Diameter of regulation baseball (73.7 mm)  *http://www.isthatabignumber.com
He used the term for the "pitch" (pitching or bowling area) in cricket, and btw, the cricket pitch is 1 chain, or 22 yards long, and that's 20.12 meters (but the batting (popping) crease is almost 1 1/4 meters in front of the stumps, so the pitching distances are very similar.  

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EVENTS

1460 Founding of the University of Basel. Both Bernoulli brothers later taught there. *VFR Johann Bernoulli took over as professor of mathematics, replacing his deceased older brother Jacob.

Founded in 1460, the University of Basel is the oldest university in Switzerland. Once a center of European humanism, it is now a highly research-oriented, internationally accessible institution that emphasizes life sciences and medicine.

Situated at the intersection of Switzerland, Germany, and France, the university is at the center of the science and innovation hub in the Basel region. As a comprehensive university, it brings together the full range of academic disciplines.

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1715 "Steal This Math Book" , William Johnson, of the Parish of St. Clement Danes, was indicted for feloniously stealing one Whiston's Astronomy, value 5 s. the Goods of Joseph Brown. Brown swore the Prisoner came into his Shop inquiring for some Mathematical Books, and took an Opportunity to steal the Book mention'd in the Indictment, which he afterwards sold to one Chapman in Chancery-lane , where the Book was found; and the Prisoner coming again to offer another Book to sell, he was secur'd. The Prisoner said he bought it of one Mohun , a Scholar of his; but could not prove it. The Jury found him Guilty to the value of 10 d. *Proceedings of the Old Bailey

I think the "Whiston" in the article may well be William Whiston, but he did not focus much on Astronomy.  But he did several lectures on astronomical topics and, in the words of Wikipedia, "His lectures were often accompanied by publications. "  One of two items that may have been printed and the stolen object were a) Solar System chart by William Whiston and John Senex he published in 1712, and b) "In 1715, he lectured on the total solar eclipse of 3 May 1715 (which fell in April Old Style in England); Whiston lectured on it at the time, in Covent Garden, and later, as a natural event and as a portent." *Wik

 Senex (1678–1740) was an English cartographer, engraver and explorer. He was also an astrologer, geologist, and geographer to Queen Anne of Great Britain.

Solar System chart by William Whiston and John Senex

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1844 In a letter to George Boole, Arthur Cayley indicated that he is “much interested” in a paper on quaternions by Sir William Rowan Hamilton: “the remarkable part of which is evidently that the factors of the product are not convertible [commutative], but as he observes, why should they be? ” Hamilton’s discovery of quaternions was an important step in the development of abstract algebra. *Desmond MacHale, George Boole, His Life and Work, Boole Press, Dublin, (1985), p. 57.  (The term "commutative" was created by Francois-Joseph Servois in a paper in Annales de Gergonne on October 1, 1814). *PB notes

  He almost discovered Quaternions well before Hamilton.    Carl Friedrich Gauss had also discovered quaternions in 1819, but this work was not published until 1900.  The idea that simple operations, such as the multiplication and addition of numbers, are commutative was for many years implicitly assumed. Thus, this property was not named until the 19th century, when mathematics started to become formalized. 

 The term then appeared in English in 1838. in Duncan Farquharson Gregory's article entitled "On the real nature of symbolical algebra" published in 1840 in the Transactions of the Royal Society of Edinburgh.*Wik

Notice the non commutative nature can be seen in this Irish stamp commemorating the discovery of quaternions.  the product of i*j is k, but the reversal j*i =-k.

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1848 Jean-Laurent Palmer, French instrument maker and inventor of the micrometer received his patent, no. 7518, for the micrometer caliper (calibre à vis et à vernier circulaire), which he exhibited at the Paris Exposition of 1867 as 'Systeme Palmer'.  

The idea for a micrometer – an instrument that measures distance or thickness by counting the turns of a screw – was 180 years old, and calipers were far older, but no one had ever combined the two into a single hand-held tool. Palmer's micrometer had two numerical scales--one to count the screw turns, and another to measure fractions of a turn. Since the threads were 1 mm apart, and since the fractional scale was divided into 20 parts, that means Palmers' instrument could measure thickness to an accuracy of .05 mm, and with a Vernier scale that could be reduced to .01 mm – one hundred-thousandth of a meter.  Impressive for such a simple instrument. [The Vernier scale is the group of lines along each side of the rotating cylinder.  Pierre Vernier (19 August 1580 – 14 September 1637) was a French mathematician and instrument inventor. He was the inventor and eponym of the vernier scale used in measuring devices.  His original use was on Astrology quadrants.]

*Linda Hall org

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1858 "Neither at Olmos nor Piura, did any enceinte woman leave her room during the eclipse, whilst some from curiosity, but more through fear, were in the streets, yet not daring to look upon the sun, lest malady befall them. The somber green light gave them the appearance of corpses, and they apprehended that a plague might be visited upon them. Afterwards, the muleteers told us that their animals stopped eating, and huddled together in evident alarm." Lieut. J M Gillis An Account of the Total Eclipse of the Sun on September 7,*NSEC 

(Gilliss (September 6, 1811 – February 9, 1865) was an astronomer, United States naval officer and founder of the United States Naval Observatory.

The first page is here, for the whole article see

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1909 The first junior high school in the United States, Indianola School, was opened in Columbus, Ohio. *Ohio and Its Resources, Ohio Chamber of Commerce, p. 7
 Its school building still exists and is owned by the Columbus City Schools, though it is now occupied by Graham Expeditionary Middle School, a charter operated by the Graham Family of Schools. *Wik

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1923 The AMS adopted a resolution “sanctioning the establishment of a lectureship to be known as the Josiah Willard Gibbs Lectureship, the lecture to deal in semi-popular form with some aspect of mathematics or its applications.” *VFR

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1927 The first Polish Mathematical Congress opened in Lwow. Presenters included Alfred Tarski, Waclaw Sierpinski, Bronislaw Knaster, Stanislaw Mazur, J.von Neumann *Kuratowski, A Half-Century of Polish Mathematics, p. 53 *John F Ptak Science books

We present electronic version of archival document. Memorial Book of the First Congress of Mathematics,

Lviv, 7-10.IX.1927

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1930 Kurt Godel, in a discussion on the foundations of mathematics organized by the Vienna Circle, announced his famous theorem on the incompleteness of arithmetic: There are true but unprovable statements. *VFR

Gödel's discoveries in the foundations of mathematics led to the proof of his completeness theorem in 1929 as part of his dissertation to earn a doctorate at the University of Vienna, and the publication of Gödel's incompleteness theorems two years later, in 1931. The incompleteness theorems address limitations of formal axiomatic systems. In particular, they imply that a formal axiomatic system satisfying certain technical conditions cannot decide the truth value of all statements about the natural numbers, and cannot prove that it is itself consistent. To prove this, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

Gödel also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted Zermelo–Fraenkel set theory, assuming that its axioms are consistent. The former result opened the door for mathematicians to assume the axiom of choice in their proofs. He also made important contributions to proof theory by clarifying the connections between classical logic, intuitionistic logic, and modal logic.

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BIRTHS

1707 Georges-Louis Leclerc, (7 September 1707 – 16 April 1788) Compte de Buffon born. Buffon’s needle experiment uses probability to estimate π. He introduced calculus into probability theory. *VFR 

A French naturalist, who formulated a crude theory of evolution and was the first to suggest that the earth might be older than suggested by the Bible. In 1739 he was appointed keeper of the Jardin du Roi, a post he occupied until his death. There he worked on a comprehensive work on natural history, for which he is remembered, Histoire naturelle, générale et particulière. He began this work in 1749, and it dominated the rest of his life. It would eventually run to 44 volumes, including quadrupeds, birds, reptiles and minerals. He proposed (1778) that the Earth was hot at its creation and, from the rate of cooling, calculated its age to be 75,000 years, with life emerging some 40,000 years ago*TIS

Thomas Jefferson in his notes Notes on the State of Virginia (1785), in which, among other topics, he famously defended his country against those Europeans who said that the Americas (North, South and Central) were unhealthy places populated by lesser animals and plants, compared with those of the Old World, and inhabited by peoples who were similarly weak and degenerate.  Leclerc was the most direct target of these rebuttals. The Histoire naturelle, générale et particulière, written in 44 quarto volumes between 1749 and 1809 by Georges-Louis Leclerc, Comte de Buffon, and his associates. Buffon had never been to the New World, but that did not prevent him from damning it. 

In 1781, in the midst of the American Revolutionary War, the British army rousted Thomas Jefferson from his home in Monticello. Politically unpopular, he retired from the governorship of Virginia and threw himself into writing. The result was his only book, Notes on the State of Virginia (1785), in which, among other topics, he famously defended his country against those Europeans.

The immediate source of these libels was Histoire naturelle, générale et particulière, written 1749 and 1809 by Georges-Louis Leclerc, Comte de Buffon, and his associates. A product of the age of French encyclopedists, Histoire naturelle pulled together a vast array of facts about natural history around the world. It was also the vehicle for Buffon's many ideas about the history of the Earth and the organisms that inhabit it. Buffon had never been to the New World, but that did not prevent him from damning it. His critique carried an importance far greater than its questionable scientific value. Anything that lessened the public opinion of America—awash in foreign debt, at war with a global superpower, supplicant to the thrones of France and Spain—had political significance. Buffon had to be answered.

The Secretary to the French delegation in Philadelphia was Francois, Marquis de Barbé-Marbois. (Later, as minister of the treasury for Napoleon I, he negotiated the Louisiana Purchase.) The French government had instructed Barbé-Marbois to assemble data on the 13 colonies, and he responded by preparing a 22-point questionnaire. A copy of this survey was given to Joseph Jones, a delegate from Virginia to the Continental Congress in Philadelphia, in late 1780. Jones realized that Jefferson would be the best person to respond. Whereas other states sent in replies of a few pages, Jefferson's response became a book in which he distilled all his knowledge of Virginia's political and constitutional history, geography and ethnography, and of the whole country's natural history. He also rebutted specific points from Histoire naturelle (although the pagination in Jefferson's octavo edition differed from the original). Using all his rhetorical skills, Jefferson destroyed Buffon's case for American inferiority.

Buffon was not the first to assert American degeneracy, and this idea was not based on natural history alone: Politics also played a part. Buffon's immediate source was a book by a Spanish naval officer, Don Antonio d'Ulloa (Relación histórica del viaje hecho de orden de su Majestad a la América Meridional, 1748). d'Ulloa's thesis was that the human condition in the Americas was degenerate as a result of a long history of colonialism, slavery, exploitation of natural resources and subjugation of the native peoples. To d'Ulloa, it was natural that America lacked the large mammals of the Old World and was rife with noxious insects and poisonous reptiles.

Buffon, focusing on North America, developed d'Ulloa's observations into a complex theory in which climate played a central role. In his ninth volume, published in 1761, Buffon compared mammalian species and noted examples in which the same species lived on both sides of the Atlantic Ocean. He claimed the New-World versions were always smaller and weaker. European livestock exported to America were always stunted. Species indigenous to the New World were always smaller than comparable species in the Old World (the largest American mammal was the tapir, nowhere near the size of an elephant). Of American Indians, he wrote, "the organs of generation (of the savage) are small and feeble. He has no hair, no beard, no ardour for the female. Though nimbler than the European, his strength is not so great. His sensations are less acute; and yet he is more timid and cowardly." And so on.

Jefferson refuted Buffon's claims, citing for example the American (black) bear at 412 pounds and the European bear at 153, the American beaver at 45 pounds and the European at 18. Jefferson's data do not bear close scrutiny (he listed the cow in America at 2,500 pounds and at 763 in Europe),

At one point, Jefferson hoped to send a complete skeleton of a mastodon (then often confused with mammoths) to France to confront Buffon with physical evidence. However, he never succeeded in getting a full skeleton shipped.

Buffon would later correct some of his previous criticisms of the New World.  *notes from New Scientist article

*Linda Hall org

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1819 Jean Claude Bouquet (7 Sept 1819 , 9 Sept 1885) was a French mathematician who worked on differential geometry and on series expansions of functions and elliptic functions. 

He worked with Charles Briot on doubly periodic functions.  Bouquet became friends with Briot at the Lycée and wanted to become a mathematics teacher.

Appointed an associate for the mathematics classes at colleges on September 16. 1842, he was immediately appointed to replace the elementary mathematics teacher at the Royal College of Marseille. In 1843, he obtained a PhD in Mathematical Sciences with a master thesis on variation of double integrals. In October 1845, at the age of 26, he became professor of pure mathematics at the Faculty of Sciences of Lyon

Bouquet was a respected teacher as well as researcher. It was rare for collaborative joint research papers such as those that Bouquet completed. His student, Jules Tannery, praised him highly as a teacher.*Wik

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1829 Friedrich August Kekulé von Stradonitz (7 September 1829–13 July 1896) Kekulé was a German theoretical chemist who figured out how carbon atoms could have a valence of four and join together to make long isomers or even rings. He was the first to discover the ring structure of benzene and greatly advanced the understanding of organic chemistry and aromatic compounds of the time.
Kekulé wrote about the method of his discovery where he was sitting by the fireplace and started to nod off. He dreamed of atoms arranging themselves in groups of ever increasing size until they became long chains. The chains started to wind and turn like snakes until one snake grabbed its own tail. He woke up suddenly and spent the rest of the night working out the structure.*This Day in Science History

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1884 Georges Jean Marie Valiron (7 September 1884, March 1955) was a French mathematician, notable for his contributions to analysis, in particular, the asymptotic behavior of entire functions of finite order and Tauberian theorems*Wik

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1903 Dudley Ernest Littlewood (7 September 1903, 6 October 1979) was a British mathematician known for his work in group representation theory.*SAU

He read mathematics at Trinity College, Cambridge, where his tutor was John Edensor Littlewood (they were not related). He was a lecturer at University College, Swansea from 1928 to 1947, and in 1948 took up the chair of mathematics at University College of North Wales, Bangor, retiring in 1970.

He worked on invariant theory and group representation theory, especially of the symmetric group, often in collaboration with Archibald Read Richardson of Swansea. They introduced the immanant of a matrix, studied Schur functions and developed the Littlewood–Richardson rule for their multiplication. Littlewood was also interested in the application of representation theory to quantum mechanics. *Wik 

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1912 David Packard (7 Sep 1912; 26 Mar 1996) U.S. entrepreneur and electrical engineer who cofounded the Hewlett-Packard Co., a leading manufacturer computers, computer printers, and analytic and measuring equipment. In 1939, he formed a partnership known as Hewlett-Packard Company with William R. Hewlett, a friend and Stanford classmate. HP's first product was a resistance-capacitance audio oscillator based on a design developed by Hewlett when he was in graduate school. The company's first "plant" was a small garage in Palo Alto, and the initial capital amounted to $538 *TIS

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1914 James Alfred Van Allen (7 Sep 1914; 9 Aug 2006)American physicist who discovered the Earth's magnetosphere, two toroidal zones of radiation due to trapped charged particles encircling the Earth (also known as the Van Allen radiation belts). During WWII he gained experience miniaturizing electronics, such as in the proximity fuse of a missile. After the war, he studied cosmic radiation, taking advantage of the unused German stock of V2 rockets launched into the outer regions of the atmosphere, carrying research devices using radio to relay back the data gathered. He was also involved in the early U.S. space program, and he had radiation measuring instruments on the first U.S. satellite, Explorer 1, launched 31 Jan 1958 with follow-up carried out by satellites Explorer 3 and 4 later the same year*TIS

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1936 Peter George Oliver Freund  (7 September 1936, Timișoara – 6 March 2018, Chicago) was a professor emeritus of theoretical physics at the University of Chicago. He made important contributions to particle physics and string theory. He is also active as a writer.

Freund was one of the originators of two-component duality which gave the original impetus to what then developed into string theory. He pioneered the modern unification of physics through the introduction of extra dimensions of space and found mechanisms by which the extra dimensions curl up.

Freund made significant contributions, to the theory of magnetic monopoles, to supersymmetry and supergravity, to number-theoretic aspects of string theory, as well as to the phenomenology of hadrons.*Wik

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1948 Cheryl Elisabeth Praeger, AM (born 7 September 1948, ) is an Australian mathematician. She is currently a professor of mathematics at the University of Western Australia. She is best known for her works in group theory, algebraic graph theory and combinatorial designs.

Her career has been largely spent in the Department of Mathematics and Statistics at the University of Western Australia. She was appointed full professor in 1983 and was head of the Department of Mathematics 1992–1994, inaugural dean of postgraduate research studies 1996–1998, chair Promotions and Tenure Committee 2000–2004, deputy dean of the Faculty of Engineering Computing and Mathematics 2003–2006, ARC Professorial Fellow 2007. and ARC Federation Fellow in 2009.

Praeger has supervised over 30 graduate students and in 1997 she supervised the Honours research work of Akshay Venkatesh who went on to win a 2018 Fields Medal, commonly regarded as the highest prize in mathematics.

*Wik

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1955 Efim Isaakovich Zelmanov (7 Sep 1955, --)Russian mathematician who was awarded the 1994 Fields Medal for his work on combinatorial problems in nonassociative algebra and group theory and particularly his solution of the Restricted Burnside problem. His Ph.D. (1980) Ph.D. thesis was on nonassociative algebra, wherein his treatment extending results from the classical theory of finite dimensional Jordan algebras to infinite dimensional Jordan algebras. In 1887, he showed that the Engel identity for Lie algebras implies nilpotence, in the previously unsolved case of infinite dimensions. The Restricted Burnside problem that he solved was a narrower condition arising out of Burnside's 1902 question whether a finitely generated group in which every element has finite order, is finite.*TIS

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DEATHS

1682 Juan Caramuel y Lobkowitz (23 May 1606, 7 Sept 1682) was a Spanish Cistercian who expounded the general principle of numbers to base n pointing out the benefits of some other bases than 10. 

He loved puzzles and published a collection containing some that he had composed when he was only ten years old. Mathematical puzzles and games of chance form part of Mathesis biceps (1670). He proposed a new method of trisecting an angle and developed a system of logarithms to base 109 where log 1010 = 0 and log 1 = 10. He was the first to publish log tables in Spanish. Among Caramuel's other scientific work we mention a system he developed to determine longitude using the position of the moon. He wrote widely on grammar, linguistics and rhetoric but perhaps his most interesting proposal in this area was to argue for the creation of a universal language.*SAU

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1719  John Harris (c. 1666 – 7 September 1719) was an English writer, scientist, and Anglican priest. He is best known as the editor of the Lexicon Technicum: Or, A Universal English Dictionary of Arts and Sciences (1704), the earliest of the English encyclopaedias; as the compiler of the Complete Collection of Voyages and Travels (1744), published under his name; and as the author of an unfinished county history of Kent..*Wik 

It was the first alphabetical scientific encyclopedia published in English, which initially appeared in a large quarto volume in 1704. Six years later he published a second volume, which also went from A to Z, but, interestingly, did not repeat anything in the first volume. 

Harris claimed that his encyclopedia was a new kind of reference work, designed not to be read piecemeal, but in large chunks, like a real book, since he took great pains to make the work a coherent whole. Out of curiosity, I tried this, opening volume 1 at random and reading a number of articles in a row. The entries are usually short, sometimes only a line or two, and I learned great deal about heraldry, and the bones of the human body (each one is listed and defined, in its proper alphabetical place, as far as I could tell), and occasionally I ran into a really interesting article, such as the one on “Engine”, where Harris discussed Thomas Savery's brand new steam engine, illustrating it with a large engraved plate . But I must confess, the coherence escaped me, especially since there were no cross references of any kind.*LH org

*LH org

 Savery's steam Engine *LH org

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1767 John Pond FRS (1767 – 7 September 1836) was a renowned English astronomer who became the sixth Astronomer Royal, serving from 1811 to 1835. Pond was born in London and, although the year of his birth is known, the records indicating the day and month have been lost to posterity. Pond's father made a fortune as a London merchant, enabling young John to enter Trinity College, Cambridge in 1784 at the age of sixteen. He took no degree, however, as his course was being interrupted by severe pulmonary attacks which compelled a long residence abroad. He was admitted to the Inner Temple in 1794, but his poor health prompted him to withdraw.
In 1811 Pond succeeded Nevil Maskelyne as Astronomer Royal. During an administration of nearly twenty-five years, he effected a reform of practical astronomy in England comparable to that brought about by Friedrich Bessel in Germany. In 1821 he began to employ the method of observation by reflection and in 1825 devised means of combining two mural circles in the determination of the place of a single object, the one serving for direct and the other for reflected vision. Under his auspices the instrumental equipment at Greenwich was completely changed and the number of assistants increased from one to six. The superior accuracy of his determinations was attested by Seth Carlo Chandler's 1894 discussion of them in the course of his researches into the variation of latitude. Between 1810 and 1824 he persistently controverted the reality of Ireland's Astronomer Royal John Brinkley's imaginary star-parallaxes. During the 1829-31 period, he briefly served as Superintendent of the Nautical Almanac. Delicacy of health obliged his retirement in the autumn of 1835.
died in Blackheath, London in the year of his 69th birthday and was buried beside and near fellow Astronomers Royal Edmond Halley and Nathaniel Bliss, respectively, in the churchyard of St Margaret's in nearby Lee. *Wik

Pole hill stands in Epping Forest at 0 degrees longitude, and 51 degrees 38 minutes north latitude. At its highest point it is 91 metres (299 ft) above sea level. It is noted for the fact that it lies directly on the Greenwich meridian and, being the highest point on that bearing directly visible from Greenwich, was at one time used as a marker by geographers at the observatory there to set their telescopes and observation equipment to a true zero degree bearing.

On the summit of the hill is an obelisk made of granite and bearing the following inscription:

"This pillar was erected in 1824 under the direction of the Reverend John Pond, MA, Astronomer Royal. It was placed on the Greenwich Meridian and its purpose was to indicate the direction of true north from the transit telescope of the Royal Observatory. The Greenwich Meridian as changed in 1850 and adopted by international agreement in 1884 as the line of zero longitude passes 19 feet to the east of this pillar."

At that point (19 feet / 5.8 m east) there is an Ordnance Survey trig point placed here to mark the top of the hill.

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1918 Peter Ludvig Mejdell Sylow  (12 December 1832 – 7 September 1918) . Sylow was a high school teacher who proved, in 1872, what is perhaps the most profound result in the theory of finite groups. The Sylow theorems are a collection of theorems that give detailed information about the number of subgroups of fixed Order of a group that a given finite group contains. The Sylow theorems form a fundamental part of finite group theory and have very important applications in the classification of finite simple groups. *Wik

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1936 Marcel Grossmann (April 9, 1878 – September 7, 1936) mathematician and a friend and classmate of Albert Einstein. He became a Professor of Mathematics at the Federal Polytechnic Institute in Zurich, today the ETH Zurich, specializing in descriptive geometry.
It was Grossmann who emphasized the importance of a non-Euclidean geometry called elliptic geometry to Einstein, which was a necessary step in the development of Einstein's general theory of relativity. Abraham Pais's book on Einstein suggests that Grossman mentored Einstein in tensor theory as well.
The community of relativists celebrates Grossmann's contributions to physics by organizing Marcel Grossman meetings every three years.*Wik

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1947 Michele Cipolla (28 October 1880; 7 September 1947) was an Italian mathematician, mainly specializing in number theory. He developed (among other things) a theory for sequences of sets and Cipolla's algorithm for finding square roots modulo a prime number. He also solved the problem of binomial congruence. *Wik

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1951 Harry Schmidt (21 June 1894, in Hamburg – 7 September 1951, in Halle) was a German mathematician who wrote on the application of mathematics to physics. *SAU

In 1945 Schmidt was appointed a professor ordinarius of applied mathematics at the Martin Luther University of Halle-Wittenberg, and later became there the director of the Institute for Applied Mathematics. After two years of severe illness, Schmidt died in September 1951 from pulmonary tuberculosis. *Wik

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1970 Percy Le Baron Spencer (9 Jul 1894, 7 Sep 1970) was the American engineer who invented the microwave oven. In 1940, Sir John Randall and Dr. H. A. Boot invented the magnetron tube to produce radar microwaves. After the war, Dr. Percy Spencer at the Raytheon Company was investigating the magnetron tube. During one experiment, he discovered that a chocolate bar in his pocket had totally melted, though the heating effect of microwaves was known earlier. Dr. Spencer deduced the magnetron radiation had melted the chocolate, not his body heat. This led Spencer to researched cooking food. The first commercial microwave ovens were made for restaurants.*TIS

Linda Hall Org

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1985 George P´olya, (December 13, 1888 – September 7, 1985) Professor Emeritus at Stanford died at the age of 97. In 1963, P´olya received the MAA award for Distinguished Service to Mathematics. The George P´olya Award for noteworthy expository articles in the College Mathematics Journal is named in his honor. *VFR Pólya worked in probability, analysis, number theory, geometry, combinatorics and mathematical physics. *Wik (Most of us remember him as an influential educator and his book "How to Solve it")

A classic quote of Polya, "There are many questions which fools can ask that wise men cannot answer."

In his popular book, How to Solve It, Polya tells this story on himself.

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1991 Edwin Mattison McMillan (September 18, 1907 – September 7, 1991) was an American physicist credited with being the first to produce a transuranium element, neptunium. For this, he shared the 1951 Nobel Prize in Chemistry with Glenn Seaborg.  Just as the planet Neptune is beyond Uranus, this new element was named neptunium, the first element beyond uranium, thus called a transuranium element. By irradiating uranium with rapid neutrons or with heavy-hydrogen nuclei (deuterons), other neptunium isotopes were soon produced in Berkeley. By 1940, McMillan with his colleagues working with Seaborg found that the radioactive decay of neptunium disintegrates yields element 94, called plutonium, after the planet Pluto beyond Neptune. During WW II he was engaged in national defence nuclear research. *TiS

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2004 Ralph Eugene Lapp (August 24, 1917 – September 7, 2004) was an American physicist who participated in the Manhattan Project.

 Lapp was an American nuclear physicist and author who began his career in high-energy physics research with Arthur H. Compton. Lapp then worked at Chicago on the Manhattan Project. With 69 others, he signed Leo Szilard’s 17 Jul 1945 petition to President Truman, the month before the attack on Hiroshima. They urged that Japan should have an opportunity to surrender before use of the atom bomb. (Nevertheless, the actual attack was by surprise.) After the war, he researched the results in Japan. Lapp lectured across the U.S. He wrote 22 books on nuclear safety, including the dangers of nuclear fallout in The Voyage of the Lucky Dragon (1958). A Post book reviewer in 1956 called him “a one-man atomic truth squad and nuclear lie detector.”

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2016 Joseph Bishop Keller (July 31, 1923 – September 7, 2016) is an American mathematician who specializes in applied mathematics. He is best known for his work on the "Geometrical Theory of Diffraction" (GTD).
He worked on the application of mathematics to problems in science and engineering, such as wave propagation. He contributed to the Einstein-Brillouin-Keller method for computing eigenvalues in quantum mechanical systems.
In 1988 he was awarded the U.S. National Medal of Science, and in 1997 he was awarded the Wolf Prize by the Israel-based Wolf Foundation. In 1996, he was awarded the Nemmers Prize in Mathematics.*Wik

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Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts

*LH Org = Linda Hall Org.

*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