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 - June 20

  

the enormous success of mathematics in the natural
sciences is something bordering on the mysterious and ...
there is no natural explanation for it.

—Eugene Wigner

The 171st day of the year; 171 has the same number of digits in Roman numerals as its cube.
CLXXI^3 =\( \overline{V}CCXI \)  5000211

\( 10^{171 } - 171 \) is a prime number with 168 9's followed by 829


Google calculator gives 171! = infinity. (close enough in many cases)

171 is the 18th triangular number and is the last year-day that is both a triangular number and a palindrome. *Ben Vitale

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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

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1686 Halley Writes to Newton that Hooke has protested his "discovery" of the inverse square law should be noted in Principia. Newton will respond On July 14, 1686, with a peace offering; "And now having sincerely told you the case between Mr Hooke and me, I hope I shall be free for the future from the prejudice of his letters. I have considered how best to compose the present dispute, and I think it may be done by the inclosed scholium to the fourth proposition." This scholium was "The inverse law of gravity holds in all the celestial motions, as was discovered also independently by my countrymen Wren, Hooke and Halley."

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1688 Newton, in a letter to Edmund Halley, again expresses his exasperation with carping critics. [Thanks to Howard Eves]*VFR

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1788; Washington Writes to Nicholas Pike to Thank him for a copy of his "A New and Complete System of Arithmetic" , published in 1786 by Nicholas Pike, a Newburyport schoolmaster. In his letter, sent June 20, 1788, from Mount Vernon, Washington writes: "The handsome manner in which that Work is printed and the elegant manner in which it is bound, are pleasing proofs of the progress which the Arts are making in this Country. Washington's letter to Pike also commended him on his accomplishments and the importance of his work.
Pike had written to  Washington on March 25,1786 requesting permission to dedicate the book to Washington. On June 20 of 1786, Washington had replied that, "I must therefore beg leave to decline the honour which you would do me, as I have before done in two or three cases of a similar kind."

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1808 Poisson submitted his first paper on the stability of the planetary system, one day before his twenty-seventh birthday. *VFR

His memoirs on celestial mechanics," in which he proved himself a worthy successor to Pierre-Simon Laplace. The most important of these are his memoirs Sur les inégalités séculaires des moyens mouvements des planètes."  In this memoir, Poisson discusses the famous question of the stability of the planetary orbits, which had already been settled by Lagrange to the first degree of approximation for the disturbing forces. Poisson showed that the result could be extended to a second approximation, and thus made an important advance in planetary theory. The memoir is remarkable inasmuch as it roused Lagrange, after an interval of inactivity, to compose in his old age one of the greatest of his memoirs, entitled Sur la théorie des variations des éléments des planètes, et en particulier des variations des grands axes de leurs orbites. So highly did he think of Poisson's memoir that he made a copy of it with his own hand, which was found among his papers after his death. Poisson made important contributions to the theory of attraction. *Wik

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1831 János Bolyai's pioneering work, The Absolutely True Science of Space, was published in 1832. This important work was published as an appendix to the first volume of his father,Farkas Bolyai's Tentamen , but its off-print had already been ready the previous year, in April 1831. The latter was the version which, together with a letter, was sent to Gauss by Farkas Bolyai on the 20th of June 1831. Gauss got the letter but János's work was lost on the way. On the 16th of January 1832 Farkas sent the Appendix to his friend again with another letter in which he wrote: ``My son appreciates Your critique more than that of whole Europe and it is the only thing he is waiting for''.
After twenty-three years of silence, Gauss replied to his ``old, unforgettable friend'' on the 6th of March 1832. One of his well-known sentences was: ``if I praised your son's work I would praise myself''. The letter deeply afflicted and upset János Bolyai, although it reflects appreciation, too: ``... I am very glad that it is my old friend's son who so splendidly preceded me'' *Komal Journal

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1877 Georg Cantor, in a letter to Dedekind, announced a proof that the points inside a square are in one-to-one correspondence with those on a line segment. Three years earlier, Cantor had intimated that this was clearly impossible. *VFR

A part of the letter, with a HatTip to Offer Pade'.

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1908 Count Zeppelin made his first flight in his fourth new airship at Friedrichshafen, Germany. The Luftschiff LZ4 had its first flight 20 Jun 1908. Its first extended flight (12 hours) was taken to Switzerland 1 Jul 1908. At the beginning of August, it embarked on an extended flight which had taken it among other places to Basel, Straussberg, and many of the major cities of southern Germany. While moored at Echterdingen on 5 Aug 1908, it was torn from the mast by high winds and destroyed. As interest in the Zeppelins ran high in German, the incident was felt as a national disaster. Spontaneous donations resulted in approximately 5.5 million Marks and made it possible for Zeppelin to continue his work. *TIS

*Wik

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In 1979, 32 solar panels on the White House roof, installed by the Carter administration, were dedicated. President Carter wished to demonstrate a committment to renewable energy use, as a model for the nation. About 3m x 1m x 10cm deep, the dark surfaces of the panels absorbed energy from sunlight, heating water passing through pipes snaking below them. Carter stated, “In the year 2000 this solar water heater behind me, which is being dedicated today, will still be here supplying cheap, efficient energy.” That was not to be. The subsequent Republican President, Ronald Reagan, with one of the worst environmental records of any president, while the roof was being resurfaced in 1986, had them removed and sent to warehouse storage. In the same year he slashed the research and development budget for renewable energy, and eliminated tax breaks for wind turbines and solar projects. *TiS

BIRTHS

1775 Jacques Frédéric Français (20 June 1775 in Saverne, Bas-Rhin, France - 9 March 1833 in Metz, France) In September 1813 Français published a work in which he gave a geometric representation of complex numbers with interesting applications. This was based on Argand's paper which had been sent, without disclosing the name of the author, by Legendre to François Français. Although Wessel had published an account of the geometric representation of complex numbers in 1799, and then Argand had done so again in 1806, the idea was still little known among mathematicians. This changed after Français' paper since a vigorous discussion between Français, Argand and Servois took place in Gergonne's Journal. In this argument Français and Argand believed in the validity of the geometric representation, while Servois argued that complex numbers must be handled using pure algebra. *SAU

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1838 Theodor Reye (20 June 1838 in Ritzebüttel, Germany and died 2 July 1919 in Würzburg, Germany) worked in Geometry and Projective Geometry.*SAU

He is best known for his introduction of configurations in the second edition of his book, Geometrie der Lage (Geometry of Position, 1876). The Reye configuration of 12 points, 12 planes, and 16 lines is named after him.

Reye also developed a novel solution to the following three-dimensional extension of the problem of Apollonius: Construct all possible spheres that are simultaneously tangent to four given spheres.

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1873 Alfred Loewy born.(20 June 1873 in Rawitsch, Germany (now Rawicz, Poznań, Poland) - 25 Jan 1935 in Freiburg im Breisgau, Germany) He worked in group theory and differential equations. *VFR

Loewy was appointed as an extraordinary professor at Freiburg in 1902. This made him secure enough financially to marry and in that year he married Therese Neuburger. Loewy became an honorary ordinary professor at Freiburg in 1916 before his appointment as ordinary professor in 1919. He was thesis advisor to a number of famous students, in particular Wolfgang Krull, who was awarded his doctorate in 1922, and Friedrich Karl Schmidt, who was awarded his doctorate in 1925. Other algebraists who spent some time in Freiburg working under Loewy are E Witt, Bernhard Neumann, R Brauer, R Baer, and A Scholz.

Anti-Semitism increased in Germany following the end of World War I. Anti-Semites joined forces with nationalists in attempting to blame the Jews for Germany's defeat. Increasing discrimination was not the only source of difficulty in Loewy's life. Already by 1916 he had lost the sight of one eye. His eyesight began to fail completely from about 1920 and he became totally blind before his death after a failed operation in 1928 left his other eye completely blind also. Despite these severe health problems Loewy continued to carry out his teaching duties. He could battle against blindness and against the hurt of anti-Semitism directed at him, but the final blow came in 1933 when anti-Semitism became part of the law of the land. On 30 January 1933 Hitler came to power and on 7 April 1933 the Civil Service Law was passed that provided the means of removing Jewish teachers from the universities, and of course also to remove those of Jewish descent from other roles. All civil servants who were not of Aryan descent (having one grandparent of the Jewish religion made someone non-Aryan) were to be retired. Loewy was forced to retire in 1933 under the Civil Service Law.

Among Loewy's most famous books are Lehrbuch der Algebra Ⓣ (1915) and Mathematik des Geld- und Zahlungsverkehrs Ⓣ (1920). The first of these was one of the first works to introduce into Germany the methodology, the terminology and the achievements of postulational analysis as it was being developed in the United States.

Loewy was Abraham Fraenkel's uncle by marriage and he exerted a large influence on Fraenkel's career in its early stages. It was Loewy who persuaded Fraenkel to travel to Marburg to study under Hensel and it was Loewy who had helped Fraenkel publish his early work in Crelle's journal with a paper about the date of Easter. But the mathematical topics Fraenkel studied were also influenced by Loewy whose interest in the study of axiomatic systems encouraged a similar interest by Fraenkel. The relationship worked both ways round, however, and Loewy's Grundlagen der Arithmetik Ⓣ, published in 1915, was prepared with Fraenkel's assistance. Loewy mentioned in this work that in the system of integers, the product of any two integers is zero, if and only if one of them is zero. Such ideas clearly influenced Fraenkel to introduce the notion of a ring, and in particular zero-divisors in rings. *SAU

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1917 Helena Rasiowa (20 June 1917 – 9 August 1994) was a Polish mathematician. She worked in the foundations of mathematics and algebraic logic.

There was an impressive collection of mathematicians at the University of Warsaw at this time including Borsuk, Łukasiewicz, Mazurkiewicz, Sierpiński, Mostowski and others. They had organised an underground version of the university which was strongly opposed by the Nazi authorities. Borsuk, for example, was imprisoned after the authorities found that he was helping to run the underground university.

In this dangerous situation Rasiowa learnt mathematics, knowing that the penalties for being discovered were extreme. Yet in this environment Rasiowa studied for her Master's Degree under Łukasiewicz's supervision.

In 1946, having obtained her Master's degree, she was appointed as an assistant at the University of Warsaw and continued to work for her doctorate under Mostowski's supervision. Her thesis, presented in 1950, was on algebra and logic Algebraic treatment of the functional calculus of Lewis and Heyting and these topics would be the main areas of her research throughout her life.

Rasiowa was promoted steadily, reaching the rank of Professor in 1957 and Full Professor in 1967. She led the Foundations of Mathematics Section from 1964 and the Mathematical Logic Section after its creation in 1970.

Her main research was in algebraic logic and the mathematical foundations of computer science. In algebraic logic she continued work by Post, Stone, Tarski and Łukasiewicz :-

... aimed at finding a precise description for the mathematical structure of formalised logical systems.

Of course Rasiowa's work on algebraic logic was in precisely the right area to make her a natural contributor to theoretical computer science. However it is one thing to be in the right area and yet another to have the ability to see the importance of a new subject such as computer science. Her contributions are described in :-

Her contribution to theoretical computer science stems from her conviction that there are deep relations between methods of algebra and logic on the one side and essential problems of foundations of computer science on the other. Among these problems she clearly distinguished inference methods characteristic of computer science and its applications. This conviction of hers had been supported by her results on many-valued and non-classical logics, especially on applications of various generalisations of Post algebras to logics of programs and approximation logics.

In fact in 1984 Rasiowa introduced an important concept of inference where the basic information was incomplete. This led to approximate reasoning and approximate logics which are now central to the study of artificial intelligence. *SAU

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1940 Leonard Susskind ( June(20ish) 1940 - )(The professor's real birthday seems difficult to determine; perhaps only known to him and his parents, perhaps only to his parents) is the Felix Bloch Professor of Theoretical Physics at Stanford University, and Director of the Stanford Institute for Theoretical Physics. His research interests include string theory, quantum field theory, quantum statistical mechanics and quantum cosmology. He is a member of the National Academy of Sciences, and the American Academy of Arts and Sciences, an associate member of the faculty of Canada's Perimeter Institute for Theoretical Physics, and a distinguished professor of the Korea Institute for Advanced Study.
Susskind is widely regarded as one of the fathers of string theory, having, with Yoichiro Nambu and Holger Bech Nielsen, independently introduced the idea that particles could in fact be states of excitation of a relativistic string. He was the first to introduce the idea of the string theory landscape in 2003. *Wik

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1942  Neil Sidney Trudinger (20 June 1942 - ) is an Australian mathematician, known particularly for his work in the field of nonlinear elliptic partial differential equations.

At the ANU Trudinger served as Head of the Department of Pure Mathematics, as Director of the Centre for Mathematical Analysis and as Director of the Centre for Mathematics and its Applications, before becoming Dean of the School of Mathematical Sciences in 1992. He currently coordinates ANU's Applied and Nonlinear Analysis program. He is co-author, together with his thesis advisor, David Gilbarg, of the book Elliptic Partial Differential Equations of Second Order.

His long list of awads includes :

2008, awarded the Leroy P. Steele Prize for Mathematical Exposition by the American Mathematical Society.

2012, elected as a fellow of the American Mathematical Society.

2014, gave the Łojasiewicz Lecture (on the "Optimal Transportation in the 21st Century") at the Jagiellonian University in Kraków. *Wik

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1946 Nigel John Kalton (June 20, 1946 – August 31, 2010) was a British-American mathematician, known for his contributions to functional analysis.

After studying mathematics at Trinity College, Cambridge, he received his PhD, which was awarded the Rayleigh Prize for research excellence, from Cambridge University in 1970. He then held positions at Lehigh University in Pennsylvania, Warwick, Swansea, University of Illinois, and Michigan State University, before becoming full professor at the University of Missouri, Columbia, in 1979.

He received the Stefan Banach Medal from the Polish Academy of Sciences in 2005] A conference in honour of his 60th birthday was held in Miami University of Ohio in 2006. He died in Columbia, Missouri, aged 64.

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David Kazhdan (Hebrew: דוד קשדן), born Dmitry Aleksandrovich Kazhdan (20 June 1946  ), is a Soviet and Israeli mathematician known for work in representation theory. Kazhdan is a 1990 MacArthur Fellow.

In 2002, he immigrated to Israel and is now a professor at the Hebrew University of Jerusalem as well as a professor emeritus at Harvard. Perhaps the most famous of the students that Kazhdan advised for a Ph.D. at Harvard was Vladimir Voevodsky who was awarded a Ph.D. in 1992 for his thesis Homology of Schemes and Covariant Motives. The ideas in this thesis eventually led to work which saw Voevodsky awarded a Fields Medal in 2002.

On October 6, 2013, Kazhdan was critically injured in a car accident while riding a bicycle in Jerusalem.

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DEATHS

1800 Abraham Kästner (27 September 1719 – 20 June 1800) was a German mathematician who compiled encyclopaedias and wrote text-books. He taught Gauss. *SAU

He was known in his professional life for writing textbooks and compiling encyclopedias rather than for original research. Georg Christoph Lichtenberg was one of his doctoral students, and admired the man greatly. He became most well-known for his epigrammatic poems. The crater Kästner on the Moon is named after him.

An epigram is a brief, interesting, memorable, sometimes surprising or satirical statement.  This literary device has been practiced for over two millennia. The presence of wit or sarcasm tends to distinguish non-poetic epigrams from aphorisms and adages, which typically do not show those qualities.

What is an Epigram? a dwarfish whole,

Its body brevity, and wit its soul.

— Samuel Taylor Coleridge ("Epigram", 1809)

Here lies my wife: here let her lie!

Now she's at rest – and so am I.

— John Dryden

*Wik 

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1807 Ferdinand Berthoud (19 March 1727 – 20 June 1807) Outstanding Swiss horologist and author of extensive treatises on timekeeping who became involved in the attempt to solve the problem of determining longitude at sea. His major achievement was his further development of an accurate and practical marine clock, or chronometer. (Such an instrument had previously been constructed in expensive and delicate prototypes by Pierre Leroy of France and John Harrison of England.) He made his first chronometer in 1754, which was sent for trial in 1761. Berthoud's improvements to the chronometer have been largely retained in present-day designs. *TIS

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1861 Sir Frederick Gowland (Hoppy) Hopkins OM PRS (20 June 1861 – 16 May 1947) was an English biochemist who was awarded the Nobel Prize in Physiology or Medicine in 1929, with Christiaan Eijkman, for the discovery of vitamins. He also discovered the amino acid tryptophan, in 1901. He was President of the Royal Society from 1930 to 1935. His Cambridge students included neurochemistry pioneer Judah Hirsch Quastel and pioneer embryologist Joseph Needham.
During his life, in addition to the Nobel Prize, Hopkins was awarded the Royal Medal of the Royal Society in 1918 and the Copley Medal of the Royal Society in 1926. Other significant honours were his election in 1905 to fellowship in the Royal Society, Great Britain's most prestigious scientific organisation; his knighthood by King George V in 1925; and the award in 1935 of the Order of Merit, Great Britain's most exclusive civilian honour. From 1930 -1935 he served as president of the Royal Society and in 1933 served as President of the British Association for the Advancement of Science. *Wik

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1865 Sir John William Lubbock, (London, England, 26 March 1803 - Downe, Kent, England, 20 June 1865 )English astronomer and mathematician. He made a special study of tides and of the lunar theory and developed a method for calculating the orbits of comets and planets. In mathematics he applied the theory of probability to life insurance problems. He was a strong proponent of Continental mathematics and astronomy.
Lubbock, third Baron Lubbock, was born into a London banking family. After attending Eton, he moved to Trinity College, Cambridge, where he became a student of William Whewell.(it was at the request of Lubbock that Whewell created the term "biometry".) He excelled in mathematics and traveled to France and Italy to deepen his knowledge of the works of Pierre-Simon de Laplace and Joseph Lagrange. Entering his father’s banking firm as a junior partner, he devoted his free time to science.
Lubbock strongly supported Lord Brougham’s Society for the Diffusion of Useful Knowledge [SDUK], which produced scientific and technical works designed for the working class. His articles on tides for the Society’s publications resulted in a book, *An Elementary Treatise on the Tides, in 1839. *Biographical Encyclopedia of Astronomers

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1963 Raphaël Salem (November 7, 1898 in Salonika, Ottoman Empire (now Thessaloniki, Greece) – June 20, 1963 in Paris, France) was a Greek mathematician after whom are named the Salem numbers and Salem–Spencer sets, and whose widow founded the Salem Prize.

 Salem left England in the autumn of 1940 and emigrated to the United States where he settled in Cambridge, Massachusetts. In 1941, he was appointed as a lecturer in mathematics at MIT, where he was rapidly promoted and became an assistant and associate professor. In 1958, he was appointed as Professor at the Sorbonne and lived in Paris until his death in 1963. In 1967, Éditions Hermann published Salem's Oeuvres mathématiques, edited by his collaborators Antoni Zygmund and Jean-Pierre Kahane. After Salem's death, his widow established the Salem Prize, an international prize given to young researchers for outstanding contributions to Fourier series.

In mathematics, a Salem number is a real algebraic integer 𝛼>1 whose conjugate roots all have absolute value no greater than 1, and at least one of which has absolute value exactly 1. Salem numbers are of interest in Diophantine approximation and harmonic analysis. They are named after Raphaël Salem. Because it has a root of absolute value 1, the minimal polynomial for a Salem number must be a reciprocal polynomial. This implies that 1/𝛼 is also a root, and that all other roots have absolute value exactly one. As a consequence α must be a unit in the ring of algebraic integers, being of norm 1.

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1966 Georges (Henri) Lemaître (17 July 1894 – 20 June 1966) was a Belgian astronomer and cosmologist, born in Charleroi, Belgium. He was also a civil engineer, army officer, and ordained priest. He did research on cosmic rays and the three-body problem. Lemaître formulated (1927) the modern big-bang theory. He reasoned that if the universe was expanding now, then the further you go in the past, the universe’s contents must have been closer together. He envisioned that at some point in the distant past, all the matter in the universe was in an exceedingly dense state, crushed into a single object he called the "primeval super-atom" which exploded, with all its constituent parts rushing away. This theory was later developed by Gamow and others.*TIS  The term "big bang" was created shortly after 6:30 am GMT on BBC's The Third Program, Fred Hoyle used the term in describing theories that contrasted with his own "continuous creation" model for the Universe. "...based on a theory that all the matter in the universe was created in one big bang ... ". *Mario Livio, Brilliant Blunders

He was the first to theorize that the recession of nearby galaxies can be explained by an expanding universe, which was observationally confirmed soon afterwards by Edwin Hubble.He first derived "Hubble's law", now called the Hubble–Lemaître law by the IAU, and published the first estimation of the Hubble constant in 1927, two years before Hubble's article. Lemaître also proposed the "Big Bang theory" of the origin of the universe, calling it the "hypothesis of the primeval atom", and later calling it "the beginning of the world".*Wik

Cosmic Anniversary: 'Big Bang Echo' Discovered 50 Years Ago ...

On May 20, 1964, American radio astronomers Robert Wilson and Arno Penzias discovered the cosmic microwave background radiation (CMB), the ancient light that began saturating the universe 380,000 years after its creation.

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1981 Henri-Gaston Busignies (29 Dec 1905; 20 Jun 1981) French-born American electronics engineer whose invention (1936) of high-frequency direction finders (HF/DF, or "Huff Duff") permitted the U.S. Navy during World War II to detect enemy transmissions and quickly pinpoint the direction from which a radio transmission was coming. Busignies invented the radiocompass (1926) while still a student at Jules Ferry College in Versailles, France. In 1934, he started developing the direction finder based on his earlier radiocompass. Busignies developed the  moving target indicator for wartime radar. It scrubbed off the radar screen every echo from stationary objects and left only echoes from moving objects, such as aircraft. *TIS

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1990 Kōsaku Yosida ( 7 February 1909, Hiroshima – 20 June 1990) was a Japanese mathematician who worked in the field of functional analysis. He is known for the Hille-Yosida theorem concerning C0-semigroups. Yosida studied mathematics at the University of Tokyo, and held posts at Osaka and Nagoya Universities. In 1955, Yosida returned to the University of Tokyo. *Wik

In 1933 Yosida was appointed as an Assistant in the Department of Mathematics at Osaka Imperial University. Osaka is on Honshu Island, roughly half way between Hiroshima and Tokyo. The Osaka Imperial University is based on educational institutions dating back to the 18th century but only became a university in 1931, two years before Yosida was appointed there. After one year, he was promoted to Associate Professor.

Moving to Osaka Imperial University led to Yosida changing the direction of his research. Two mathematicians who joined the Department of Mathematics shortly after him and were to strongly influence him were Mitio Nagumo (1905-1995) and Shizuo Kakutani. Nagumo had graduated from Tokyo Imperial University in March 1928 and spent two years at the University of Göttingen, Germany, before being appointed to Osaka Imperial University in March 1934. Kakutani had studied at Tohoku University in Sendai before being appointed as a teaching assistant at Osaka Imperial University in 1934. Yosida became interested in functional analysis through discussions with these two mathematicians. He published several joint papers with Kakutani. *SAU

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2003  I. Bernard Cohen (1 March 1914 – 20 June 2003) was the Victor S. Thomas Professor of the history of science at Harvard University and the author of many books on the history of science and, in particular, Isaac Newton.
Cohen was the first American to receive a Ph.D. in history of science, was a Harvard undergraduate ('37) and then a Ph.D. student and protégé of George Sarton who was the founder of Isis and the History of Science Society. Cohen taught at Harvard from 1942 until his death, and his tenure was marked by the development of Harvard's program in the history of science. *Wik

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2005 Jack St. Clair Kilby (8 November 1923 - 20 June 2005) was an American electrical engineer who took part, along with Robert Noyce of Fairchild Semiconductor, in the realization of the first integrated circuit while working at Texas Instruments (TI) in 1958. He was awarded the Nobel Prize in Physics on 10 December 2000.

Kilby was also the co-inventor of the handheld calculator and the thermal printer, for which he had the patents. He also had patents for seven other inventions. *Wik 

Jack Kilby's original integrated circuit

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2012 William Wager Cooper (July 23, 1914 – June 20, 2012) was an American operations researcher, known as a father of management science and as "Mr. Linear Programming". He was the founding president of The Institute of Management Sciences, founding editor-in-chief of Auditing: A Journal of Practice and Theory, a founding faculty member of the Graduate School of Industrial Administration at the Carnegie Institute of Technology (now the Tepper School of Business at Carnegie Mellon University), founding dean of the School of Urban and Public Affairs (now the Heinz College) at CMU, the former Arthur Lowes Dickinson Professor of Accounting at Harvard University, and the Foster Parker Professor Emeritus of Management, Finance and Accounting at the University of Texas at Austin.

 Cooper was born in Birmingham, Alabama and grew up in Chicago, where his father (a former bookkeeper) owned several gasoline stations that closed in the Great Depression. Cooper, in his second year of high school, dropped out to help support his family. He worked in a bowling alley, on a golf course, and as a professional boxer. As a boxer, he won 58 bouts, lost three, and drew two. While commuting to the golf course, he met Eric Kohler, a professor at Northwestern University, who pushed him to go back to school and bankrolled his entry to the University of Chicago. At Chicago, he began studying physical chemistry but was inspired by his work for Kohler on a legal case to switch to economics, graduating with a B.A. and Phi Beta Kappa honors in 1938.

After graduation, from 1938 to 1940, he worked as an accountant for the Tennessee Valley Authority, where Kohler had become Controller. There, he worked on performance auditing and the mathematical allocation of resources, and helped Kohler testify to a congressional investigative committee. In 1940, Cooper started doing graduate studies at Columbia University; however, in 1942, with his coursework completed but his thesis unwritten, he left Columbia to serve his country during World War II. He worked in the Division of Statistical Standards of the U.S. Bureau of the Budget coordinating the government programs that collected accounting statistics; his 1945 paper describing his wartime activities was the first recipient of an award from the American Institute of Accountants for the best paper of the year.

Cooper began his academic career with a brief teaching stint, from 1944 to 1946, back at the University of Chicago. In 1945, Cooper married his wife Ruth, a lawyer and human activist, and in 1946 he joined the newly formed Graduate School of Industrial Administration at the Carnegie Institute of Technology (now the Tepper School of Business at Carnegie Mellon University). There, he formed important research collaborations with Abraham Charnes, George Leland Bach, and Herbert A. Simon, and eventually became University Professor. While at CMU, from 1949 to 1950, he also worked again as an assistant to Eric Kohler, who had by this time become Comptroller of the Marshall Plan.In 1969 he left GSIA but stayed at CMU, becoming dean of the new School of Urban and Public Affairs (now the Heinz College) there. As dean, he realized that there would soon be a much greater role in American business management for African-Americans, and worked to increase African-American representation within the school.

In 1975, Harvard University hired Cooper away from CMU to become the Dickinson Professor of Accounting, and in 1980 he moved again, to the University of Texas at Austin, where he became the Foster Parker Professor of Management, Finance and Accounting. He retired in 1993, but continued to be active in research until his death on June 20, 2012.

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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