On This Day in Math - June 22

The mathematical education of the young physicist [Albert Einstein ] was not very solid, which I am in a good position to evaluate since he obtained it from me in Zurich some time ago.
~Hermann Minkowski

The 173rd day of the year; the only prime whose sum of cubed digits equals its reversal: 1³ + 7³ + 3³ = 371. *Prime Curios

The smallest prime inconsummate number, i.e., no number is 173 times the sum of its digits. (The term inconsummate number was created by John Conway from the Latin for unfinished. [when?])

173 is the largest known prime whose square (29929) and cube (5177717) consist of totally different digits.

173 = 87^2 - 86^2 ,

173 is a Sophie German Prime since 2*173+1 = 347 is also prime. Sophie Germain primes are named after French mathematician Sophie Germain, who used them in her investigations of Fermat's Last Theorem. Sophie Germain primes and safe primes have applications in public key cryptography and primality testing. It has been conjectured that there are infinitely many Sophie Germain primes, but this remains unproven.

See More Math Facts here.

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EVENTS

1633 Galileo, under threat of torture from the inquisition, was forced to  "abjure, curse, and detest" his Copernican heliocentric views.
The recantation of GALILEO took place in the Great Hall of the former monastery of Santa Maria sopra Minerva, then the headquarters of the Dominican order.  This is where he supposedly said "E pur si muove" (Nevertheless, it does move).  For a long time, these words were believed to be a much later invention, but they probably date back to c1643 [Fahie, pp. 72 75].   Galileo was never officially imprisoned except for the few hours between his trial and the sentencing. In 1992, the Vatican officially declared that Galileo had been the victim of an error.

Galileo before the Holy Office, a 19th-century painting by Joseph-Nicolas Robert-Fleury

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In 1675, the Royal Greenwich Observatory was created by Royal Warrant in England by Charles II. Building designed by Sir Christopher Wren (who was also a Professor of Astronomy) was commenced 10 Aug 1675 and finished the following year by  John Flamsteed was appointed as the first Astronomer Royal. Its primary uses were in practical astronomy - navigation, timekeeping, determination of star positions. In 1767 the observatory began publishing The Nautical Almanac, which established the longitude of Greenwich as a baseline for time calculations. The almanac's popularity among navigators led in part to the adoption (1884) of the Greenwich meridian as the Earth's prime meridian (0° longitude) and the international time zones.*TIS

Royal Observatory, Greenwich. A time ball sits atop the Octagon Room.1714 second reading of the Longitude Bill in British Parliament *@Lordoflongitude

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1799 France adopted the metric system of weights and measures. *VFR

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1902 In response to a letter from Bertrand Russell dated 16 June 1902, Gottlob Frege responded with characteristic scientific honesty that “your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build arithmetic.” [van Heijenoort, From Frege to G¨odel, 125–128] *VFR
Russell had found a class of contradictions to Frege's 1879 Begriffsschrift.  This contradiction can be stated as "the class of all classes that do not contain themselves as elements". 

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1959 According to Steven Krantz's Mathematical Apocrypha Redux, it was Marshall McLuhan who created the phrase, "Publish or Perish." In a letter to Ezra Pound he wrote about "beaneries", which was Pound's favorite term for a university:

"The beaneries are on their knees to these gents (foundation administrators).  They regard them as Santa Claus.  They will do 'research on anything' that Santa approves. They will think his thoughts as long as he will pay the bill for getting them before the public signed by the profesorry-rat.  'Publish or perish' is the beanery motto."

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1978  evidence of the first moon of Pluto was discovered by astronomer James W. Christy of the Naval Observatory in Flagstaff, Ariz. when he obtained a photograph of Pluto that showed the orb to be distinctly elongated.. Furthermore, the elongations appeared to change position with respect to the stars over time. After eliminating the possibility that the elongations were produced by plate defects and background stars, the only plausible explanation was that they were caused by a previously unknown moon orbiting Pluto at a distance of about 19,600 kilometers (12,100 miles) with a period of 6.4 days. The moon was named Charon, after the boatman in Greek mythology who took the souls of the dead across the River Styx to Pluto's underworld. *TIS (actually Christy created the name in honor of his wife, whose nickname was Char.  He did not know the mythical name when he proposed it. It is said he still persists in pronouncing the moon with a "sh" sound rather than the hard k sound used in mythology.)

Charon, is the largest of the five known natural satellites of the dwarf planet Pluto. With half the diameter and one eighth the mass of Pluto, Charon is a very large moon in comparison to its parent body. Its gravitational influence is such that the barycenter of the Plutonian system lies outside Pluto, and the two bodies are tidally locked to each other.

The reddish-brown cap of the north pole of Charon is composed of tholins, organic macromolecules that may be essential ingredients of life. These tholins were produced from methane, nitrogen and related gases which may have been released by cryovolcanic eruptions on the moon, or may have been transferred over 19,000 km (12,000 mi) from the atmosphere of Pluto to the orbiting moon

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2004  Humans are officially slow learners... In 2004, a study led by Richard Doll was published in the British Medical Journal, the first research that quantified the damage over the lifetime of a generation, based on a 50-year study of a group of almost 35,000 British doctors who smoked. The study found that almost half of persistent cigarette smokers were killed by their habit, and a quarter died before age 70. Further, those who quit by age 30 had the same life expectancy as a nonsmoker. Even quitting at age 50 saved six more years of life over those who continued smoking. At age 80, 65% of non-smokers were still alive, but only 32% of smokers. Fifty years before, Doll published in the same journal the first report of a study that linked cigarette smoking to lung cancer*TIS 

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2011  One of the 15th century copies of a manuscript of Fibonacci's Liber Abacci that was owned by Boncompagni and was until recently in Brown University Maths library is for sale, by auction, on June 22, 2011, in New York and is estimated to fetch in excess of \( $120,000\). (It seems it brought even more,"Fibonacci, manuscript copy of the Liber Flos, \($338,000\) at Bonhams New York on June 22. "

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BIRTHS

1837 Paul Gustav Heinrich Bachmann born (22 June 1837 – 31 March 1920). He wrote (1892–1923) a five volume survey of the state of number theory including an evaluation of the various methods of proof. He also devoted time to composing, playing the piano, and serving as a music critic for various newspapers. *VFR Bachmann studied mathematics at the university of his native city of Berlin and received his doctorate in 1862 for his thesis on group theory. He then went to Breslau to study for his habilitation, which he received in 1864 for his thesis on Complex Units. He was a professor at Breslau and later at Münster.The symbols O(·) and o(·) are usually called the Landau symbols. This name is only partially correct, since it seems that the first of them appeared first in the second volume of P. Bachmann's treatise on number theory (Bachmann, 1894). In any case Landau (1909a, p. 883) states that he had seen it for the first time in Bachmann's book. *SAU

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1852 Eduard Weyr (June 22, 1852 – July 23, 1903) He and his brother, Emil Weyr (1848–1894) were the leading members of the Austrian geometrical school. They worked in descriptive geometry, projective geometry, and then became interested in algebraic and synthetic methods. Eduard found a canonical form for matrices that deserves to be better known (American Mathematical Monthly, December 1999). *VFR

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1860 Mario Pieri (22 June 1860 in Lucca, Italy - 1 March 1913 in S Andrea di Compito (near Lucca), Italy) Pieri's main area was projective geometry and he is an important member of the Italian School of Geometers. However, after he moved to Turin, Pieri became influenced by Peano at the University and Burali-Forti who was a colleague at the Military Academy. This influence led Pieri to study the foundations of geometry.
In 1895 he set up an axiomatic system for projective geometry with three undefined terms, namely points, lines and segments. He improved on results of Pasch and Peano and then, in 1905, Pieri gave the first axiomatic definition of complex projective geometry which does not build on real projective geometry.
In 1898 Pieri published the memoir The principles of the geometry of position through the Academy of Sciences of Turin. Russell was impressed by this memoir and wrote, in his Principia, "This is, in my opinion, the best work on the present subject." *SAU

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1864 Herman Minkowski born (June 22,  1864 – January 12, 1909) . The motto on his Akademie-Schrift was “Rien n’est beau que le vrai, le vrai seul est aimable” (Nothing is beautiful but the truth, only the truth is lovable). *VFR 

He developed the geometrical theory of numbers and used geometrical methods to solve difficult problems in number theory, mathematical physics, and the theory of relativity. By 1907, Minkowski realized that the work of Lorentz and Einstein could be best understood in a non-euclidean space. He considered space and time, which were formerly thought to be independent, to be coupled together in a four-dimensional "space-time continuum". Minkowski worked out a four-dimensional treatment of electrodynamics. His idea of a four-dimensional space (since known as "Minkowski space"), combining the three dimensions of physical space with that of time, laid the mathematical foundation of Albert Einstein's general theory of relativity.*TIS My favorite Minkowski story from Constance Reid's Hilbert, Once in a topology lecture he brought up the Four-color theorem.  "This theorem has not been proved,  but that is because only mathematicians of the third rank have occupied themselves with it" he announced with unusual arrogance.  "I belive I can prove it."  He began on the spot to work out the problem and continued over several classes to develop the work.  After several weeks he entered one rainy day and a crash of thunder accompanied his entrance.  Turning to his students he announced, "Heaven is angered by my arrogance, My proof is defective." 

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1866 Kazimierz Żorawski (June 22, 1866 – January 23, 1953) was a Polish mathematician. His work earned him an honored place in mathematics alongside such Polish mathematicians as Wojciech Brudzewski, Jan Brożek (Broscius), Nicolas Copernicus, Samuel Dickstein, Stefan Banach, Stefan Bergman, Marian Rejewski, Wacław Sierpiński, Stanisław Zaremba and Witold Hurewicz.
Żorawski's main interests were invariants of differential forms, integral invariants of Lie groups, differential geometry and fluid mechanics. His work in these disciplines was to prove important in other fields of mathematics and science, such as differential equations, geometry and physics (especially astrophysics and cosmology).*Wik

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1880 Alfred Rosenblatt (July 22, 1880, Krakow -  1947, Lima ), was a mathematician born in Poland , nationalized Peruvian, worked in Peru in teaching and research in mathematics.

He began his university studies at the Vienna Polytechnic School, continuing them at the Faculty of Philosophy at the Jagiellonian University of Krakow; He also pursued postgraduate courses at the University of Gottingen, Germany. In Europe he obtained the degree of electrical engineer and doctor of philosophy. 

He arrived in Peru in 1936 and remained in Lima until his death. He works intensively alongside Godofredo García at the University of San Marcos where he publishes more than 130 works in Polish, German, French, Italian and Spanish on Real and Complex Analysis, Geometry, Topology, Differential Equations, Rational and Celestial Mechanics and Hydrodynamics . He was hired in Peru to occupy the chair of Astronomy and Geodesy, replacing Captain José R. Gálvez in 1936. He carried out profuse scientific work in Peru, being a great promoter of the National Academy of Exact, Physical and Natural Sciences of the Peru . He published 206 articles in scientific journals.

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1892 Pierre Ossian Bonnet (22 December 1819, Montpellier – 22 June 1892, Paris) was a French mathematician. He made some important contributions to the differential geometry of surfaces, including the Gauss–Bonnet theorem.

Bonnet was elected to the Academy of Sciences in 1862 to replace Biot. He defeated Bour for this position. From 1868 Bonnet assisted Chasles at the Ecole Polytechnique, and three years later he became a director of studies there. In addition to this post he also taught at the Ecole Normale Supérieure.

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

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

In the mathematical field of differential geometry, the Gauss–Bonnet theorem (or Gauss–Bonnet formula) is a fundamental formula which links the curvature of a surface to its underlying topology.

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

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1906 Eduard Ott-Heinrich Keller (22 June 1906 in Frankfurt – 5 December 1990 in Halle) was a German mathematician who worked in the fields of geometry, topology and algebraic geometry. He formulated the celebrated problem which is now called the Jacobian conjecture in 1939.

[In mathematics, the Jacobian conjecture is a famous unsolved problem concerning polynomials in several variables. It states that if a polynomial function from an n-dimensional space to itself has Jacobian determinant which is a non-zero constant, then the function has a polynomial inverse. It was first conjectured in 1939]

 He was born in Frankfurt–am-Main, and studied at the universities of Frankfurt, Vienna, Berlin and Göttingen. As a student of Max Dehn he wrote a dissertation on the tiling of space with cubes. This led to another 'Keller conjecture': the Keller cube-tiling conjecture from 1930.

Subsequently he worked with Georg Hamel in Berlin, habilitating in 1933 with a thesis on Cremona transformations. The Jacobian conjecture is quite naturally posed in that setting. The motivation for looking at rather general polynomial transformations, say of the projective plane, came from the singularity theory for algebraic curves.

During World War II he taught in a naval college in Flensburg. After the war he had several positions, and was appointed a professor at Martin Luther University of Halle-Wittenberg in 1952, as successor of H. W. E. Jung. *Wik

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1910 Konrad Zuse (22 Jun 1910, 18 Dec 1995) German engineer who in 1941 constructed the first fully operational program-controlled electromechanical binary calculating machine, or digital computer, called the Z3. Earlier, Zuse developed and built the Z1 the first binary digital computer in the world (1936-8) and two more machines before the end of WW II, but he was unable to convince the Nazi government to support his work. He created a basic programming system known as Plankalkül with which he designed a chess playing program.The Z3 was destroyed in 1944 during the war. Next came the more sophisticated Z4, which was the only Zuse Z-machine to survive the war, by several moves to new locations away from air raids. During the last days of war it was hidden. In 1950, he took it to Zurich. *TIS In an interesting coincidence, the first paper of Roger Lyndon, who was born on this date) was on the Zuse computer . In the paper he described the Z4, Zuse's relay-type digital computer which was discovered by advancing British and American troops. The nearly completed computer had been hidden by Zuse in the cellar of a house in the small village of Hinterstein in Bavaria. *SAU

Much of his early work was financed by his family and commerce, but after 1939 he was given resources by the Nazi German government. Due to World War II, Zuse's work went largely unnoticed in the United Kingdom and the United States. Possibly his first documented influence on a US company was IBM's option on his patents in 1946. *Wik

Zuse Z3 replica on display at
 Deutsches Museum in Munich

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1920 James H. Pomerene (June 22, 1920 – December 7, 2008) American computer pioneer. In Apr 1946 he joined John von Neumann and Herman Goldstine in their newly organized Electronic Computer Project at the Institute for Advanced Study in Princeton, New Jersey. This project was to build a parallel stored-program computer. He designed the adder portion of the arithmetic unit and then was entirely responsible for the development and construction of the electrostatic (Williams tube) memory and became the chief engineer of the project 1951-56. Then he joined IBM to assist development of the HARVEST computer,  a special system built for the National Security Agency. It had two levels of program control and also had a tape and tape library system that was fully automatic and of great capacity.*TIS  

The IBM 7030, also known as Stretch, was IBM's first transistorized supercomputer. It was the fastest computer in the world from 1961 until the first CDC 6600 became operational in 1964

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1932 Mary Wynne Warner née Davies; (22 June 1932 – 1 April 1998) was a Welsh mathematician, specializing in fuzzy mathematics. Her obituary in the Bulletin of the London Mathematical Society noted that fuzzy topology was "the field in which she was one of the pioneers and recognized as one of the leading figures for the past thirty years.

"Warner's output between 1980 and 1985 of 20 papers on the subjects of tolerance spaces and automata, and her conceptualisation of the 'lattice-valued relation' towards the end of this period rendered her eminent in the field of fuzzy topology, and these achievements culminated in her promotion to a readership at the City University in 1983, and then a professorship in 1996. During her tenure at the university's Mathematics department, she developed a curriculum for and implemented an MSc in mathematics, and her aptitude in teaching at both the undergraduate and postgraduate level was noted.

Warner is generally acknowledged as having been imperative in providing early fuzzy topology research with a stabilising foundation, from which new results could be found, which were not purely descriptive of existing topological definitions. The quantity of people with whom she co-authored papers is indicative of her role in bolstering the profile of the field of fuzzy topology.

The broader application of Mary's work in fuzzy topology involves the prediction of real-world events which are always imprecise – nuclear reactor failure and the occurrence of earthquakes.*Wik

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1940 Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. From 1984 to 2006, he was the Waynflete Professor of Pure Mathematics at Magdalen College, Oxford. He is renowned for being the "prime architect" of higher algebraic K-theory, for which he was awarded the Cole Prize in 1975 and the Fields Medal in 1978.

Quillen was a Putnam Fellow in 1959.
Quillen retired at the end of 2006. He died from complications of Alzheimer's disease on April 30, 2011, aged 70, in Florida. *Wik

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1947 William Edward Caswell (June 22, 1947 – September 11, 2001) was an American physicist. He made early application (mid 1970s) of the power of computer calculations to the synthesis of gauge symmetry and renormalization group ideas. His techniques still apply in the interpretation of many experiments in high-energy physics. His work led to methods for multiloop quantum chromodynamics calculations. Caswell made many other valuable and influential contributions used as tools for calculations in particle physics. In 1983, he joined the Naval Surface Weapons Center in Silver Spring, Maryland. By 1985, he was leading a team of 100 scientists on a major classified defense technology project. He died aboard the airplane crashed by 9/11 terrorists into the Pentagon. *TiS

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1950 Benedict Hyman Gross (June 22, 1950;  ) is an American mathematician, the George Vasmer Leverett Professor of Mathematics at Harvard University and former Dean of Harvard College.
He is known for his work in number theory, particularly the Gross–Zagier theorem on L-functions of elliptic curves, which was work with Don Zagier.  *Wik

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DEATHS

1388 Giovanni Dondi died (1330–1388). In 1381 he built one of the earliest geared equatoria driven by clockwork. There is a model of it in the Smithsonian. It has a heptagonal frame with a planet on each face. Dials show the time of sunrise, sunset, movable feasts, and the nodes of the moon’s orbit. *VFR He is remembered today as a pioneer in the art of clock design and construction. The Astrarium, which he designed and built over a period of 16 years, was a highly complex astronomical clock and planetarium, constructed only 60 or so years after the very first mechanical clocks had been built in Europe, and demonstrated an ambitious attempt to describe and model the solar system with mathematical precision and technological sophistication. *Wik

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1429  Jamshid al-Kashi (1380 -? 22 June 1429 (several different dates are given for his death)
was an Islamic mathematician who published some important teaching works and anticipated Stevin's work on decimals.*SAU
Al-Kashi was one of the best mathematicians in the Islamic world. He was born in 1380, in Kashan, in central Iran. This region was controlled by Tamurlane, better known as Timur. Al-Kashi lived in poverty during his childhood and the beginning years of his adulthood.

The situation changed for the better when Timur died in 1405, and his son, Shah Rokh, ascended into power. Shah Rokh and his wife, Goharshad, a Persian princess, were very interested in the sciences, and they encouraged their court to study the various fields in great depth. Consequently, the period of their power became one of many scholarly accomplishments. This was the perfect environment for al-Kashi to begin his career as one of the world’s greatest mathematicians.

Eight years after he came into power in 1409, their son, Ulugh Beg, founded an institute in Samarkand which soon became a prominent university. Students from all over the Middle East, and beyond, flocked to this academy in the capital city of Ulugh Beg’s empire. Consequently, Ulugh Beg harvested many great mathematicians and scientists of the Muslim world. In 1414, al-Kashi took this opportunity to contribute vast amounts of knowledge to his people. His best work was done in the court of Ulugh Beg, and it is said that he was the king’s favourite student.

Al-Kashi was still working on his book, called “Risala al-watar wa’l-jaib” meaning “The Treatise on the Chord and Sine”, when he died in 1429. Some scholars believe that Ulugh Beg may have ordered his murder, while others say he died a natural death. The details are unclear. *Wik

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1925 Felix Christian Klein (25 April 1849 – 22 June 1925)  died on the birthday of his dear friend, Minkowski. *VFR A German mathematician whose synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Programm, profoundly influenced mathematical development. He created the Klein bottle, a one-sided closed surface. A Klein bottle cannot be constructed in Euclidean space. It is best pictured as a cylinder looped back through itself to join with its other end. However this is not a continuous surface in 3-space as the surface cannot go through itself without a discontinuity. It is possible to construct a Klein bottle in non-Euclidean space.*TIS

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1936 Friedrich Albert Moritz Schlick (14 April 1882 – 22 June 1936) was a German philosopher, physicist, and the founding father of logical positivism and the Vienna Circle. He was a philosopher of science and leader of the Vienna Circle, was murdered by a deranged former student, on the steps of an academic building. *VFR

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1977 Harold Calvin Marston Morse (24 March 1892 in Waterville, Maine, USA - 22 June 1977 in Princeton, New Jersey, USA) developed variational theory in the large with applications to equilibrium problems in mathematical physics, a theory which is now called Morse theory and forms a vital role in global analysis*SAU

The Morse–Palais lemma, one of the key results in Morse theory, is named after him, as is the Thue–Morse sequence, an infinite binary sequence with many applications.

He was elected to the American Academy of Arts and Sciences in 1929, the United States National Academy of Sciences in 1932, and the American Philosophical Society in 1936. In 1933 he was awarded the Bôcher Memorial Prize for his work in mathematical analysis. J. Robert Oppenheimer described Morse as "almost a statesman of mathematics.

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1990 Ilya Mikhailovich Frank (23 October 1908 – 22 June 1990) Russian physicist who, with Igor Tamm, theoretically explained the mechanism of Cherenkov radiation. In 1934, Cherenkov discovered that a peculiar blue light is emitted by charged particles traveling at very high speeds through water. Frank and Tamm provided the theoretical explanation of this effect, which occurs when the particles travel through an optically transparent medium at speeds greater than the speed of light in that medium. This discovery resulted in the development of new methods for detecting and measuring the velocity of high-speed particles and became of great importance for research in nuclear physics. For this, Frank received the Nobel Prize for Physics in 1958 (jointly with Pavel A. Cherenkov and Igor Y. Tamm).*TIS

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1994 Julius Adams Stratton (May 18, 1901 – June 22, 1994) was a U.S. electrical engineer and university administrator. He attended the University of Washington for one year, then transferred to the Massachusetts Institute of Technology (MIT), from which he graduated with a bachelor's degree in 1923 and a master's degree in electrical engineering (EE) in 1926. He then followed graduate studies in Europe and the Technische Hochschule of Zurich (ETH Zurich), Switzerland, awarded him the degree of Doctor of Science in 1927. *Wik  He worked with the blind-landing research program during WWII to help develop Glide-slope-approach radar. 

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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 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

When I posted this on LinkedIn, Michael Hirschhorn commented:

"No one believes me, in  particular George Szekeres did not believe me, when I told him that Paul Erdos said to me about that postal canceller, “Perhaps in the year 5000 they will have a canceller which says “2^p-1 is prime infinitely often”.  

Turns out he was right.....No one believes him.  

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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