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


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

1798 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

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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 ealier, on 21 Jun 1808*TIS

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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

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In 1893, the first Ferris wheel premiered at Chicago's Columbian 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

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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)

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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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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  {A really nice article on the four color theorem and its history}

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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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2011  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.*Wik

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BIRTHS
 1781 Siméon-Denis Poisson 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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1852 Eduard Weyr born (died 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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1863  Maximilian Franz Joseph Cornelius Wolf 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

1918  Tibor Szele. He 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 at the 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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DEATHS
1874  Anders Jonas Ångström 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 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 D'Arcy Thompson 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 German physicist who won the 1919 Nobel Prize for Physics for his discovery in 1913 that an electric field would cause splitting of the lines in the spectrum of light emitted by a luminous substance; the phenomenon is called the Stark effect. *TIS

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Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History

On This Day in Math - June 18

 I began to understand that pure mathematics was more than a collection of random tools mainly fashioned for use in the Cambridge treatment of natural philosophy. 

Andrew Forsyth


EVENTS
1558 Robert Recorde’s will was admitted to probate, after he died in prison. He introduced the equals sign in The Whetstone of Witte (1557) with the words: “And to avoide the tediouse repetition of these woordes: is equalle to: I will sette as I doe often in woorke use, a pair of paralleles, or Gemowe lines of one lenghte, thus:  because noe .2. thynges, can be moare equalle.” “Gemowe” is an old French work meaning “twin.”. *VFR  When they are asked what they would use if this was not available, it seems difficult for students to imagine a different symbol.  

Image from Wikipedia.


1584 Jacob Christmann appointed professor of Hebrew at Heidelberg. In 1595 he defended the view that the circle could only be approximately squared. *VFR

1864 Lewis Carroll finally decided to write up Alice’s Adventures in Wonderland. [Stuart Dodgson Collingwook, The Life and Letters of Lewis Carroll (1898), p. 96] 

 1928, aviator Amelia Earhart became the first woman to fly across the Atlantic Ocean. She had accepted the invitation of the American pilots Wilmer Stultz (1900-29) and Louis Gordon to join them on the transatlantic flight. The crossing from Newfoundland to Wales took about 21 hours. Amelia Earhart went on to establish herself as a respected role model, tirelessly demonstrating that young women were as capable as men in succeeding in their chosen vocations. In 1935 she crossed the Atlantic solo in record time: 13 hr 30 min.  *TIS

1983 Sally Ride, astrophysicist, becomes the first American woman in space. The Soviets were ahead by twenty years and two days.*VFR

BIRTHS
1799 William Lassell was a wealthy amateur English astronomer. He set up an observatory at Starfield, near Liverpool. England, He built his own 24" diameter telescope, and devised steam-driven equipment for grinding an polishing the speculum metal mirror. This telescope was the first of its size to be mounted "equitorially" to allow easy tracking of the stars. He discovered Triton, a moon of Neptune, and Ariel and Umbriel, satellites of Uranus. Later, Lassell built a 48" diameter telescope with th same design and took it to Malta for observations with clearer skies.*TIS

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1818 Pietro Angelo Secchi (18 Jun 1818, 26 Feb 1878 at age 59) Italian Jesuit priest and astrophysicist, who made the first survey of the spectra of over 4000 stars and suggested that stars be classified according to their spectral type. He studied the planets, especially Jupiter, which he discovered was composed of gasses. Secchi studied the dark lines which join the two hemispheres of Mars; he called them canals as if they where the works of living beings. (These studies were later continued by Schiaparelli.) Beyond astronomy, his interests ranged from archaeology to geodesy, from geophysics to meteorology. He also invented a meteorograph, an automated device for recording barometric pressure, temperature, wind direction and velocity, and rainfall.*TIS

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1858 Andrew Russell Forsyth born in Glasgow, Scotland. He studied at Liverpool College and was tutored by Richard Pendlebury before entering Trinity College, Cambridge, graduating senior wrangler in 1881.^[1] He was elected a fellow of Trinity and then appointed to the chair of mathematics at the University of Liverpool at the age of 24. He returned to Cambridge as a lecturer in 1884 and became Sadleirian Professor of Pure Mathematics in 1895. *Wik 

In 1893 he published Theory of functions of a complex variable which had such an impact at Cambridge that function theory dominated there for many years. Whittaker writes... that this text:-

... had a greater influence on British mathematics than any work since Newton's Principia.

However the reputation of the book outside Britain was not high. In fact this is not surprising since the whole thrust of the book was to bring the great advances of Continental mathematics to Cambridge which Forsyth rightly saw as living in the past. He was well equipped to undertake this task for he traveled widely and, being a good linguist, was able to appreciate the advances made by authors writing in French and German.

On Cayley's death Forsyth was appointed to his chair in 1895 becoming the Sadleirian professor of Pure Mathematics. However his preference for technical mastery rather than rigorous analysis meant that he failed to inspire future pure mathematicians. In fact one would have to say that Forsyth was unlucky, for although he saw the importance of Continental mathematics, at the same time his greatest strengths lay in his ability to handle complex formulae. He therefore excelled at precisely the style of mathematics which he himself campaigned successfully to replace at Cambridge.

1884  Charles Weatherburn worked on vector analysis and differential geometry.*SAU

1884 Frieda Nugel was a German mathematician who was one of the first women to receive a doctorate in Germany *SAU 

1913  Oswald Teichmüller's main contribution is in the area of geometric function theory.*SAU

1926 Allan Rex Sandage  U.S. astronomer who (with Thomas A. Matthews) discovered, in 1960, the first optical identification of a quasi-stellar radio source (quasar), a starlike object that is a strong emitter of radio waves. Although a strange source of radio emission, in visible light, it looked like a faint star. Yet this object was emitting more intense radio waves and ultraviolet radiation than a typical star. He is best known for determining the first reasonably accurate value for the Hubble constant and the age of the universe.*TIS & Wik


DEATHS
1922 Jacobus Cornelius Kapteyn,  Dutch astronomer who used photography and statistical methods in determining the motions and spatial distribution of stars. Such work was the first major step after the works of William and John Herschel. He tried to solve the questions of space density of stars as a function of distance from the sun, and the distribution of starts according to brightness per unit volume. Some of his results had lasting value, but some were superceded because he had failed to account for the interstellar absorption. In studies using proper motion to determine stellar distances, he discovered stellar motions are not random, as previously thought, but that stars move in two "star streams" (1904). He introduced absolute magnitude and colour index as standard concepts.*TIS

1935 Alexander von Brill died. He worked on algebraic geometry and the theory of algebraic func­tions.

Born in Darmstadt, Hesse, he attended University of Giessen where he earned his doctorate under supervision of Alfred Clebsch. He held a chair at the University of Tübingen, where Max Planck was among his students.*Wik

1980 Kazimierz Kuratowski died. He worked in the area of topology and set theory. He is best known for his theorem giving a necessary and sufficient condition for a graph to be planar.*SAU   

Kuratowski's theorem:  "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)."  (in simpler, 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)  (see June 21)

Credits:
*VFR = V Frederick Rickey, USMA
*TIS= Today in Science History
*Wik = Wikipedia
*SAU=St Andrews Univ. Math History