## Tuesday, 3 May 2016

### On This Day in Math - May 3

As for everything else, so for a mathematical theory:
beauty can be perceived but not explained.
Arthur Cayley

The 124th day of the year;124 =σ( 1! * 2! * 4!) *Prime Curios (The sigma function of a positive integer n is the sum of the positive divisors of n)

124 is also an Odious number: a number with an odd number of 1's in its binary expansion.

124 in base two is expressed as 1111100.

and ±1 ± 2 ± 3 ± 4 ± 5 ± 6 ± 7 ± 8 ± 9 ± 10 ± 11 ± 12 = 0 has 124 solutions (collect the whole set) *Math Year-Round ‏@MathYearRound

EVENTS
1375 BC, the oldest recorded eclipse occurred, according to one plausible interpretation of a date inscribed on a clay tablet retrieved from the ancient city of Ugarit, Syria (as it is now). This date is one of two plausible dates usually cited from the record, though 5 Mar 1223 is the more favoured date by most recent authors on the subject. Certainly by the 8th century BC, the Babylonians were keeping a systematic record of solar eclipses, and possibly by this time they may have been able to apply numerological rules to make fairly accurate predictions of the occurrence of solar eclipses. The first total solar eclipse reliably recorded by the Chinese occurred on 4 Jun 180 *TIS
(A new historical dating of the tablet, and mention in the text of the visibility of the planet Mars during the eclipse as well as the month in which it occurred enables us to show that the recorded eclipse in fact occurred on 5 March 1223 BC. This new date implies that the secular deceleration of the Earth's rotation has changed very little during the past 3,000 years. *nature.com) With thanks to Bill Thayer ‏@LacusCurtius

1661 Equipment used by Hevelius with a telescope to project an astronomical image onto a sheet of paper. This arrangement was used in his historic observation of the transit of Mercury on May 3, 1661. His surviving books are filled with great images by himself and his second wife, Elisabeth Koopman whom he would marry two years after this transit. * Maria Popova at brainpickings.org

This was the first observation of a transit of Mercury inthe MOnth of May. The two previous transits had both been in November in 1631 and 1651. This observation was visible in London and occurred on the day of the Coronation of King Charles II . It was observed by Christiaan Huygens in London. *Wik

1715 May 3 A total solar eclipse was observed in England from Cornwall in the south-west to Lincolnshire and Norfolk in the east. This eclipse is known as Halley's Eclipse, after Edmund Halley (1656–1742) who predicted this eclipse to within 4 minutes accuracy. Halley observed the eclipse from London where the city of London enjoyed 3 minutes 33 seconds of totality. He also drew a predictive map showing the path of totality across England. The original map was about 30 km off the observed eclipse path. After the eclipse, he corrected the eclipse path, and added the path and description of the 1724 total solar eclipse.Note: Great Britain didn't adopt the Gregorian calendar until 1752, so the date was considered 22 April 1715. *Wik… The Royal Society reports: Edmund Halley, a Fellow of the Royal Society, is most famous for his work on the orbits of comets, predicting when the one that now bears his name would be seen; however, his interests were more widespread. In 1715 the first total solar eclipse for 500 years took place over England and Wales. Halley, a talented mathematician, realized that such an event would generate a general curiosity and requested that the ‘curious’ across the country should observe ‘what they could’ and make a record of the time and duration of the eclipse. At the time, there were only two universities in England and their astronomy professors did not have much luck in observing the event: ‘the Reverend Mr Cotes at Cambridge had the misfortune to be oppressed by too much company’ and ‘Dr John Keill by reason of clouds, saw nothing distinctly at Oxford but the end’. The event did indeed capture the imagination of the nation and the timings collected allowed Halley to work out the shape of the eclipse shadow and the speed at which it passed over the Earth (29 miles per minute).

1834 In response to a letter from William Whewell at Cambridge suggesting the names "anode" and "cathode"; Faraday says ,"All your names I and my friend approve of or nearly all as to sense & expression, but I am frightened by their length & sound when compounded. As you will see I have taken deoxide and skaiode because they agree best with my natural standard East and West. I like Anode & Cathode better as to sound, but all to whom I have shewn them have supposed at first that by Anode I meant No way." (within a few weeks he would change his mind about using the two terms, see 15 may, 1834)

1841 L. G. J. Jacobi, who made a lengthy study of Euler’s and d’Alembert’s works, wrote “It is worth noting that it is impossible today to choke down a single line of d’Alembert’s mathematics, while most of Euler’s works can be read with delight, and they died in the same year [1783]. D’Alembert seems to have been entirely absorbed in belles-lettres.” [Hawkins, Jean D’Alembert, p 63]. *VFR

1849 Arthur Cayley called to the Bar. He abandoned his fellowship at Cambridge and took up law as he didn’t want to take Holy Orders. During his 14 years at the bar he wrote nearly 300 mathematical papers. *VFR

1902 The San Francisco Section of the AMS was founded at a gathering of twenty mathematicians at the Academy of Sciences, San Francisco, CA. [AMS Semicentennial Publications, vol 1, p 8].

1934 Henri-Leon Lebesgue elected foreign member of the Royal Society. From 1899 until 1903 he taught at the Lyc´ee at Nancy, France, where he wrote his famous doctoral thesis “Int´egrale, longueur, aire,” which proposed a now standard extension of the Riemann integral. See The Mathematical Intelligencer, 6(1984), no. 2, p. 8. *VFR

1997 Garry Kasparov beat IBM's Deep Blue in the first match of what many considered a test of artificial intelligence. The world's best chess player, Kasparov eventually lost the match and $1.1 million purse to the IBM supercomputer, which he had claimed could never surpass human chess ability. After losing the sixth and final game of the match, Kasparov accused IBM of building a machine specifically to beat him. Observers said he was frustrated by Deep Blue's quickness although they expected him to win with unconventional moves. *CHM On February 10, 1996, Deep Blue became the first machine to win a chess game against a reigning world champion (Garry Kasparov) under regular time controls. However, Kasparov won three and drew two of the following five games, beating Deep Blue by a score of 4–2 (wins count 1 point, draws count ½ point). The match concluded on February 17, 1996. Deep Blue was then heavily upgraded (unofficially nicknamed "Deeper Blue")[11] and played Kasparov again in May 1997, winning the six-game rematch 3½–2½, ending on May 11. *Wik 2016 Three computer scientists have announced the largest-ever mathematics proof: a file that comes in at a whopping 200 terabytes1, roughly equivalent to all the digitized text held by the US Library of Congress. The researchers have created a 68-gigabyte compressed version of their solution — which would allow anyone with about 30,000 hours of spare processor time to download, reconstruct and verify it — but a human could never hope to read through it. Computer-assisted proofs too large to be directly verifiable by humans have become commonplace, and mathematicians are familiar with computers that solve problems in combinatorics — the study of finite discrete structures — by checking through umpteen individual cases. Still, “200 terabytes is unbelievable”, says Ronald Graham, a mathematician at the University of California, San Diego. The previous record-holder is thought to be a 13-gigabyte proof2, published in 2014. The puzzle that required the 200-terabyte proof, called the Boolean Pythagorean triples problem, has eluded mathematicians for decades. In the 1980s, Graham offered a prize of US$100 for anyone who could solve it. (He duly presented the cheque to one of the three computer scientists, Marijn Heule of the University of Texas at Austin, earlier this month.) The problem asks whether it is possible to colour each positive integer either red or blue, so that no trio of integers a, b and c that satisfy Pythagoras’ famous equation a2 + b2 = c2 are all the same colour. For example, for the Pythagorean triple 3, 4 and 5, if 3 and 5 were coloured blue, 4 would have to be red.
In a paper posted on the arXiv server on 3 May, Heule, Oliver Kullmann of Swansea University, UK, and Victor Marek of the University of Kentucky in Lexington have now shown that there are many allowable ways to colour the integers up to 7,824 — but when you reach 7,825, it is impossible for every Pythagorean triple to be multicoloured1. There are more than 102,300 ways to colour the integers up to 7,825, but the researchers took advantage of symmetries and several techniques from number theory to reduce the total number of possibilities that the computer had to check to just under 1 trillion. It took the team about 2 days running 800 processors in parallel on the University of Texas’s Stampede supercomputer to zip through all the possibilities. The researchers then verified the proof using another computer program. *Evelyn Lamb, nature.com

BIRTHS
1695 Henri Pitot (3 May 1695; 27 Dec 1771 at age 76) French hydraulic engineer who invented the Pitot tube (1732), an instrument to measure flow velocity either in liquids or gases. With subsequent improvements by Henri Darcy, its modern form is used to determine the airspeed of aircraft. Although originally a trained mathematician and astronomer, he became involved with an investigation of the velocity of flowing water at different depths, for which purpose he first created the Pitot tube. He disproved the prevailing belief that the velocity of flowing water increased with depth. Pitot became an engineer in charge of maintenance and construction of canals, bridges, drainage projects, and is particularly remembered for his kilometer-long Roman-arched Saint-Clément Aqueduct (1772) at Montpellier, France.*TIS

1860 Vito Volterra (3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations.In 1922, he joined the opposition to the Fascist regime of Benito Mussolini and in 1931 he was one of only 12 out of 1,250 professors who refused to take a mandatory oath of loyalty. His political philosophy can be seen from a postcard he sent in the 1930s, on which he wrote what can be seen as an epitaph for Mussolini’s Italy: Empires die, but Euclid’s theorems keep their youth forever. However, Volterra was no radical firebrand; he might have been equally appalled if the leftist opposition to Mussolini had come to power, since he was a lifelong royalist and nationalist. As a result of his refusal to sign the oath of allegiance to the fascist government he was compelled to resign his university post and his membership of scientific academies, and, during the following years, he lived largely abroad, returning to Rome just before his death.*Wik
André WEIL spent 1925-1926 studying with Volterra. Volterra was President of the the ACCADEMIA DEI LINCEI (or Lyncei). This was the first modern learned society. It was founded in Rome by Prince Federigo Cesi in 1603. The word 'lincei' means 'lynx-eyed', but actually derives from the Greek argonaut Linkeus, the eponym of the animal. Lynxes are on the crest of the Accademia

1874 V(agn) Walfrid Ekman (3 May 1874, 9 Mar 1954 at age 79) Swedish physical oceanographer and mathematical physicist whose research into the dynamics of ocean currents led to his name remaining associated with terms for particular phenomena of the ocean or atmosphere, including Ekman spiral, Ekman transport and Ekman layer. Fridtjof Nansen pointed out to Ekman that he had noticed that icebergs drift at an angle of 20°-40° to the prevailing wind, rather than directly with the wind. In 1902, Ekman published an explanation, known now as the Ekman spiral, describing movement of ocean currents influenced by the Earth's rotation. He also developed experimental techniques and instruments such as the Ekman current meter and Ekman water bottle.*TIS

1892 Sir George Paget Thomson (3 May 1892; 10 Sep 1975 at age 83) English physicist who shared (with Clinton J. Davisson of the U.S.) the Nobel Prize for Physics in 1937 for demonstrating that electrons undergo diffraction, a behaviour peculiar to waves that is widely exploited in determining the atomic structure of solids and liquids. He was the son of Sir J.J. Thomson who discovered the electron as a particle. *TIS

1902 Alfred Kastler (3 May 1902; 7 Jan 1984 at age 81) French physicist who won the Nobel Prize for Physics in 1966 for his discovery and development of methods for observing Hertzian resonances within atoms. This research facilitated the greater understanding of the structure of the atom by studying the radiations that atoms emit when excited by light and radio waves. He developed a method called "optical pumping" which caused atoms in a sample substance to enter higher energy states. This idea was an important predecessor to the development of masers and the lasers which utilized the light energy that was re-emitted when excited atoms released the extra energy obtained from optical pumping. *TIS

1924 Isadore Manuel Singer (April 24, 1924), Detroit Michigan. "Singer is justifiably famous among mathematicians for his deep and spectacular work in geometry, analysis, and topology, culminating in the Atiyah-Singer Index theorem and its many ramifications in modern mathematics and quantum physics." *SAU

1933 Steven Weinberg (3 May 1933, )American nuclear physicist who shared the 1979 Nobel Prize for Physics (with Sheldon Lee Glashow and Abdus Salam) for work in formulating the electroweak theory, which explains the unity of electromagnetism with the weak nuclear force. *TIS

DEATHS
1657 Johann Baptist Cysat (1586, 3 May 1657), Latinized as Cysatus was a Swiss astronomer who entered the Jesuit order (1604), and by 1611 was studying at the Jesuit college in Ingolstadt, Bavaria, under Christoph Scheiner, whom he assisted in the observation of sunspots. From 1618, he taught mathematics there. As an early user of a telescope, he was the first to make substantial telescopic observation of a comet (1 Dec 1618 to 22 Jan 1619), Although he discovered the Orion Nebula independently (1619), it had been first noted by Peiresc in 1610. Cysat wrote to Kepler describing a lunar eclipse (1620) and observed the transit of Mercury (1631). It is the comet study for which Cysat is noted. His measurements of its position were made using a 6-foot radius wooden sextant. He published his data and analysis in an 80-page booklet, Mathemata astronomica de locu...cometae... (1619). *TIS

1764 Francesco Algarotti (11 Dec 1712, 3 May 1764 at age 51) Italian scholar of the arts and sciences, recognized for his wide knowledge and elegant presentation of advanced ideas. At age 21, he wrote Il Newtonianismo per le dame (1737; "Newtonianism for Ladies"), a popular exposition of Newtonian optics. He also wrote about architecture, opera and painting. *TIS

1779 John Winthrop (December 19, 1714 – May 3, 1779) was the 2nd Hollis Professor of Mathematics and Natural Philosophy in Harvard College. He was a distinguished mathematician, physicist and astronomer, born in Boston, Mass. His great-great-grandfather, also named John Winthrop, was founder of the Massachusetts Bay Colony. He graduated in 1732 from Harvard, where, from 1738 until his death he served as professor of mathematics and natural philosophy. Professor Winthrop was one of the foremost men of science in America during the 18th century, and his impact on its early advance in New England was particularly significant. Both Benjamin Franklin and Benjamin Thompson (Count Rumford) probably owed much of their early interest in scientific research to his influence. He also had a decisive influence in the early philosophical education of John Adams, during the latter's time at Harvard. He corresponded regularly with the Royal Society in London—as such, one of the first American intellectuals of his time to be taken seriously in Europe. He was noted for attempting to explain the great Lisbon earthquake of 1755 as a scientific—rather than religious—phenomenon, and his application of mathematical computations to earthquake activity following the great quake has formed the basis of the claim made on his behalf as the founder of the science of seismology. Additionally, he observed the transits of Mercury in 1740 and 1761 and journeyed to Newfoundland to observe a transit of Venus. He traveled in a ship provided by the Province of Massachusetts - probably the first scientific expedition ever sent out by any incipient American state. *Wik

1880 Jonathan Homer Lane (August 9, 1819, Geneseo, New York – May 3, 1880, Washington D.C.) U.S. astrophysicist who was the first to investigate mathematically the Sun as a gaseous body. His work demonstrated the interrelationships of pressure, temperature, and density inside the Sun and was fundamental to the emergence of modern theories of stellar evolution. *TIS Simon Newcomb, in his memoirs, describes Lane as "an odd-looking and odd-mannered little man, rather intellectual in appearance, who listened attentively to what others said, but who, so far as I noticed, never said a word himself." Newcomb recounts his own role in bringing Lane's work, in 1876, to the attention of William Thomson who further popularized the work. Newcomb notes, "it is very singular that a man of such acuteness never achieved anything else of significance." *Wik

1885 Ernst Ferdinand Adolf Minding (23 Jan 1806 in Kalisz,Russian Empire (now Poland) - 3 May 1885 in Dorpat, Russia (now Tartu, Estonia))His work, which continued Gauss's study of 1828 on the differential geometry of surfaces, greatly influenced Peterson. In 1830 Minding published on the problem of the shortest closed curve on a given surface enclosing a given area. He introduced the geodesic curvature although he did not use the term which was due to Bonnet who discovered it independently in 1848. In fact Gauss had proved these results, before either Minding of Bonnet, in 1825 but he had not published them.
Minding also studied the bending of surfaces proving what is today called Minding's theorem in 1839. The following year he published in Crelle's Journal a paper giving results about trigonometric formulae on surfaces of constant curvature. Lobachevsky had published, also in Crelle's Journal, related results three years earlier and these results by Lobachevsky and Minding formed the basis of Beltrami's interpretation of hyperbolic geometry in 1868.
Minding also worked on differential equations, algebraic functions, continued fractions and analytic mechanics. In differential equations he used integrating factor methods. This work won Minding the Demidov prize of the St Petersburg Academy in 1861. It was further developed by A N Korkin. Darboux and Émile Picard pushed these results still further in 1878. *SAU

1988 Lev Semenovich Pontryagin (3 September 1908 – 3 May 1988) One of the 23 problems posed by Hilbert in 1900 was to prove his conjecture that any locally Euclidean topological group can be given the structure of an analytic manifold so as to become a Lie group. This became known as Hilbert's Fifth Problem. In 1929 von Neumann, using integration on general compact groups which he had introduced, was able to solve Hilbert's Fifth Problem for compact groups. In 1934 Pontryagin was able to prove Hilbert's Fifth Problem for abelian groups using the theory of characters on locally compact abelian groups which he had introduced. *SAU [He was buried at the Novodevichie Memorial Cemetery in Moscow.

1988 Abraham Seidenberg (June 2, 1916 – May 3, 1988) was an American mathematician. He was known for his research to commutative algebra, algebraic geometry, differential algebra, and the history of mathematics. He published Prime ideals and integral dependence written jointly with I S Cohen which greatly simplified the existing proofs of the going-up and going-down theorems of ideal theory. He also made important contributions to algebraic geometry. In 1950, he published a paper called The hyperplane sections of normal varieties which has proved fundamental in later advances. In 1968, he wrote Elements of the theory of algebraic curves, a book on algebraic geometry. He published several important papers.*Wik

Credits :
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*RMAT= The Renaissance Mathematicus, Thony Christie
*SAU=St Andrews Univ. Math History
*TIA = Today in Astronomy
*TIS= Today in Science History
*VFR = V Frederick Rickey, USMA
*Wik = Wikipedia
*WM = Women of Mathematics, Grinstein & Campbell