## Tuesday, 30 January 2018

### On This Day in Math - January 30

God may not play dice with the universe,
but something strange is going on with the prime numbers.
~Paul Erdos **

(Not realy,Referencing Albert Einstein's famous remark that "God does not play dice with the universe", this is attributed to Erdős in "Mathematics : Homage to an Itinerant Master" by D. Mackenzie, in Science 275:759 (1997), but has also been stated to be a comment originating in a talk given by Carl Pomerance on the Erdős-Kac theorem, in San Diego in January 1997, a few months after Erdős's death. Confirmation of this by Pomerance is reported in a statement posted to the School of Engineering, Computer Science & Mathematics, University of Exeter, where he states it was a paraphrase of something he imagined Erdős and Mark Kac might have said, and presented in a slide-show, which subsequently became reported in a newspaper as a genuine quote of Erdős the next day. In his slide show he had them both reply to Einstein's assertion: "Maybe so, but something is going on with the primes.")

The 30th day of the year; both the dodecahedron and the icosahedron have 30 edges. They may be positioned at a common center so that in the center of each of the 12 faces of the dodecahedron is one of the 12 vertices of the icosahedron, in the center of each of the 20 faces of the icosahedron is one of the 20 vertices of the dodecahedron, and the 30 edges of the dodecahedron and the 30 edges of the icosahedron cross each other at right angles at their midpoints. (I find this incredibly wonderful)

astounding to me, but 11+22+33...+3030 = 208492413443704093346554910065262730566475781 is prime Republic of Math ‏@republicofmath If there is another prime of this type, it will have over 20025 digits.

7! hours is 30 weeks

and from *@MathYearRound
30 = 2*3*5 (first 3 primes).
30 =$1^2+2^2+3^2+4^2$(first 4 perfect squares).
30 = 1*1*2*3*5 (first 5 Fibonacci #).

EVENTS

10 BCE Solar eclipse in Iran, as reported on a cuneiform tablet from the British Museum *History of Astronomy ‏@hist_astro  (I have to admit that every time I look at this image it reminds me of the map of Michigan's lower peninsula, and that little chip up by the little finger is Grand Traverse Bay, which I see from my dining room)

1610 Galileo writes to Belisario Vinta, with notes on his long observation of the moon with a new twenty-power scope. A letter containing much of what was to appear about the Moon in Sidereus Nuncius, two months later. *Drake, Galileo at Work; 1978

1830 In a letter to Laplace, Gauss writes about a "curious problem" that he had been working on for twelve years.  He gives the limiting value of  the frequency of distribution of positive integers in the continued fraction of a random number (now called the Gauss-Kuzmin Distribution) as $log_2(1+x)$ . He then asks if Laplace can offer help in finding the error term. *Math World

1897 Mary Frances Winston elected to membership in the American Mathematical Society. The previous year she received her PhD at G¨ottingen, being the ﬁrst American woman to receive a PhD in mathematics at a German university. *G. B. Price, History of the Department of Mathematics of the University of Kansas, 1866–1970, p. 70

1884 Sonja Kovelevskiaya gives her ﬁrst university lecturer. This was the ﬁrst regular lecture by a woman at a research institution in any ﬁeld in modern times. [The Mathematical Intelligencer, 6(1984), no. 1, p. 29] *VFR

1925 The U.S. History of Science Society was incorporated under the laws of the District of Columbia. The ﬁrst president was Lawrence Joseph Henderson (1878–1924). The movement to form the society was begun by David Eugene Smith and today is the most important historical society in the world. *VFR

1952 Two New Primes Found with SWAC. Using the Standards Western Automatic Computer (SWAC), researchers found two new prime numbers the first time they attempted a prime-searching program on the computer. Within the year, three other primes had been found. The National Bureau of Standards funded construction of the SWAC in Los Angeles in 1950 and it ran, in one form or another, until 1967.
*CHM {The first two primes found with SWAC were M521, M607. In 1951 Ferrier used a mechanical desk calculator to find the 44 digit prime (2148+1)/17 = 20988936657440586486151264256610222593863921.
The first primes found with an electronic computer were by Miller and Wheeler (Nature, 168 (1951) 838) in 1951 when they found several new primes, including the 79 digit 180(2127-1)2+1 }

1982 First computer virus, the Elk Cloner, written by 15-year old Rich Skrenta, is found in the wild. It infects Apple II computers via floppy disk. *Wik

1988 Science News reports that Noam D. Elkies, age 21, of Harvard found four fourth-powers whose sum is another fourth-power, thereby providing a counterexample to a conjecture of Euler in 1769. (Euler's conjecture was that the sum of the first n integers each raised to the nth power can not be an nth power.) The smallest number in his counterexample had eight digits. Later Roger Frye of Thinking Machines Corporation, Cambridge, MA, found the smallest counterexample:
95,8004 + 217,5194 + 414,5604 + 414 5604 = 422,4184 .
This took some 100 hours on a Connection Machine. Can you ﬁgure out how to verify this example using your calculator (which only displays 8 or 10 digits)? [Mathematics Magazine 61 (1988), p 130; Science 239 (1988), p 464]. *VFR
(Euler's general conjecture had been proven false by L. J. Lander and T. R. Parkin in 1966 when they found a counterexample for fifth powers. Elkies had suggested the computer approach that provided the minimal solution. It is still unknown if there are counterexamples above n=5)

1990 Ruth Lawrence sends a paper on homological representations of the Hecke algebra, introducing, among other things, certain novel linear representations of the braid group, the Lawrence–Krammer representation to the journal, Communications in Mathematical Physics
*Wik

1996 Yuji Hyakutake in Japan discovered a new comet using 25x150 binoculars. The comet was designated Comet C/1996 B2 (Hyakutake). As subsequent observations of the new comet were obtained, Brian Marsden from the IAU Central Bureau was able to compute the comet's orbital elements, and these computations indicated that the comet will pass as close as 0.10 AU (9.3 million miles) from the Earth on March 25, 1996! The comet has become a bright naked-eye object and remained so in March, April and May in 1996. The comet had exceeded expectations, becoming the brighest comet since Comet West in 1976. A long tail of up to 100 degrees was reported, and small fragments have been observed to break off the main nucleus. Comet Hyakutake is indeed the Great Comet of 1996. *jpl.nasa
Hyakutake discovered C/1996 B2 while looking for C/1995 Y1, a comet he had discovered a few weeks before. He died in Kokubu, Kagoshima, in 2002 at age 51 of an aneurysm which had led to internal bleeding. *Wik

BIRTHS

1619 Michelangelo Ricci  (30 Jan 1619 in Rome, Italy - : 12 May 1682 in Rome) In 1666, he found the tangent lines to the parabolas of Fermat. *VFR Michelangelo Ricci was a friend of Torricelli; in fact both were taught by Benedetti Castelli. He studied theology and law in Rome and at this time he became friends with René de Sluze. It is clear that Sluze, Torricelli and Ricci had a considerable influence on each other in the mathematics which they studied.
Ricci made his career in the Church. His income came from the Church, certainly from 1650 he received such funds, but perhaps surprisingly he was never ordained. Ricci served the Pope in several different roles before being made a cardinal by Pope Innocent XI in 1681.
Ricci's main work was Exercitatio geometrica, De maximis et minimis (1666) which was later reprinted as an appendix to Nicolaus Mercator's Logarithmo-technia (1668). It only consisted of 19 pages and it is remarkable that his high reputation rests solely on such a short publication.
In this work Ricci finds the maximum of xm(a - x)n and the tangents to ym = kxn. The methods are early examples of induction. He also studied spirals (1644), generalised cycloids (1674) and states explicitly that finding tangents and finding areas are inverse operations (1668). *SAU

1755 Nikolai Fuss (30 Jan 1755 in Basel, Switzerland - 4 Jan 1826 in St Petersburg, Russia) was a Swiss mathematician whose most important contribution was as amanuensis to Euler after he lost his sight. Most of Fuss's papers are solutions to problems posed by Euler on spherical geometry, trigonometry, series, differential geometry and differential equations. His best papers are in spherical trigonometry, a topic he worked on with A J Lexell and F T Schubert. Fuss also worked on geometrical problems of Apollonius and Pappus. He made contributions to differential geometry and won a prize from the French Academy in 1778 for a paper on the motion of comets near some planet Recherche sur le dérangement d'une comète qui passe près d'une planète. Fuss won other prizes from Sweden and Denmark. He contributed much in the field of education, writing many fine textbooks. *SAU

1805 Edward Sang,(30 Jan 1805 in Kirkcaldy, Fife, Scotland - 23 Dec 1890) A native of Fife, Sang wrote extensively on mathematical, mechanical, optical and actuarial topics. *SAU

1865 Georg Landsberg (30 Jan 1865 , 14 Sept 1912) studied the theory of functions of two variables and also the theory of higher dimensional curves. In particular he studied the role of these curves in the calculus of variations and in mechanics.
He worked with ideas related to those of Weierstrass, Riemann and Heinrich Weber on theta functions and Gaussian sums. His most important work, however was his contribution to the development of the theory of algebraic functions of a single variable. Here he studied the Riemann-Roch theorem.
He was able to combine Riemann's function theoretic approach with the Italian geometric approach and with the Weierstrass arithmetical approach. His arithmetic setting of this result led eventually to the modern abstract theory of algebraic functions.
One of his most important works was Theorie der algebraischen Funktionen einer Varaiblen (Leipzig, 1902) which he wrote jointly with Kurt Hensel. This work remained the standard text on the subject for many years. *SAU

1918 Heinz Rutishauser (30 January 1918 in Weinfelden, Switzerland; 10 November 1970 in Zürich) was a Swiss mathematician and a pioneer of modern numerical mathematics and computer science. *Wik

1925 Douglas Engelbart is Born, best known for inventing the computer mouse. Engelbart publically demonstrated the mouse at a computer conference in 1968, where he also showed off work his group had done in hypermedia and on-screen video teleconferencing. The founder of the Bootstrap Institute, Engelbart has 20 patents to his name.*CHM

DEATHS

1954 Gino Benedetto Loria (19 May 1862 in Mantua, Italy - 30 Jan 1954 in Genoa, Italy) In his day, Loria was arguably the pre-eminent historian of mathematics in Italy. A full professor of higher geometry at the University of Genoa beginning in 1891, Loria wrote the history of mathematics as a mathematician writing for other mathematicians. He emphasised this approach repeatedly in his works. For instance, in the introduction to his 'Storia delle matematiche dall'alba della civilità al tramonto del secolo XIX' (History of Mathematics from the Dawn of Civilisation to the End of the 19th Century), he stated that general history of mathematics was written "by a mathematician for mathematicians". *SAU

1977 Harry Clyde Carver (December 4, 1890 – January 30, 1977) was an American mathematician and academic, primarily associated with the University of Michigan. He was a major influence in the development of mathematical statistics as an academic discipline.
Born in Waterbury, Connecticut, Carver was educated at the University of Michigan, earning his B.S. degree in 1915, and the next year becoming an instructor in mathematics; he taught statistics in actuarial applications. At the time, the University of Michigan was only the second such institution in the United States to offer this type of course, after the pioneering Iowa State University. Carver was appointed assistant professor at Michigan in 1918, then associate professor (1921) and full professor (1936); during this period the University's program in mathematical statistics and probability underwent significant expansion.
In 1930 Carver founded the journal Annals of Mathematical Statistics, which over time became an important periodical in the field. Financial support, however, was lacking in the midst of the Great Depression; in January 1934 Carver undertook financial responsibility for the Annals and maintained the existence of the journal at his own expense. In 1935 he helped to start the Institute of Mathematical Statistics, which in 1938 assumed control over the journal; Samuel S. Wilks succeeded Carver as editor in the same year. The Institute has named its Harry C. Carver Medal after him.
With the coming of World War II, Carver devoted his energies to solving problems in aerial navigation, an interest he maintained for the remainder of his life. *Wik

1991 John Bardeen (23 May 1908, 30 Jan 1991) American physicist who was cowinner of the Nobel Prize for Physics in both 1956 and 1972. He shared the 1956 prize with William B. Shockley and Walter H. Brattain for their joint invention of the transistor. With Leon N. Cooper and John R. Schrieffer he was awarded the 1972 prize for development of the theory of superconductors, usually called the BCS-theory (after the initials of their names). *TIS

1992 Dom George Frederick James Temple​ FRS(born 2 December 1901, London; died 30 January 1992, Isle of Wight) was an English mathematician, recipient of the Sylvester Medal in 1969. He was President of the London Mathematical Society in the years 1951-1953.[2]
Temple took his first degree as an evening student at Birkbeck College, London, between 1918 and 1922, and also worked there as a research assistant. In 1924 he moved to Imperial College as a demonstrator, where he worked with Professor Sydney Chapman. After a period spent with Eddington at Cambridge, he returned to Imperial as reader in mathematics. He was appointed professor of mathematics at King's College London in 1932, where he returned after war service with the Royal Aircraft Establishment at Farnborough. In 1953 he was appointed Sedleian Professor of Natural Philosophy at the University of Oxford, a chair which he held until 1968, and in which he succeeded Chapman. He was also an honorary Fellow of Queen's College, Oxford.
After the death of his wife in 1980, Temple, a devout Christian, took monastic vows in the Benedictine order and entered Quarr Abbey on the Isle of Wight, where he remained until his death. *Wik

1998 Samuel Eilenberg (September 30, 1913 – January 30, 1998) was a Polish and American mathematician born in Warsaw, Russian Empire (now in Poland) and died in New York City, USA, where he had spent much of his career as a professor at Columbia University.
He earned his Ph.D. from University of Warsaw in 1936. His thesis advisor was Karol Borsuk. His main interest was algebraic topology. He worked on the axiomatic treatment of homology theory with Norman Steenrod (whose names the Eilenberg–Steenrod axioms bear), and on homological algebra with Saunders Mac Lane. In the process, Eilenberg and Mac Lane created category theory.
Eilenberg was a member of Bourbaki and with Henri Cartan, wrote the 1956 book Homological Algebra, which became a classic.
Later in life he worked mainly in pure category theory, being one of the founders of the field. The Eilenberg swindle (or telescope) is a construction applying the telescoping cancellation idea to projective modules.
Eilenberg also wrote an important book on automata theory. The X-machine, a form of automaton, was introduced by Eilenberg in 1974. *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