Sunday, 6 August 2017

On This Day in Math - August 6

God exists since mathematics is consistent,
and the Devil exists since we cannot prove it
.
~André Weil

This is the 218th day of the year; 218 = 72 + 132

218 is the number of nonequivalent ways to color the 12 edges of a cube using at most 2 colors, where two colorings are equivalent if they differ only by a rotation of the cube.

218 is the smallest number with a Merten funtion =3. (an acceptable definition for students is that the Merten number for n, M(n), is the count of square-free integers up to n that have an even number of prime factors, minus the count of those that have an odd number.) The function is named in honor of Franz Merten, who was a teacher of Schrodinger.

EVENTS

1181 a supernova was observed by Chinese astronomers in the constellation now known as Cassiopeia, and independently found one day later from Japan. The "guest star" remained visible for 185 days (over 6 months). A supernova remnant, 3C58, found by radio astronomers in the 1960's, was first proposed to be the remnant of the supernova 1181 by F. Richard Stephenson. 3C58 is a filled-center supernova remnant, extends now about 9x5 arc minutes and contains a pulsar which rotates about 15 times per second. In addition, an extended X-ray source surrounding the pulsar has been observed, thought to be produced by a cloud of high-energy particles about 20 light years across. *TIS

1456 According to one story that first appeared in a 1475 posthumous biography and was subsequently embellished and popularized by Pierre-Simon Laplace, Callixtus III excommunicated the 1456 apparition of Halley's Comet, believing it to be an ill omen for the Christian defenders of Belgrade from the besieging armies of the Ottoman Empire. No known primary source supports the authenticity of this account. The 29 June 1456 papal bull of Callixtus III calling for a public prayer for the success of the crusade, makes no mention of the comet. By 6 August, when the Turkish siege was broken the comet had not been visible in either Europe or Turkey for several weeks. *Wik

1618 Johannes Kepler determent the distance to the sun to be 22.5 mil km. *NSEC

In 1753, Professor Georg Richmann of St. Petersburg, Moscow, was killed by his experiment with lightning. One year after Benjamin Franklin's kite experiment, Richmann attached a wire to the top of his house and led it down to an iron bar suspended above "the electric needle" and a bowl of water partly filled with iron filings*. It was reported that during a storm, Richmann was struck while about a foot from the bar, and closely observing the needle. "A globe of blue and whitish fire about four inches diameter" from the bar struck Richmann's forehead" with "an explosion like that of a small cannon." His assistant, M. Sokolaw, who survived, was thrown to the floor feeling blows on his back. He found marks of burning hot wire fragments on the back of his clothes.*TIS

1855 Thomas Penyngton Kirkman presented a paper on the general question of determining a condition under which a graph is Hamiltonian. Unlike Hamilton, who was primarily
interested in the algebraic connections of one specific graph, Kirkman was interested in the general study of ‘Hamiltonian circuits’ in arbitrary graphs. He was the rector of a small and isolated English parish, but made regular and important contributions to mathematics. His solution of the problem was incorrect; but he did present a second paper in 1856 in which he described a general class of graphs which do not contain such a circuit. Kirkman also studied the existence of Hamiltonian circuits on the dodecahedron, a variation of the Icosian Game which Hamilton also studied. In fact, the two men met once in 1861 when Hamilton visited Kirkman at his rectory. That Hamilton’s name became associated with the circuits, and not Kirkman’s, appears to be one of the accidents of history, or perhaps a credit to the fame of Hamilton’s quarternions and work in mathematical physics. *Janet Barnett, Early Writings on Graph Theory

1945 First atomic bomb explosion over a populated area, Hiroshima, Japan, from the Enola Gay, a B-29 bomber. The pilot was Colonel Paul Tibbits, the bombardier, Major Thomas Ferebee. *VFR The city was chosen because it had not been bombed and its area was perfect for evaluating the effect of the bomb.

2002 The first Polynomial-time primality test was published. The first provably polynomial time test for primality was invented by Manindra Agrawal, Neeraj Kayal and Nitin Saxena. The AKS primality test, runs in Õ((log n)12) (improved to Õ((log n)7.5) in the published revision of their paper), which can be further reduced to Õ((log n)6) if the Sophie Germain conjecture is true. Subsequently, Lenstra and Pomerance presented a version of the test which runs in time Õ((log n)6) unconditionally. *Wik

2003 After 61.40 days of computation, a 150-year-old unsolved problem has finally been answered, there is no 8x8 knights tour which forms a magic square. A knight's tour is a sequence of moves of a knight on a chessboard such that the knight visits every square only once. The earliest known reference to the knight's tour problem dates back to the 9th century AD. In Rudraṭa's Kavyalankara, a Sanskrit work on Poetics. If starting square is labled "one" and each square it lands on is numbered sequentially, an 8x8 number square is formed. If that square is a magic square, then you have formed a magic knights tour (except now we know you can't). It has long been known that magic knight's tours are not possible on n x n boards for n odd. It was also known that such tours are possible for all boards of size 4k x 4k for k > 2.
This longstanding open problem has now been settled in the negative by an exhaustive computer enumeration of all possibilities. The software for the computation was written by J. C. Meyrignac, and the website was established by Guenter Stertenbrink to distribute and collect results for all possible tours. After 61.40 CPU-days, corresponding to 138.25 days of computation at 1 GHz, the project was completed on August 5, 2003. What are the results? In addition to netting a total of 140 distinct semimagic knight's tours, the computation demonstrated for the first time that no 8 x 8 magic knight's tour is possible, thus finally laying this long-open problem to rest. *Mathworld

2011 During the first excavation campaign of the Paphos Agora Project (3rd July – 6th August 2011), an interesting object was discovered. An ancient, two-sided amulet with a 59-letter palindromic inscription. It was translated in the following way: “Yahweh is the bearer of the secret name, the lion of Re secure in his shrine”.
The opposite side of the amulet has several images, including a bandaged mummy (likely representing the Egyptian god Osiris) lying on a boat and an image of Harpocrates, the god of silence, who is shown sitting on a stool while holding his right hand up to his lips. Strangely, the amulet also displays a mythical dog-headed creature called a cynocephalus, which is shown holding a paw up to its lips, as if mimicking Harpocrates' gesture. *livescience

BIRTHS

1638 Nicolas Malebranche(6 August 1638 – 13 October 1715) was a major French philosopher and follower of Descartes whose ideas he developed to bring them more in line with standard Roman Catholic orthodox belief.*SAU

1667 Johann (Jean) I Bernoulli born. ( August 6, 1667– 1 January 1748) was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is known for his contributions to infinitesimal calculus and educated Leonhard Euler in his youth. In 1691 Johann Bernoulli again fueled the tensions between himself and his brother when he solved the problem of the catenary presented by Jakob. In 1696 Johann Bernoulli proposed the problem of the brachistochrone, despite already having solved the problem himself. Within two years he received five answers, one of which was from his older brother, Jacob. Bernoulli also proposed a fluid energy perpetual motion machine.
Bernoulli was hired by Guillaume François Antoine de L'Hôpital to tutor him in mathematics. Bernoulli and L'Hôpital signed a contract which gave L'Hôpital the right to use Bernoulli’s discoveries as he pleased. L'Hôpital authored the first textbook on infinitesimal calculus, "Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes", which mainly consisted of the work of Bernoulli, including what is now known as L'Hôpital's rule. *Wik

1741 John Wilson (6 August 1741, Applethwaite, Westmorland – 18 October 1793, Kendal, Westmorland) born English laywer and mathematician. The theorem that bears his name [If p is prime, then (p − 1)! ≡−1 (mod p)] was published without proof in Waring’s Meditationes algebraicae of 1770, but we now know that Leibniz knew the result. The ﬁrst published proof was by Lagrange (1773), who showed that it is equivalent to Fermat’s Little Theorem of 1640: If p is prime and  p divides a Then ap−1 ≡ 1 (mod p).
Euler ﬁrst proved this in 1736. Lagrange also showed that the converse of Wilson’s Theorem is true. (The converse of Fermat’s is false—the counterexamples are called pseudoprimes.) Sir Frederick Pollack has conjectured that Wilson’s Theorem was a guess that neither he nor Waring could prove. See DeMorgan’s Budget of Paradoxes. *VFR In the 11th century Alhazen (Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham )solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Alhazen considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the Chinese remainder theorem.

1766 William Hyde Wollaston (6 August 1766 – 22 December 1828), British Doctor and chemist. He saw in 1802 the Fraunhoferlines in the Solar spectrum but considered it as a limitation of colors. *NSEC
He is also known for discovering two chemical elements and for developing a way to process platinum ore. Wollaston also performed important work in electricity. In 1801, he performed an experiment showing that the electricity from friction was identical to that produced by voltaic piles. *Wik

1838 George James Symons (6 Aug 1838 - 10 Mar 1900) British meteorologist who strove to provide reliable observational data by imposing standards of accuracy and uniformity on meteorological measurements and by substantially increasing the number of reporting stations from 168 to 3,500. He was elected to Royal Meteorological Society (1856) when only 17 years old. He established the British Rainfall Organization (1860) and issued annual rainfall reports (1860-98). Symons's Monthly Meteorological Magazine first appeared in 1866. He wrote hundreds of articles and several books, and he amassed the UK's most comprehensive collection of meteorological books, many of great historical interest.*TIS

1943 Jonathan Bruce Postel (August 6, 1943 – October 16, 1998) was an American computer scientist who played a pivotal role in creating and administering the Internet. In the late 1960s, Postel was a graduate student developing the ARPANET, a forerunner of the Internet for use by the U.S. Dept. of Defense. As director of the Internet Assigned Numbers Authority (IANA), which he formed, Postel was a creator of the Internet's address system. The Internet grew rapidly in the 1990s, and there was concern about its lack of regulation. Shortly before his death, Postel submitted a proposal to the U.S. government for an international nonprofit organization that would oversee the Internet and its assigned names and numbers. He died at age 55, from complications after heart surgery.*TIS

DEATHS

1694 Antoine Arnauld was a French supporter of Jansen who published some important works on logic and philosphy. *SAU

1879 Johann Von Lamont (December 13, 1805; Corriemulzie, Scotland - August 6, 1879 Munich, Germany) Scottish-born German astronomer noted for discovering (1852) that the magnetic field of the Earth fluctuates with a 10.3-year activity cycle, but does not correlate it with the period of the sunspot cycle. From 1 Aug 1840, Johann von Lamont (as director of the Royal Astronomical Observatory in Munich) started regular and permanent observations of the earth's magnetic field. In the 1850's he started making regional magnetic surveys in the kingdom of Bavaria, later extended to other states in south Germany, France, Holland, Belgium, Spain, Portugal, Prussia and Denmark. His central European maps with isolines of geomagnetic elements, reduced to 1854, were the first worldwide*TIS

1925 Gregorio Ricci-Curbastro (12 January 1853 – 6 August 1925) Much of Ricci-Curbastro's work ... was done jointly with his student Levi-Civita. In a fundamental joint paper that year Méthodes de calcul différentiel absolu et leurs applications he used (for the only time) the name Ricci instead of his full name. This paper had been requested five years earlier by Klein. The authors state their aims in the preface to their important seventy-seven page paper:-
The algorithm of absolute differential calculus, the instrument matériel of the methods ... can be found complete in a remark due to Christoffel. But the methods themselves and the advantages they offer have their raison d'être and their source in the intimate relationships that join them to the notion of an n-dimensional variety, which we owe to the brilliant minds of Gauss and Riemann. ... Being thus associated in an essential way with Vn, it is the natural instrument of all those studies that have as their subject, such a variety, or in which one encounters as a characteristic element a positive quadratic form of the differentials of n variables or of their derivatives.
In the paper, applications are given by Ricci-Curbastro and Levi-Civita to the classification of the quadratic forms of differentials and there are other analytic applications; they give applications to geometry including the theory of surfaces and groups of motions; and mechanical applications including dynamics and solutions to Lagrange's equations. The main ideas of this paper are discussed in. Ricci-Curbastro's absolute differential calculus became the foundation of tensor analysis and was used by Einstein in his theory of general relativity. *SAU

1945 Paul Koebe; (February 15, 1882, Luckenwalde, Brandenburg – August 6, 1945) Koebe's work was all on complex functions, his most important results being on the uniformisation of Riemann surfaces. Shortly after 1900 Koebe established the general principle of uniformisation which had been originally conceived by Klein and Poincaré. Koebe's proof of the uniformisation theorem has been described as: ... arguably one of the great theorems of the century. *SAU

1998 André Weil (6 May 1906 – 6 August 1998) was a French mathematician who worked on algebraic geometry and number theory.*SAU ..renowned for the breadth and quality of his research output, its influence on future work, and the elegance of his exposition. He is especially known for his foundational work in number theory and algebraic geometry. He was a founding member and the de facto early leader of the influential Bourbaki group. The philosopher Simone Weil was his sister.*Wik
To avoid the draft, he went to Finland. ''As a soldier,'' he said, ''I would be entirely useless, but as a mathematician I could be of some use.'' The Finns returned him to the French, who imprisoned him for six months. In prison, he created the Riemann hypothesis -- named for a German mathematician -- which became a basic element of number theory and is regarded as one of his most insightful mathematical achievements, Dr. Phillips said.

2002 Edsger Wybe Dijkstra (May 11, 1930 – August 6, 2002)was a Dutch computer scientist. He received the 1972 Turing Award for fundamental contributions to developing programming languages, and was the Schlumberger Centennial Chair of Computer Sciences at The University of Texas at Austin from 1984 until 2000. Among his contributions to computer science are the shortest path-algorithm, also known as Dijkstra's algorithm; Reverse Polish Notation and related Shunting yard algorithm; the THE multiprogramming system, an important early example of structuring a system as a set of layers; Banker's algorithm; and the semaphore construct for coordinating multiple processors and programs. Another concept due to Dijkstra in the field of distributed computing is that of self-stabilization – an alternative way to ensure the reliability of the system. Dijkstra's algorithm is used in SPF, Shortest Path First, which is used in the routing protocols OSPF and IS-IS. *Wik

2007 Atle Selberg (14 June 1917 – 6 August 2007) was a Norwegian mathematician known for his work in analytic number theory, and in the theory of automorphic forms, in particular bringing them into relation with spectral theory. He was awarded the Fields Medal in 1950.*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