## Thursday, 13 November 2014

### On This Day in Math - November 13

Mathematics is the only instructional material that can be presented in an entirely undogmatic way.
~Max Dehn

317th day of the year; 317 is a prime number. The number made up of 317 consecutive ones is also prime. It is the fourth prime repunit. The smallest is 11. Find the other two. *Wik
Not only is 317 the sum of two squares, but 3172 is also the sum of two squares. Can you find other primes for which both these conditions are true?

EVENTS
354 Saint Augustine of Hippo born. He wrote: “The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and conﬁne men in the bonds of Hell.” See D. W. Robinson, “From pebbles to commutators,” American Scientist, 55(1967), no. 3, pp. 329–337. *VFR Thony Christie pointed out in a recent Renaissance Mathematicus blog that, ".. the three terms astrologus, astronomus and mathematicus are used totally synonymously from antiquity up to the seventeenth century. In a famous passage from Augustinus, where he seems to be condemning mathematics, because he warns Christians to beware of the mathematici, he is actually condemning astrology, which he thought worked because it was fueled by evil."

1665 Newton tries a new approach to finding tangents "to crooked lines, however they may be related to straight ones", and develops his "fluxions", although he will not use that term until 1671. He uses a small letter o to represent a small change in time and uses p and q for what we would now call dx/dt and dy/dt and writes, "What is x and y in one moment will be x + o and y + o q/p in the next." All this will be rewritten into a single, more coherent paper in October of 1666.

1833 The Night the Stars Fell. "Birthdates of Indians of the 19th Century have generally been determined by the Government in relation to the awe-inspiring shower of meteorites that burned through the American skies just before dawn on 13 November 1833. The Leonids are famous because their meteor showers, or storms, can be among the most spectacular. Because of the superlative storm of 1833 and the recent developments in scientific thought of the time (see for example the identification of Halley's Comet) the Leonids have had a major effect on the development of the scientific study of meteors which had previously been thought to be atmospheric phenomena. The meteor storm of 1833 was of truly superlative strength. One estimate is over one hundred thousand meteors an hour, but another, done as the storm abated, estimated in excess of two hundred thousand meteors an hour over the entire region of North America east of the Rocky Mountains. It was marked by the Native Americans, abolitionists like Harriet Tubman and Frederick Douglass and slave-owners and others. Near Independence, Missouri, it was taken as a sign to push the growing Mormon community out of the area. The founder and first leader of Mormonism, Joseph Smith, noted in his journal that this event was a literal fulfillment of the word of God and a sure sign that the coming of Christ is close at hand. Denison Olmsted explained the event most accurately. After spending the last weeks of 1833 collecting information he presented his findings in January 1834 to the American Journal of Science and Arts, published in January–April 1834, and January 1836. He noted the shower was of short duration and was not seen in Europe, and that the meteors radiated from a point in the constellation of Leo and he speculated the meteors had originated from a cloud of particles in space. Accounts of the 1866 repeat of the Leonids counted hundreds per minute/a few thousand per hr in Europe. The Leonids were again seen in 1867, when moonlight reduced the rates to 1000 per hour. Another strong appearance of the Leonids in 1868 reached an intensity of 1000 per hour in dark skies. It was in 1866–67 that information on Comet Tempel-Tuttle was gathered pointing it out as the source of the meteor shower. When the storms failed to return in 1899, it was generally thought that the dust had moved on and storms were a thing of the past. *Wik

1843 Hamilton presents paper on Quaternions to the Royal Irish Academy
Hamilton describes his memory of the discovery of the Quaternions to his son,
"Every morning in the early part of the above-cited month, on my coming down to breakfast, your (then) little brother, William Edwin, and yourself, used to ask me, Well, papa, can you multiply triplets?' Whereto I was always obliged to reply, with a sad shake of the head: No, I can only add and subtract them. But on the 16th day of the same month (Oct) - which happened to be Monday, and a Council day of the Royal Irish Academy - I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven; and although she talked with me now and then, yet an undercurrent of thought was going on in my mind which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close; and a spark flashed forth the herald (as I foresaw immediately) of many long years to come of definitely directed thought and work by myself, if spared, and, at all events, on the part of others if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse - unphilosophical as it may have been - to cut with a knife on a stone of Brougham Bridge, as we passed it, the fundamental formula which contains the Solution of the Problem, but, of course, the inscription has long since mouldered away. A more durable notice remains, however, on the Council Books of the Academy for that day (October 16, 1843), which records the fact that I then asked for and obtained leave to read a Paper on `Quaternions,' at the First General Meeting of the Session; which reading took place accordingly, on Monday, the 13th of November following.'' *Sir Robert Stawell Ball, Hamilton

1845 Faraday writes in a letter to Christian Schonbein, “I happen to have discovered a direct relation between magnetism and light, also electricity and light, and the field it opens is so large and I think rich.” * The Letters of Faraday and Schoenbein

1871 Sir Robert S Ball presents the first paper using the term "Theory of Screws" to the Royal Irish Academy. He would use the term for the title of his book on the theory in 1876, and an updated version in 1900. The 1900 version was republished in the early part of the 21st Century. In the introduction to the 1900 book, he describes his creation of the term:

1884 The London Mathematical Society awarded its ﬁrst DeMorgan Medal to Arthur Cayley who “has invented and worked out the theory of invariants, and in steady life-long work connected it with nearly every branch of mathematics, enriching everything he touches, and everywhere throwing open new vistas of future work.” [Mathematical Intelligencer 6, no. 4, p. 8] *VFR
The DE MORGAN MEDAL is awarded in memory of Professor Augustus De Morgan, the Society's first President. It is the Society's premier award and is awarded every third year (in years numbered by a multiple of three). The De Morgan Medal for year X can only be awarded to a mathematician who is normally resident in the United Kingdom on 1 January of year X. The only grounds for the award of the Medal are the candidate's contributions to mathematics. The most recent winner (2010) was K.W. MORTON.

1946 First man made snow: Vincent Joseph Schaefer flew over Mount Greylock in Massachusetts, successfully seeding clouds with pellets of dry ice (solid carbon dioxide) to produce the first snowstorm initiated by man.*TIS

1948 The Nov 13th issue of the Journal, Notes and Queries, contained an article by recreational mathematician, and generally hard to classify, Leigh Mercer. The article was titled A FEW MORE PALINDROMES. Among them was one of the most commonly known palindromes, “A man, a plan, a canal — Panama”.
A popular math equation/limerick was also included, although not a palindrome.
A dozen, a gross, and a score
Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared and not a bit more.

With a hat-tip to John Golden @mathhombre for reminding me of this old beauty.

1957 Gordan Gould, a 37-year-old Columbia University graduate student, leaped out of bed at 1 a.m. to begin furiously scribbling notes for the world’s ﬁrst laser (his acronym for Light Ampliﬁcation by Stimulated Emission of Radiation). It took 20 years of legal battles to receive his “candy store patent,” so called because he had his notebook notarized in a candy store. [UPI press release, Nov. 12, 1982]*VFR He continued developing the idea, and filed a patent application in April 1959. The U.S. Patent Office denied his application, and awarded a patent to Bell Labs, in 1960. That provoked a twenty-eight-year lawsuit, featuring scientific prestige and money as the stakes. Gould won his first minor patent in 1977, yet it was not until 1987 that he won the first significant patent lawsuit victory, when a Federal judge ordered the U.S. Patent Office to issue patents to Gould for the optically pumped and the gas discharge laser devices.*Wik

In 1971, Mariner-9, the first man-made object to orbit another planet, entered Martian orbit. The mission of the unmanned craft was to return photographs mapping 70% of the surface, and to study the planet's thin atmosphere, clouds, and hazes, together with its surface chemistry and seasonal changes.*TIS

1983 The MIT TX-0, an experimental transistorized computer, is brought back to life for the third (and final) time at The Computer Museum in Marlboro, Massachusetts. The resurrection was achieved under the care of its devoted technician, John McKenzie, MIT Professor Jack Dennis, who was in charge of the machine, and a number of users. The TX-0 was built at Lincoln Laboratories in 1955 then dismantled and moved to MIT in 1956 where it was deemed to be obsolete in two years. The TX-0 is considered to be one the earliest transistorized computers ever designed.*TIS

BIRTHS

354 Saint Augustine of Hippo  He wrote: “The good Christian should beware of mathematicians and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and conﬁne men in the bonds of Hell.” See D. W. Robinson, “From pebbles to commutators,” American Scientist, 55(1967), no. 3, pp. 329–337. *VFR

1786 James Thomson (13 November 1786 - 12 January 1849) campaigned to reform Glasgow University, and is remembered for his role in the formation of the thermodynamics school there. He wrote many textbooks. He was the father of Lord Kelvin.*SAU

1876 Ernest Julius Wilczynski (November 13, 1876-September 14, 1932) was an American mathematician considered the founder of projective differential geometry.
Born in Hamburg, Germany, Wilczynski's family emigrated to America and settled in Chicago, Illinois when he was very young. He attended public school in the US but went to college in Germany and received his PhD from the University of Berlin in 1897. He taught at the University of California until 1907, the University of Illinois from 1907 to 1910, and the University of Chicago from 1910 until illness forced his absence from the classroom.*Wik

1878 Max Wilhelm Dehn (13 Nov 1878 in Hamburg, Germany - 27 June 1952 in Black Mountain, North Carolina, USA) wrote one of the first systematic expositions of topology (1907) and later formulated important problems on group presentations, namely the word problem and the isomorphism problem.He was an intuitive geometer, stimulated by Hilbert's axiomatic approach to the subject. Dehn had solved the third of Hilbert's 23 problems on the congruence of polyhedra. In 1907 Dehn wrote one of the first systematic expositions of topology jointly with Heegaard. At that time topology was called 'analysis situs'.
Dehn's work in topology had led him into the study of groups, particularly group presentations which arise naturally from topological considerations. Dehn formulated important problems on group presentations, namely the word problem and the isomorphism problem.
The word problem asks the fundamental question of whether there is an algorithm to determine whether a word in a group given by a presentation is trivial. It has since been shown that no such algorithm exists in general. Research on questions of this type are still of major importance in combinatorial group theory.
Dehn also wrote on statics, projective planes and the history of mathematics. *SAU

1920 Kollagunta Gopalaiyer Ramanathan (November 13, 1920 - May 10, 1992) was an Indian mathematician known for his work in number theory. His contributions are also to the general development of mathematical research and teaching in India.
At TIFR, he built up the number theory group of young mathematicians from India. For several years, he took interest to study Ramanujan's unpublished and published work. He was a Editorial board member of Acta Arithmetica for over 30 years. He retired from TIFR in 1985.
His wrote a paper with Mathukumalli V. Subbarao giving him an Erdős number of 2.*WIK

1959 Lene Vestergaard Hau (November 13, 1959) is a Danish physicist. In 1999, she led a Harvard University team who, by use of a superfluid, succeeded in slowing a beam of light to about 17 metres per second, and, in 2001, was able to momentarily stop a beam.
In 1989, Hau accepted a two-year appointment as a postdoctoral fellow at Harvard University. She received her degree from the University of Aarhus in Denmark in 1991. Her formalized training is in theoretical physics but her interest moved to experimental research in an effort to create a new form of matter known as a Bose-Einstein condensate. In 1991 she joined the Rowland Institute for Science at Cambridge as a scientific staff member. Since 1999 she has held the Gordon McKay Professor of Applied Physics and Professor of Physics at Harvard. She now is the Mallinckrodt Professor of Physics and Applied Physics at Harvard. *Wik

DEATHS
1830 Thomas Parkinson (1744 or 1745 – 13 November 1830) was a British clergymen.
He was born and educated in Kirkham, Lancashire, the son of Adam Parkinson. He entered Christ's College, Cambridge University in 1764 at age 19 and was senior wrangler and 2nd Smith's prizeman in 1769. He received an M.A. in 1772, a B.D. in 1789, and a D.D. in 1795.
He was Rector of Kegworth, Leicestershire from 1789 until his death. He became Archdeacon of Huntingdon from 1794 to 1812 and Archdeacon of Leicester from 1812 until his death in 1830.
He was the author of A System of Mechanics and Hydrostatics and was elected a Fellow of the Royal Society in 1786.
He died in Kegworth in 1830. *Wik

2002 Frederick Valentine Atkinson (January 25 1916 in Pinner (London, Middlesex ); November 13 2002 in Toronto , Canada) was a British mathematician .
Atkinson studied mathematics at Queen's College in Oxford. In 1939 he wrote a thesis on mean value theorems of the Riemann zeta function doctorate. He then received a scholarship, but he gave up in 1940 to serve as a cryptanalyst to do military service in military intelligence. He has spent three years in India to decipher Japanese codes.
Atkinson's main areas of work were the number theory (Riemann zeta-function) and differential equations ( boundary value problems ). His name is associated with the set of Atkinson on Fredholm operators connected. *Wik

2014 Alexander Grothendieck (28 Mar 1928-13 November 2014) In 1966 he won a Fields Medal for his work in algebraic geometry. He introduced the idea of K-theory and revolutionized homological algebra. Within algebraic geometry itself, his theory of schemes is used in technical work. His generalization of the classical Riemann-Roch theorem started the study of algebraic and topological K-theory. His construction of new cohomology theories has left consequences for algebraic number theory, algebraic topology, and representation theory. His creation of topos theory has appeared in set theory and logic.
One of his results is the discovery of the first arithmetic Weil cohomology theory: the ℓ-adic étale cohomology. This result opened the way for a proof of the Weil conjectures, ultimately completed by his student Pierre Deligne. To this day, ℓ-adic cohomology remains a fundamental tool for number theorists, with applications to the Langlands program.
Grothendieck influenced generations of mathematicians after his departure from mathematics. His emphasis on the role of universal properties brought category theory into the mainstream as an organizing principle. His notion of abelian category is now the basic object of study in homological algebra. His conjectural theory of motives has been behind modern developments in algebraic K-theory, motivic homotopy theory, and motivic integration. *Wik

Credits
*CHM=Computer History Museum
*FFF=Kane, Famous First Facts
*NSEC= NASA Solar Eclipse Calendar
*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