## Wednesday, 8 August 2012

### On This Day in Math - August 8

This result is too beautiful to be false;
it is more important to have beauty in one's equations
than to have them fit experiment.
Paul A M Dirac

The 221st day of the year; 221 the sum of consecutive prime numbers in two different ways 221 = (37 + 41 + 43 + 47 + 53) = (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41) (Can you find another number that is the sum of consecutive primes in more than one way? here's one you might have overlooked.)

EVENTS

1576 Laying of the cornerstone of Tycho Brahe’s observatory on the island of Hveen. *VFR

1786 Standards for the decimal system of money established (in the USA). *VFR The first really popular English language arithmetic by an American born author was in 1788 when Nicholas Pike published A New and Complete System of Arithmetic, which he said was "Composed for the use of the citizens of the United States". Well, patriotism probably won't hurt sells in a new country. Pikes book carried endorsements from several noted persons, including the governor of Massachusetts, James Bowdoin, and Yale President Ezra Stiles. The book even included a copy of the Act of Congress of 1786 which created the U. S. Federal Money System with denominations of mills (1/1000 of a dollar), cents, dimes, dollars, and Eagles (ten dollars). With all this emphasis on the new USA, it seems strange that none of the problems in the book involved the new American money, but instead were based on the English system. [The 2nd edition, in 1797, includes in the (very long) title; "adapted to the Federal Currency by Nathaniel Lord, A.M.;Boston]"

In 1854, metal bullet cartridges were patented by Smith & Wesson.*TIS Prior to this, cartridges were formed from paper. In 1776 a schoolmaster in Vienna named Felkel completed a factor table to 408,000 that was intended to be part of a larger work to reach several million. The tables were published at the expense of the Austrian government in the hope that subscriptions would pay for the cost. When the subscriptions failed to meet expectations, the printed volumes were supposedly used for cartridge paper. *Oystein Ore.. Number Theorey and Its History, pg 54

1876 Thomas Alva Edison, of Menlo Park, New Jersey, obtained patent #180,857 for a “method of preparing autographic stencils for printing,” the ﬁrst mimeograph machine. *VFR Only those of us who have been in the classroom a loooong time will remember these handy machines (and their intoxicating aroma). (addendum; Charles Wells has advised me "The solvent in mimeo ink was castor oil.")

1900 Hilbert delivers his address to the International Congress of Mathematicians. Hilbert's problems form a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900. The problems were all unsolved at the time, and several of them were very influential for 20th century mathematics. Hilbert presented only ten of the problems (1, 2, 6, 7, 8, 13, 16, 19, 21 and 22) at the Paris conference of the Second International Congress of Mathematicians, speaking on 8 August in the Sorbonne.
"Who of us would not be glad to lift the veil behind which the future is hidden..."
He had provided an extract of the speech (most unusual at that time) in French before hand for those who were not fluent in French.

1931 George Birkhoff publishes “A Set of Postulates for Plane Geometry Based on Scale and Protractor" in Annals of Mathematics. The system has undefined elements of point and line, and undefined relations of distance and angle. (pb)
in 1932, G. D. Birkhoff created a set of four postulates of Euclidean geometry sometimes referred to as Birkhoff's axioms. These postulates are all based on basic geometry that can be confirmed experimentally with a scale and protractor. Since the postulates build upon the real numbers, the approach is similar to a model-based introduction to Euclidean geometry. Other often-used axiomizations of plane geometry are Hilbert's axioms and Tarski's axioms. Birkhoff's axiom system was utilized in the secondary-school text Basic Geometry (first edition, 1940) *Wik

1977 Derek T. Whiteside received the Sarton Medal, the highest honor that the History of Science Society can bestow, for his editorship of The Mathematical Papers of Isaac Newton. In delivering the award Richard S. Westfall said “Before Tom began, Newton’s mathematics was largely a land of myth and fable.” In his 25 years work on the papers, Whiteside has changed all that. *VFR

BIRTHS
1832 John Emory Clark (August 8, 1832 - )was born at Northampton, New York, son of the Reverend John and Sarah Miller (Foote) Clark. He was prepared for college at the Troy Conference Academy of West Poultney, Vermont, and entered the University of Michigan, where he was graduated Bachelor of Arts in 1856. The degree of Master of Arts followed in 1859. He was Professor of Mathematics in the Michigan State Normal School from 1856 to 1857, and Assistant Professor of Mathematics in the University of Michigan from 1857 to 1859. During the year 1859-1860 he studied at the universities of Heidelberg, Munich, and Berlin. From 1861 to 1862 he was a United States deputy surveyor in Dakota. In August, 1862, he entered the Union Army as Captain of the Fifth Michigan Cavalry. On July 3, 1863, he was promoted to the rank of Major, and was honorably discharged February 25, 1865. On March 13, 1865, he was made Brevet Lieutenant-Colonel, United States Volunteers. In 1866 he returned to teaching, and was Professor of Mathematics and Physics, and, after one year, of Mathematics and Astronomy, in Antioch College, Ohio, till 1872. In the summer and fall of 1869 he again served the government as deputy surveyor in Colorado, and in the summer and fall of 1872 he was assistant astronomer to the United States Northern Boundary Commission. The latter part of the academic year 1872-1873 he was instructor in Mathematics in the Sheffield Scientific School of Yale University, and in June, 1873, was appointed Professor of Mathematics in that institution. He held that position till June, 1901, when on account of impaired health he resigned his chair and retired to Longmeadow, Massachusetts. He was married August 20, 1856, to Caroline C. Doty, and has four children: John Frederick, Helen (wife of the Reverend Harry R. Miles), William Russel, and Alice Tucker. *Burke A. Hinsdale and Isaac Newton Demmon, History of the University of Michigan (Ann Arbor: University of Michigan Press, 1906), pp. 343-344.

1901 Ernest Orlando Lawrence (August 8, 1901 – August 27, 1958) American physicist who was awarded the 1939 Nobel Prize for Physics for his invention of the cyclotron, the first device for the production of high energy particles. His first device, built in 1930 used a 10-cm magnet. He accelerated particles within a cyclinder at high vacuum between the poles of an electromagnetic to confine the beam to a spiral path while a high A.C. voltage increased the particle energy. Larger models built later created 8 x 104 eV beams. By colliding particles with atomic nuclei, he produced new elements and artificial radioactivity. By 1940, he had created plutonium and neptunium. He extended the use of atomic radiation into the fields of biology and medicine. Element 103 was named Lawrencium as a tribute to him.*TIS

1902 Paul Adrien Maurice Dirac, OM, FRS (8 August 1902 – 20 October 1984) English theoretical physicist known for his work in quantum mechanics and for his theory of the spinning electron. In 1933 he shared the Nobel Prize for Physics with the Austrian physicist Erwin Schrödinger. *TIS One of my favorite Dirac anecdotes (of which there are many)
Dirac was watching Anya Kapitza knitting while he was talking physics with Peter Kapitza. A couple of hours after he left, Dirac rushed back, very excited. "You know, Anya," he said, "watching the way you were making this sweater I got interested in the topological aspect of the problem. I found that there is another way of doing it and that there are only two possible ways. One is the one you were using; another is like that. . . . " And he demonstrated the other way, using his long fingers. His newly discovered "other way," Anya informed him, is well known to women and is none other than "purling."

1931 Sir Roger Penrose, British mathematician and theoretical physicist who in the 1960s calculated many of the basic features of black holes.*TIS A Penrose tiling is a non-periodic tiling generated by an aperiodic set of prototiles named after Sir Roger Penrose, who investigated these sets in the 1970s. Because all tilings obtained with the Penrose tiles are non-periodic, Penrose tiles are considered aperiodic tiles. A Penrose tiling may be constructed so as to exhibit both reflection symmetry and fivefold rotational symmetry, as in the diagram at the right.*Wik

1952 Roman Juszkiewicz (born 8 August 1952, died 28 January 2012) is a Polish astrophysicist whose work is concerned with fundamental issues of cosmology.
Juszkiewicz's scientific interests include the theory of gravitational instability, origins of the large-scale structure, microwave background radiation and Big Bang nucleosynthesis. He wrote nearly one hundred research papers, mostly in the area of cosmology. Calculated results based on observed motions of pairs of galaxies, obtained in 2000 by Roman Juszkiewicz and the group led by him, aimed at estimating the amount of dark matter in the Universe, were confirmed by the recently published data from the South Pole's ACBAR detector. *Wik

DEATHS

1555 Oronce Fine (20 December 1494 - 8 August 1555) was a French mathematician who published a major work on mathematics and astronomy.*SAU Although primarily a popularizer, Fine was one of the most prolific authors of mathematical books of his age. He worked in a wide range of mathematical fields, including practical geometry, arithmetic, optics, gnomonics, astronomy, and instrumentalism.
He gave the value of pi to be (22 2/9)/7 in 1544. Later, he gave 47/15 and, in De rebus mathematicis (1556), he gave 3 11/78. *Wik

1853 Josef-Maria Hoëné de Wronski (23 August 1776 – 9 August 1853)wrote on the philosophy of mathematics. *SAU He wrote exclusively in French, desirous that his ideas, of whose immortality he was convinced, should be accessible to all; he worked, he said, "through France for Poland." He published over a hundred works, and left many more in manuscript. When dying in the seventy-fifth year of his life, he exclaimed: "God Almighty, there's still so much more I wanted to say!"
In science, Hoene-Wroński set himself maximal tasks: the complete reform of philosophy and of mathematics, astronomy, technology. He not only elaborated a system of philosophy, but applications to politics, history, economics, law, psychology, music, pedagogy. It was his aspiration to reform human knowledge in an "absolute, that is, ultimate" manner.
Though during his lifetime nearly all his work was dismissed as nonsense, some of it has come in later years to be seen in a more favorable light. Although nearly all his grandiose claims were in fact unfounded, his mathematical work contains flashes of deep insight and many important intermediary results. Most significant was his work on series. He had strongly criticized Lagrange's use of infinite series, introducing instead a novel series expansion for a function. His criticisms of Lagrange were for the most part unfounded, but the coefficients in Wroński's new series were found to be important after his death, forming the determinants now known as the Wronskians (the name was given them by Thomas Muir in 1882).
The level of Wroński's scientific and scholarly accomplishments, and the amplitude of his objectives, placed Wroński in the first rank of European metaphysicians in the early 19th century. But the abstractness, formalism and obscurity of his thought, the difficulty of his language, his boundless self-assurance, his uncompromising judgments of others—alienated. He was perhaps the most original of the Polish metaphysicians, but others were more representative of the Polish outlook. *Wik

1989 Taro Morishima (22 April 1903 in Wakayama, Japan - 8 Aug 1989 in Tokyo, Japan)...His passion was algebraic number theory and he had a particular love of Fermat's Last Theorem. His first paper on Fermat's Last Theorem was published in the Proceedings of the Imperial Academy of Japan in 1928. It was the first of 12 papers written in German with the title Über die Fermatsche Vermutung, with 10 of these papers being in the Proceedings of the Imperial Academy of Japan between the years 1928 and 1935. By 1935 he had published a total of 16 papers, the other 6 being: Über den Fermatschen Quotienten (1931); On recent results about Fermat's last Theorem (Japanese) (1932); Über die Einheiten und Idealklassen des Galoisschen Zahlkörpers und die Theorie der Kreiskörper der l-ten Einheitswurzein (1933); and Über die Theorie der Kreiskörper der l-ten Einheitswurzein (1935). He also published a monograph Fermat's Problem (1934) in Japanese. All his papers are full of good ideas but they are extremely difficult to read since Morishima did not present enough detail.
Morishima's high research activity seems to have greatly lessened after 1935. Although difficulties relating to World War II​ and the difficult years in Japan following the war were partly responsible, nevertheless it does appear that he had already reduced his research activities. He did publish the book Higher Algebra in 1940 (in Japanese) but this and one further paper on Fermat's Last Theorem (in 1952) was all in published in the 30 years between 1935 and 1965.*SAU

1996 Sir Nevill F(rancis) Mott (30 September 1905 – 8 August 1996) English physicist who shared (with P.W. Anderson and J.H. Van Vleck of the U.S.) the 1977 Nobel Prize for Physics for his independent researches on the magnetic and electrical properties of amorphous semiconductors. Whereas the electric properties of crystals are described by the Band Theory - which compares the conductivity of metals, semiconductors, and insulators - a famous exception is provided by nickel oxide. According to band theory, nickel oxide ought to be a metallic conductor but in reality is an insulator. Mott refined the theory to include electron-electron interaction and explained so-called Mott transitions, by which some metals become insulators as the electron density decreases by separating the atoms from each other in some convenient way.*TIS

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