John Cassels

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John William Scott Cassels , also Ian Cassels, (born June 11, 1922 in Durham ; † July 27, 2015 ) was a British mathematician who dealt with number theory and arithmetic - algebraic geometry .

Cassels, whose father oversaw agriculture in County Durham , went to school in Durham and Edinburgh and studied at the University of Edinburgh (Masters degree in 1943) and at the University of Cambridge ( Trinity College ), where he received his doctorate in 1949 under Louis Mordell . In between he worked like many other mathematicians on the Enigma deciphering project in Bletchley Park during the Second World War . In 1949 he was made a Fellow of Trinity College. Cassels was then a lecturer in Manchester and from 1950 in Cambridge, where he became a reader in arithmetic in 1963 . In 1967 he became Sadleirian Professor of Pure Mathematics at Cambridge. From 1969 he was also chairman of the faculty for pure mathematics and mathematical statistics in Cambridge, which he remained until his retirement in 1984.

Cassels worked on the geometry of numbers, rational quadratic forms , the arithmetic of elliptical curves (a series of works Arithmetic of Curves of Genus 1 in the Journal of the London Mathematical Society and in the Journal for Pure and Applied Mathematics 1959 to 1965), Diophantine approximation and local bodies. For example, he proved that the order of the Tate-Shafarevich group is a square number if it is finite.

Cassels has been a member (" Fellow ") of the Royal Society since 1963 , and he received its 1973 New Year's Medal . From 1976 to 1978 he was President of the London Mathematical Society , whose De Morgan Medal he received in 1986. He has been a Fellow of the Royal Society of Edinburgh since 1981 . From 1978 to 1982 he was on the Council of the International Mathematical Union . 1974 to 1978 he was Vice President of the Royal Society in London. In 1970 he was invited speaker at the International Congress of Mathematicians in Nice ( On cubic trigonometric sums ).

Fonts

  • An Introduction to Diophantine approximation (= Cambridge Tracts in Mathematics and Mathematical Physics. 45, ISSN  0068-6824 ). Cambridge University Press, Cambridge 1957, (Reprinted by Hafner, New York NY 1972).
  • An introduction to the geometry of numbers (= basic teachings of the mathematical sciences . 99). Springer, Berlin et al. 1959, (2nd printing, corrected. Ibid. 1971, ISBN 3-540-02397-6 ).
  • Arithmetic on an elliptic curve. In: Proceedings of the International Congress of Mathematicians, Saltsjöbaden near Stockholm, 15-22 August 1962. Institut Mittag-Leffler, Djursholm 1963, pp. 234-246, ( digitized ).
  • Diophantine equations with special reference to elliptic curves. In: Journal of the London Mathematical Society . Vol. 41, 1966, pp. 193-291, doi : 10.1112 / jlms / s1-41.1.193 .
  • as editor with Albrecht Fröhlich : Algebraic Number Theory. Proceedings of an Instructional Conference organized by the London Mathematical Society (a NATO Advanced Study Institute) with the Support of the International Mathematical Union. Academic Press, New York NY 1967.
  • Rational quadratic forms (= LMS Monographs. 13). Academic Press, London et al. 1978, ISBN 0-12-163260-1 .
  • Rational quadratic forms. In: Annual report of the German Mathematicians Association . Vol. 82, No. 2, 1980, pp. 81-93.
  • Economics for mathematicians (= London Mathematical Society. Lecture Note Series. 62). Cambridge University Press, Cambridge et al. 1981, ISBN 0-521-28614-X .
  • Local Fields (= London Mathematical Society Student Texts. 3). Cambridge University Press, Cambridge et al. 1986, ISBN 0-521-30484-9 .
  • Lectures on Elliptic Curves (= London Mathematical Society Student Texts. 24). Cambridge University Press, Cambridge et al. 1991, ISBN 0-521-41517-9 .
  • with Eugene Victor Flynn: Prolegomena to a Middlebrow Arithmetic of Curves of Genus 2 (= London Mathematical Society. Lecture Note Series. 230). Cambridge University Press, Cambridge et al. 1996, ISBN 0-521-48370-0 .

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personal data
SURNAME Cassels, John
ALTERNATIVE NAMES Cassels, John William Scott (full name)
BRIEF DESCRIPTION English mathematician
DATE OF BIRTH June 11, 1922
PLACE OF BIRTH Durham
DATE OF DEATH July 27, 2015