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John William Scott "Ian" Cassels, FRS (11 July 1922 – 27 July 2015) was a British mathematician.


Biography

Cassels was educated at Neville's Cross Council School in Durham and George Heriot's School in Edinburgh. He went on to study at the University of Edinburgh and graduated with an undergraduate Master of Arts (MA) degree in 1943. His academic career was interrupted in World War II when he was involved in cryptography at Bletchley Park. After the war he became a research student of Louis Mordell at Trinity College, Cambridge; he received his PhD in 1949 and was elected a fellow of Trinity in the same year. Cassels then spent a year lecturing in mathematics at the University of Manchester before returning to Cambridge as a lecturer in 1950. He was appointed Reader in Arithmetic in 1963, the same year he was elected as a fellow of the Royal Society of London. In 1967 he was appointed as Sadleirian Professor of Pure Mathematics at Cambridge. In 1969 he became Head of the Department of Pure Mathematics and Mathematical Statistics. He retired in 1984.


Mathematical work

He initially worked on elliptic curves. After a period when he worked on geometry of numbers and diophantine approximation, he returned in the later 1950s to the arithmetic of elliptic curves, writing a series of papers connecting the Selmer group with Galois cohomology and laying some of the foundations of the modern theory of infinite descent. His best-known single result may be the proof that the Tate-Shafarevich group of an elliptic curve, if it is finite, must have order that is a square; the proof being by construction of an alternating form. Cassels often studied individual
Diophantine equation In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a c ...
s by
algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...
and
p-adic methods In mathematics, the -adic number system for any prime number  extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems. The extension ...
. His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades.


Publications

*. Reviewed in *. Reviewed in * * * Reviewed in: Johnson, Charles (1983) Economics For Mathematicians (J. W. S. Cassels), SIAM Rev., 25(4), 596–597. AND Binmore, Ken (1982) CASSELS, J. W. S., Economics for mathematicians, The Bulletin of the London Mathematical Society, Volume XIV . G. Binmorep 269 * * *


See also

* Cassels' conjecture *
Littlewood conjecture In mathematics, the Littlewood conjecture is an open problem () in Diophantine approximation, proposed by John Edensor Littlewood around 1930. It states that for any two real numbers α and β, :\liminf_ \ n\,\Vert n\alpha\Vert \,\Vert n\beta\Ver ...


References

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External links

* {{DEFAULTSORT:Cassels, John William Scott 1922 births 2015 deaths English mathematicians Number theorists Fellows of the Royal Society Alumni of the University of Edinburgh Alumni of Trinity College, Cambridge Fellows of Trinity College, Cambridge Bletchley Park people People educated at George Heriot's School Sadleirian Professors of Pure Mathematics