J. W. S. Cassels
|J. W. S. Cassels|
11 July 1922 |
Durham, North East England
|Other names||Ian Cassels|
|Institutions||University of Cambridge|
|Alma mater||University of Edinburgh|
|Doctoral advisor||Louis Mordell|
|Doctoral students||Bryan John Birch
José Felipe Voloch
|Notable awards||De Morgan Medal (1986)
Royal Society Sylvester Medal (1973)
Fellow of the Royal Society (1963)
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.
After finishing his major, Cassels 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.
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, if it is finite, must have order that is a square; the proof being by construction of an alternating form.
His publications include 200 papers. His advanced textbooks have influenced generations of mathematicians; some of Cassels's books have remained in print for decades.
- ——— (1957), An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics 45, Cambridge University Press.
- ——— (1997), An Introduction to the Geometry of Numbers, Springer Classics in Mathematics (reprint of 1959 and 1971 Springer-Verlag ed.), Springer-Verlag.
- Cassels, J.W.S. (1975). "Measures of the non-convexity of sets and the Shapley–Folkman–Starr theorem". Mathematical Proceedings of the Cambridge Philosophical Society 78 (3). pp. 433–436. doi:10.1017/S0305004100051884. MR 385711. (Shapley–Folkman lemma)
- Cassels, J.W.S. (1981). Economics for mathematicians. London Mathematical Society Lecture Note Series 62. Cambridge-New York: Cambridge University Press. pp. xi+145. ISBN 0-521-28614-X. MR 657578.
- LeVeque, W. J. (1958). "Review: J. W. S. Cassels, An introduction to Diophantine approximation". Bull. Amer. Math. Soc. 1958 (2): 65–68.
- Mordell, L. J. (1961). "Review: An introduction to the geometry of numbers, by J. W. S. Cassels". Bull. Amer. Math. Soc. 67 (1): 89–94.