John William Scott Cassels, FRS (born 11 July 1922 in Durham) is a leading English mathematician.
Educated at Neville's Cross Council School in Durham and George Heriot's School in Edinburgh, Cassels graduated from the University of Edinburgh with an MA 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.
Cassels has often studied individual Diophantine equations by algebraic number theory and p-adic methods.
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 .
* J. W. S. Cassels at the Mathematics Genealogy Project