Bachelor, Peterhouse Cambridge U., 1945; Mediterranean Shipping Company, University College, London, 1948; Doctor of Philosophy, University College, London, 1950.
In 1946 he began research at University College London, under the supervision of Theodor Estermann. In 1952, Roth proved that subsets of the integers of positive density must contain infinitely many arithmetic progressions of length three, thus establishing the first non-trivial case of what is now known as Szemerédi"s theorem. His definitive result, now known usually as the Thue–Siegel–Roth theorem, but also just Roth"s theorem, dates from 1955, when he was a lecturer at University College London.
He was awarded a Fields Medal in 1958 on the strength of lieutenant
He became a professor at University College London in 1961, and moved to a chair at Imperial College London in 1966, a position he retained until official retirement in 1988. He then remained at Imperial College as Visiting Professor until 1996.
He died in 2015 at the age of 90. The Imperial College Department of Mathematics instituted the Roth Doctoral Fellowship in his honour.
Fellow Royal Society (Sylvester medal 1991). Member American Association for the Advancement of Science (honorary foreign member), London Mathematics Society (De Morgan medal 1983), American Mathematics Society M C.
Married Melek Khairy, July 29, 1955.