Roth was born in Breslau, Germany, now Wroclaw, Poland and came to England with his parents in 1933. He attended St Paul's School, London, from 1939 to 1943 before coming to Peterhouse. He was appointed, as war work, an assistant master at Gordonstoun, Scotland, but came to London in 1946 to pursue research at University College London with Harold Davenport. Here he obtained first an M.Sc. and an assistant lectureship in 1948 and a Ph.D. in 1950. He was promoted to a lectureship, then a readership in 1956 and a professorship in 1961 having been awarded the Fields medal in 1958, the first Briton to be so honoured, for proving that any irrational algebraic number has an approximation exponent equal to two. He was a visiting professor at M.I.T. in 1965-66 and Professor of Pure Mathematics at Imperial College from 1966 to 1988.
For an account of his other honours see items 11and 17 below and for reminiscens of him see 'Analytic Number Theory: essays in honour of Klaus Roth' (Cambridge University Press, 2009) pp. xiii-xviii.