Roth was born in 1925 in Breslau, the son of Jewish parents. He came as a teenager on the run from the Nazis to England and attended St Paul's School in London from 1939 to 1943, then studied at Peterhouse College, Cambridge University, among others, Harold Davenport. After graduation in 1945 he became assistant to the internationally famous Gordonstoun School near Elgin in Scotland. The school was founded in 1934 by the German educationalist Kurt Hahn as a boys' school, and should the character development as well as academic education serve. Roth but returned in 1946 to London to do research at the university. The Master's degree (master) he made in 1948. Two years later he received his doctorate in 1961 and appointed professor. In 1966 he accepted a position on a chair of mathematics at the University of London and has held this position until 1988.
He worked mainly in the field of number theory, especially the diophantine approximation. His most important result was reflected in the set of Thue -Siegel -Roth. He states that for every algebraic number and any inequality ( p, q relatively prime )
Only finitely many solutions has. This is the " best" possible such set and improved versions of Axel Thue precursor and Carl Ludwig Siegel. He is, however, no effective method for the determination of such solutions.
In 1953 he proved a theorem (Theorem of Roth) on the minimum density of sets of natural numbers, the existence of non-trivial arithmetic progressions with three terms to make sure ( a special case of a later Endre Szemeredi proved and designated pursuant to this sentence). The sentence was later aggravated by Jean Bourgain, Roger Heath- Brown and Tom Sanders.
In the 1960s, he developed simultaneously with Enrico Bombieri on the method of " Big screen " of Yuri Linnik and Rényi Alfréd in analytic number theory. With Halberstam he is the author of a book " sieving ".
In addition to the Fields Medal Roth received further honors for his work. In 1960 he was made an honorary member of the Royal Society of London and in 1983 the Royal Society of Edinburgh. He received in 1983 the De Morgan Medal of the London Mathematical Society, and in 1991 the Sylvester Medal of the Royal Society. In 1958 he gave a plenary lecture at the International Congress of Mathematicians in Edinburgh ( Rational Approximations to Algebraic Numbers ).