Klaus Friedrich Roth, who died in Inverness on 10 November 2015 aged 90, made fundamental contributions to different areas of number theory, including diophantine approximation, the large sieve, irregularities of distribution and what is nowadays known as arithmetic combinatorics. He was the first British winner of the Fields Medal, awarded in 1958 for his solution in 1955 of the famous Siegel conjecture concerning approximation of algebraic numbers by rationals. He was elected a Fellow of the Royal Society in 1960, and received its Sylvester Medal in 1991. He was also awarded the De Morgan Medal of the London Mathematical Society in 1983, and elected Fellow of University College London in 1979, Honorary Fellow of Peterhouse in 1989, Honorary Fellow of the Royal Society of Edinburgh in 1993 and Fellow of Imperial College London in 1999.
Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory