Clay Research Award 2004
Ben Green was recognized for his joint work with Terry Tao on arithmetic progressions of prime numbers. These are equally spaced sequences of primes such as 31, 37, 43 or 13, 43, 73, 103. Results in the area go back to the work of Lagrange and Waring in the 1770's. A major breakthrough came in 1939 when the Dutch mathematician Johannes van der Corput showed that there are an infinite number of three-term arithmetic progressions of primes. Green and Tao showed that for any n, there are infinitely many n-term progressions of primes. Their proof, which relies on results of Szemerédi (1975) and Goldston and Yildirim (2003), uses ideas from combinatorics, ergodic theory, and the theory of pseudorandom numbers. The Green-Tao result is a major advance in our understanding of the primes.
Green was born in 1977 in Bristol, England. He was educated at Trinity College, Cambridge first as an undergraduate and later as a research student of Fields Medalist Tim Gowers. Since 2001 he has been a Fellow of Trinity College, and in that time he has visited Princeton, the Renyi Institute in Budapest and University of British Columbia, Vancouver, for extended periods. In January 2005 he will take up a Chair in Pure Mathematics at the University of Bristol.
Green will hold an appointment as a Clay Research Fellow from July 1, 2005 to June 30, 2007.