Ben Green

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This article is about the mathematician. For the British World War II internee, see: Ben Greene.

Ben Joseph Green (born February 27 1977, Bristol, United Kingdom) is a British mathematician, specializing in combinatorics and number theory. He studied at Trinity College, Cambridge, earning his doctorate under Tim Gowers in 2003 before being appointed a Junior Research Fellow. He subsequently became a Professor of Mathematics at Bristol University and also a Research Fellow of the Clay Mathematics Institute. In September 2006 he returned to Cambridge as the first Herchel Smith Professor of Pure Mathematics. He received the Clay Research Award in 2004 and the Salem Prize in 2005 for his contributions to combinatorial number theory related to progressions of primes. In 2007 he was awarded the SASTRA Ramanujan Prize.

Mathematics

Ben Green has published several important results in both combinatorics and number theory. These include improving the estimate by Jean Bourgain of the size of arithmetic progressions in sumsets, as well as a proof of the Cameron–Erdős conjecture on sum-free sets of natural numbers.

His work in demonstrating that every set of primes of positive relative upper density contains an arithmetic progression of length three then led to his breakthrough 2004 work with Terence Tao that showed that for all n there exist infinitely many arithmetic progressions of length n in the prime numbers. See Green–Tao theorem.