Ben Joseph Green FRS (born 27 February 1977) is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford. Early life and education Ben Green was born on 27 February 1977 in Bristol, England. He studied at local schools in Bristol, Bishop Road Primary School and Fairfield Grammar School, competing in the International Mathematical Olympiad in 1994 and 1995. He entered Trinity College, Cambridge in 1995 and completed his BA in mathematics in 1998, winning the Senior Wrangler title. He stayed on for Part III and earned his doctorate under the supervision of Timothy Gowers, with a thesis entitled Topics in arithmetic combinatorics (2003). During his PhD he spent a year as a visiting student at Princeton University. He was a research Fellow at Trinity College, Cambridge between 2001 and 2005, before becoming a Professor of Mathematics at the University of Bristol from January 2005 to September 2006 and then the first Herchel Smith Professor of Pure Mathematics at the University of Cambridge from September 2006 to August 2013. He became the Waynflete Professor of Pure Mathematics at the University of Oxford on 1 August 2013. He was also a Research Fellow of the Clay Mathematics Institute and held various positions at institutes such as Princeton University, University of British Columbia, and Massachusetts Institute of Technology. Mathematics The majority of Green's research is in the fields of analytic number theory and additive combinatorics, but he also has results in harmonic analysis and in group theory. His best known theorem, proved jointly with his frequent collaborator Terence Tao, states that there exist arbitrarily long arithmetic progressions in the prime numbers: this is now known as the Green–Tao theorem. Amongst Green's early results in additive combinatorics are an improvement of a result of 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. He also proved an arithmetic regularity lemma for functions defined on the first natural numbers, somewhat analogous to the Szemerédi regularity lemma for graphs. From 2004–2010, in joint work with Terence Tao and Tamar Ziegler, he developed so-called higher order Fourier analysis. This theory relates Gowers norms with objects known as nilsequences. The theory derives its name from these nilsequences, which play an analogous role to the role that characters play in