Ben Joseph Green FRS (born 27 February 1977) is a British mathematician, specialising in combinatorics and number theory.

[1] 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).

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.

From 2004–2010, in joint work with Terence Tao and Tamar Ziegler, he developed so-called higher order Fourier analysis.

Green and Tao used higher order Fourier analysis to present a new method for counting the number of solutions to simultaneous equations in certain sets of integers, including in the primes.

Green also has worked, jointly with Kevin Ford and Sean Eberhard, on the theory of the symmetric group, in particular on what proportion of its elements fix a set of size

[9] Green and Tao also have a paper[10] on algebraic combinatorial geometry, resolving the Dirac-Motzkin conjecture (see Sylvester–Gallai theorem).

Kevin Ford, Ben Green, Sergei Konyagin, James Maynard and Terence Tao, initially in two separate research groups and then in combination, improved the lower bound for the size of the longest gap between two consecutive primes of size at most

[11] The form of the previously best-known bound, essentially due to Rankin, had not been improved for 76 years.

[12] Green has also been involved with the new developments of Croot-Lev-Pach-Ellenberg-Gijswijt on applying the polynomial method to bound the size of subsets of a finite vector space without solutions to linear equations.

He adapted these methods to prove, in function fields, a strong version of Sárközy's theorem.