William Timothy Gowers FRS (born 20 November 1963, Wiltshire) is a British mathematician. He is Rouse Ball Professor of Mathematics in the Department of Pure Mathematics and Mathematical Statistics at Cambridge University and a Fellow of Trinity College. In 1998 he received the Fields Medal for his research connecting the fields of functional analysis andcombinatorics.
His early education was at King's College School, Cambridge, and Eton College where he was a King's Scholar. He completed his PhD entitled 'Symmetric Structures in Banach Spaces' at theUniversity of Cambridge (Trinity College) in 1990 under the supervision of Béla Bollobás.
From 1991 to 1995 he was a member of the Department of Mathematics at University College London. In 1996 he received the Prize of the European Mathematical Society and in 1998 theFields Medal for research on functional analysis and combinatorics. He utilized tools from combinatorics to prove several of Stefan Banach's conjectures on Banach spaces and constructed a Banach space with almost no symmetry, serving as a counterexample to several other conjectures. With Bernard Maurey he resolved the "unconditional basic sequence problem" in 1992, showing that not every infinite-dimensional Banach space has an infinite-dimensional subspace that admits an unconditional Schauder basis. Another work which has proved highly influential is his proof ofSzemerédi's theorem by Fourier-analytic methods. He has also made substantial contributions in combinatorics, particularly to the study of regularity for graphs and hypergraphs. In 1999 he was elected Fellow of the Royal Society.
In addition to scholarly papers on mathematics, Gowers is also the author of several works popularizing mathematics, including the 2002 book Mathematics: A Very Short Introduction which describes modern research mathematics to the layman. He was consulted about the 2005 film Proof, starring Gwyneth Paltrow and Anthony Hopkins. Recently, he has been the editor for The Princeton Companion to Mathematics, a voluminous book published in 2008 that introduces and traces the development of various branches and concepts of modern mathematics.
In 2009, Gowers started the polymath project, using the comment functionality of his blog to produce mathematics collaboratively. The initial problem considered was finding a second proof to the density version of the Hales–Jewett theorem. After 7 weeks, Gowers announced the problem was "probably solved"with contributions from around 23 people. Jason Dyer's A gentle introduction to the Polymath projectprovides a good explanation of the work of the project for a non-mathematical audience.
Tricki.org is a Wikipedia-style project collecting methods of mathematical problem solving conceived in 2008 and launched by Gowers, Olof Sisask and Alex Frolkin in March 2009. Terence Tao and Ben Green are among those to have already contributed articles.