Timothy Gowers

Sir William Timothy Gowers, (born 20 November 1963) is a British mathematician.

He is Professeur titulaire of the Combinatorics chair at the Collège de France, and director of research at the University of Cambridge and Fellow of Trinity College, Cambridge.

In 1981, Gowers won a gold medal at the International Mathematical Olympiad with a perfect score.

He completed his PhD, with a dissertation on Symmetric Structures in Banach Spaces at Trinity College, Cambridge in 1990, supervised by Béla Bollobás.

After his PhD, Gowers was elected to a Junior Research Fellowship at Trinity College.

From 1991 until his return to Cambridge in 1995 he was lecturer at University College London.

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.

After this, Gowers turned to combinatorics and combinatorial number theory.

In 1994, Gowers was an invited speaker at the International Congress of Mathematicians in Zürich where he discussed the theory of infinite-dimensional Banach spaces.

In 1997 he proved that the Szemerédi regularity lemma necessarily comes with tower-type bounds.

In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.

Gowers attended King's College School, Cambridge, as a choirboy in the King's College choir, and then Eton College as a King's Scholar, where he was taught mathematics by Norman Routledge.

He was elected to the Rouse Ball Professorship at Cambridge in 1998.

In 1998, Gowers proved the first effective bounds for Szemerédi's theorem, showing that any subset free of k-term arithmetic progressions has cardinality for an appropriate c_k > 0.

One of the ingredients in Gowers's argument is a tool now known as the Balog–Szemerédi–Gowers theorem, which has found many further applications.

He also introduced the Gowers norms, a tool in arithmetic combinatorics, and provided the basic techniques for analysing them.

This work was further developed by Ben Green and Terence Tao, leading to the Green–Tao theorem.

During 2000–2 he was visiting professor at Princeton University.

Gowers has written several works popularising mathematics, including Mathematics: A Very Short Introduction (2002), which describes modern mathematical research for the general reader.

In 2003, Gowers established a regularity lemma for hypergraphs, analogous to the Szemerédi regularity lemma for graphs.

In 2005, he introduced the notion of a quasirandom group.

More recently, Gowers has worked on Ramsey theory in random graphs and random sets with David Conlon, and has turned his attention to other problems such as the P versus NP problem.

He has also developed an interest, in joint work with Mohan Ganesalingam, in automated problem solving.

Gowers has an Erdős number of three.

He was consulted about the 2005 film Proof, starring Gwyneth Paltrow and Anthony Hopkins.

He edited The Princeton Companion to Mathematics (2008), which traces the development of various branches and concepts of modern mathematics.

In 2009, with Olof Sisask and Alex Frolkin, he invited people to post comments to his blog to contribute to a collection of methods of mathematical problem solving.

Contributors to this Wikipedia-style project, called Tricki.org, include Terence Tao and Ben Green.

For his work on this book, he won the 2011 Euler Book Prize of the Mathematical Association of America.

In 2012, Gowers posted to his blog to call for a boycott of the publishing house Elsevier.

A petition ensued, branded the Cost of Knowledge project, in which researchers commit to stop supporting Elsevier journals.

Commenting on the petition in The Guardian, Alok Jha credited Gowers with starting an Academic Spring.

In 2016, Gowers started Discrete Analysis to demonstrate that a high-quality mathematics journal could be inexpensively produced outside of the traditional academic publishing industry.

In May 2020 it was announced that he would be assuming the title chaire de combinatoire at the College de France beginning in October 2020, though he intends to continue to reside in Cambridge and maintain a part-time affiliation at the university, as well as enjoy the privileges of his life fellowship of Trinity College.

Gowers initially worked on Banach spaces.

He used combinatorial tools in proving several of Stefan Banach's conjectures in the subject, in particular constructing a Banach space with almost no symmetry, serving as a counterexample to several other conjectures.

In May 2020 he was made a professor at the Collège de France, a historic institution dedicated to popularising science.

After asking on his blog whether "massively collaborative mathematics" was possible, he solicited comments on his blog from people who wanted to try to solve mathematical problems collaboratively.

The first problem in what is called the Polymath Project, Polymath1, was to find a new combinatorial proof to the density version of the Hales–Jewett theorem.

After seven weeks, Gowers wrote on his blog that the problem was "probably solved".