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. He was elected to the Rouse Ball Professorship at Cambridge in 1998. During 2000–2 he was visiting professor at
Princeton University. In May 2020 it was announced that he would be taking up the
Chaire de Combinatoire at the
College de France beginning in October 2020, though he continues 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. 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 1997 he proved that the
Szemerédi regularity lemma necessarily comes with tower-type bounds. In 1998, Gowers proved the first effective bounds for
Szemerédi's theorem, showing that any subset A \subset \{1,\dots, N\} free of
k-term arithmetic progressions has cardinality O(N (\log \log N)^{-c_k}) 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. 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.
Popularisation work Gowers has written several works popularising mathematics, including
Mathematics: A Very Short Introduction (2002), which describes modern mathematical research for the general reader. 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. For his work on this book, he won the 2011
Euler Book Prize of the
Mathematical Association of America. In May 2020 he was made a professor at the Collège de France, a historic institution dedicated to popularising science.
Blogging 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". 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.
Elsevier boycott 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.
Awards and honours In 1994, Gowers was an invited speaker at the
International Congress of Mathematicians in
Zurich where he discussed the theory of infinite-dimensional Banach spaces. In 1996, Gowers received the Prize of the
European Mathematical Society, and in 1998 the
Fields Medal for research on
functional analysis and
combinatorics. In 1999 he became a Fellow of the
Royal Society and a member of the
American Philosophical Society in 2010. In 2012 he was knighted by the British monarch for services to mathematics. He also sits on the selection committee for the Mathematics award, given under the auspices of the
Shaw Prize. He was listed in
Nature's 10 people who mattered in 2012. ==Personal life==