Timothy Gowers

Timothy Gowers
Born	William Timothy Gowers 20 11, 1963
Birthplace	Marlborough, Wiltshire, England, United Kingdom
Nationality	British
Occupation	Mathematician
Title	Combinatorics Chair (Collège de France), Research Professor (University of Cambridge)
Employer	Collège de France, University of Cambridge
Known for	Fields Medal (1998), contributions to functional analysis and combinatorics, Polymath Project, open access advocacy
Education	PhD, University of Cambridge
Awards	Fields Medal (1998), Knight Bachelor (2012)

Sir William Timothy Gowers (born 20 November 1963) is a British mathematician who holds the Combinatorics chair at the Collège de France and serves as a Research Professor at the University of Cambridge, where he is also a Fellow of Trinity College. He received the Fields Medal in 1998 for research that forged deep connections between functional analysis and combinatorics, two fields that had previously been considered largely separate. Beyond his contributions to pure mathematics, Gowers has become one of the most publicly visible mathematicians of his generation through his advocacy for open-access academic publishing, his initiation of the Polymath Project — an experiment in large-scale collaborative mathematics — and his writings on mathematical reasoning aimed at both specialists and general audiences. In 2012, he was appointed Knight Bachelor for services to mathematics. More recently, Gowers has been involved in efforts at the intersection of mathematics and artificial intelligence, including serving on the advisory committee for the Artificial Intelligence Mathematical Olympiad Prize.

Early Life

William Timothy Gowers was born on 20 November 1963 in Marlborough, Wiltshire, England. He was educated at King's College School, Cambridge, and subsequently at Eton College, one of England's most prominent independent schools. Details of his family background and childhood have not been extensively documented in public sources, though his surname carries mathematical resonance — his great-grandfather was Sir William Gowers, the distinguished neurologist.

From an early age, Gowers showed aptitude in mathematics. He went on to study at the University of Cambridge, where he would remain for the bulk of his academic career.

Education

Gowers attended the University of Cambridge, where he earned a Bachelor of Arts degree, followed by a Master of Arts. He continued at Cambridge for his doctoral studies, completing his PhD in 1990 with a thesis titled "Symmetric Structures in Banach Spaces." His doctoral advisor was the Hungarian-British mathematician Béla Bollobás, himself a prominent figure in combinatorics and graph theory. The thesis addressed structural questions in Banach space theory, a branch of functional analysis concerned with infinite-dimensional vector spaces equipped with a norm. This early work laid the groundwork for the research programme that would eventually lead to Gowers's most celebrated mathematical achievements.

Career

Early Academic Career and Banach Space Theory

After completing his doctorate, Gowers embarked on an academic career at the University of Cambridge. His early research focused on the geometry of Banach spaces, a subject with roots in the work of Stefan Banach in the early twentieth century. One of the central questions in the field concerned the structure of infinite-dimensional Banach spaces — specifically, whether every such space must contain a subspace with certain desirable properties, such as being isomorphic to a classical sequence space.

Gowers made a series of breakthroughs that resolved longstanding open problems. He constructed an infinite-dimensional Banach space that does not contain any subspace isomorphic to any of the classical sequence spaces, settling a problem that had been open for decades. He also solved the so-called "unconditional basic sequence problem" by constructing a Banach space in which no subspace has an unconditional basis. These results fundamentally altered the landscape of Banach space theory and demonstrated that the structure of infinite-dimensional spaces could be far more exotic than previously imagined.

Fields Medal and Combinatorics

In 1998, Gowers was awarded the Fields Medal at the International Congress of Mathematicians in Berlin. The citation recognised his work connecting functional analysis and combinatorics. A key aspect of the research that led to the medal was Gowers's innovative use of combinatorial methods to solve problems in analysis, and vice versa. In particular, his work drew on and advanced Szemerédi's regularity lemma and related combinatorial tools, bringing them to bear on questions that had seemed purely analytical in nature.

One of the landmark results associated with the Fields Medal was Gowers's new proof of Szemerédi's theorem, which states that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions. Gowers's proof introduced what are now known as "Gowers norms" (or "Gowers uniformity norms"), a hierarchy of norms that measure the pseudorandomness of functions on groups. These norms provided a quantitative framework for understanding the structure of sets and functions, and they have since become fundamental tools in additive combinatorics and ergodic theory. The proof also yielded the best-known bounds for Szemerédi's theorem at the time, a significant quantitative improvement over earlier arguments.

Rouse Ball Professorship and Continued Research

Gowers served as Rouse Ball Professor of Mathematics at the University of Cambridge, one of the most distinguished chairs in the department. During this period, he continued to develop the research programme connecting combinatorics and analysis. He supervised a number of doctoral students who went on to make significant contributions of their own, including Ben Green and David Conlon. Ben Green, together with Terence Tao, later proved the celebrated Green–Tao theorem on arithmetic progressions in the primes, work that was influenced by and built upon Gowers's methods.

Gowers also contributed to the development of higher-order Fourier analysis, a generalisation of classical Fourier analysis that is adapted to the study of patterns in sets of integers. This area has grown substantially since the early 2000s and has connections to number theory, ergodic theory, and theoretical computer science.

In November 2019, Quanta Magazine reported on work by Sarah Peluse, building on the framework developed by Gowers and others, which established new results about "polynomial progressions" — generalisations of arithmetic progressions in which the common differences follow polynomial patterns.

In December 2023, Quanta Magazine reported that a team of four mathematicians, including two Fields medalists, proved a conjecture described as a "holy grail of additive combinatorics," establishing a critical link between addition and sets — work firmly within the tradition pioneered by Gowers.

Collège de France

Gowers was appointed to the Combinatorics chair at the Collège de France in Paris, one of the most prestigious academic positions in the French academic system. At the Collège de France, professors are expected to deliver annual lecture series on original research topics, and the appointment reflected the international standing of Gowers's contributions to combinatorics and related fields. He maintained his affiliation with the University of Cambridge as a Research Professor and Fellow of Trinity College.

The Polymath Project

In January 2009, Gowers published a blog post titled "Is massively collaborative mathematics possible?" in which he proposed an experiment: could a large number of mathematicians, working together openly online, solve a significant mathematical problem more efficiently than individuals or small groups working in the traditional manner? The idea attracted immediate attention from the mathematical community and from science commentators.

The first Polymath project (Polymath1) tackled the problem of finding a new proof of the density Hales–Jewett theorem, a result in combinatorics. The project succeeded: over a period of weeks, dozens of contributors produced a new combinatorial proof that was subsequently published under the collective pseudonym "D.H.J. Polymath." Gowers provided a status update on the project's progress in November 2010.

The Polymath Project represented a new model for mathematical research and attracted significant interest from those studying open science and collaborative knowledge production. It demonstrated that open, online collaboration could produce publishable mathematics of the highest quality. Several further Polymath projects followed, addressing a range of problems in number theory, combinatorics, and other areas.

Tricki

In April 2009, Gowers and collaborators launched the "Tricki" (short for "Tricks Wiki"), an online resource intended to catalogue mathematical problem-solving techniques and strategies. The goal was to create a repository of mathematical tricks, indexed and searchable, that would be useful to researchers and students alike. The project was announced in coordination with Terence Tao, another Fields Medalist. Although the Tricki did not achieve the level of sustained community contribution that its founders had hoped for, it represented an early and influential experiment in open mathematical knowledge-sharing.

Open Access Advocacy and the Elsevier Boycott

Gowers has been a prominent advocate for open-access publishing in mathematics and the sciences. In January 2012, he published a blog post explaining why he would no longer submit papers to journals published by Elsevier, one of the largest academic publishers. He cited concerns about high subscription prices, the bundling of journals, and what he described as practices that were detrimental to the academic community.

The blog post ignited what became known as the "Cost of Knowledge" campaign. Thousands of academics signed an online petition pledging to boycott Elsevier journals in various capacities — declining to publish in, referee for, or serve on the editorial boards of Elsevier journals. The movement attracted widespread media attention and was described by The Scientist as part of an "Occupy Elsevier" phenomenon.

In September 2015, Gowers announced the launch of Discrete Analysis, a new mathematics journal that operates as an "arXiv overlay journal." Rather than hosting papers on its own servers, the journal links to papers deposited on the arXiv preprint server, with the editorial board providing peer review and curation. The journal charges no fees to authors or readers. In a 2016 interview with the London School of Economics Impact Blog, Gowers stated that "academics can publish journals of the highest quality without a commercial entity," articulating his vision for a more equitable academic publishing system.

Mathematics and Artificial Intelligence

Gowers has expressed interest in the relationship between mathematics and computers, particularly the prospects for automated mathematical reasoning. In August 2020, Quanta Magazine published an article exploring how close computers were to automating mathematical reasoning, a topic on which Gowers had been an engaged commentator.

In early 2023, Prospect Magazine reported that Gowers had floated an idea on his blog concerning the capabilities and implications of modern AI systems for mathematics, continuing his longstanding engagement with questions about the nature of mathematical thought and its potential mechanisation.

In February 2024, it was announced that Gowers and fellow Fields Medalist Terence Tao had been appointed to the advisory committee for the $10 million Artificial Intelligence Mathematical Olympiad (AIMO) Prize, an initiative aimed at stimulating the development of AI systems capable of solving competition-level mathematics problems.

Public Engagement and COVID-19

In 2021, the New Statesman profiled Gowers under the headline "The man who changed Dominic Cummings's mind on Covid-19." The article described how Gowers, drawing on mathematical modelling and analysis, had influenced the thinking of Dominic Cummings, then chief adviser to UK Prime Minister Boris Johnson, regarding the severity of the COVID-19 pandemic in its early stages. In the article, Gowers reflected on the relationship between mathematical thinking and public policy, noting, "When you see a flashy new building that gets built, you think about the architect. But you don't think quite so much" about the underlying mathematical and scientific reasoning that shapes decisions.

Gowers had earlier written about the intersection of mathematics and real-life problems on his blog, addressing how mathematical thinking could inform everyday and policy decisions.

Lectures and Public Talks

Gowers has delivered public lectures on mathematics at a number of institutions. He gave a lecture at Gresham College in London, one of the oldest academic institutions in England, as part of their public lecture series. The University of Cambridge has hosted collections of his lectures and talks.

In February 2025, Central Michigan University featured the Fleming Lecture Series, which has invited world-renowned mathematicians to campus, continuing a legacy of mathematical excellence in public engagement.

Personal Life

Gowers resides in England and has maintained a public-facing presence through his blog, "Gowers's Weblog," where he writes about mathematics, academic publishing, education, and related topics. His blog posts have been widely cited in academic and journalistic contexts. He has written about his personal mathematical experiences, including a post titled "What I did in my summer holidays," which discussed mathematical work undertaken during a holiday period.

Gowers was knighted in the 2012 Birthday Honours for services to mathematics. He was included in the Who's Who directory.

Recognition

Gowers's most prominent honour is the Fields Medal, awarded in 1998 for his work connecting functional analysis and combinatorics. The Fields Medal is often described as the highest honour a mathematician under the age of 40 can receive, and Gowers's award was noted for the breadth and originality of the work it recognised.

In 2012, Gowers was appointed Knight Bachelor in the Queen's Birthday Honours list for his services to mathematics.

Gowers received the Prize of the European Mathematical Society, as documented in the newsletter of the European Mathematical Society.

He was a co-recipient of the 2011 Levi L. Conant Prize from the American Mathematical Society, which recognises the best expository paper published in either the Notices of the AMS or the Bulletin of the AMS.

His appointment to the Combinatorics chair at the Collège de France represented further international recognition of his standing in the mathematical community.

Legacy

Timothy Gowers's contributions to mathematics span both the resolution of major open problems and the development of new conceptual frameworks. His work on Banach spaces resolved questions that had been open for decades, while his introduction of Gowers norms and his new proof of Szemerédi's theorem established foundational tools in additive combinatorics that continue to shape the field. The influence of these tools is evident in subsequent breakthroughs by his doctoral students and others, including the Green–Tao theorem on primes in arithmetic progression.

Beyond technical mathematics, Gowers has had a substantial impact on the culture and infrastructure of mathematical research. The Polymath Project demonstrated that open, massively collaborative research could produce significant mathematical results and inspired similar experiments in other scientific disciplines. His advocacy for open-access publishing, crystallised in the Elsevier boycott and the founding of Discrete Analysis, contributed to a broader movement that has reshaped academic publishing norms across the sciences.

Gowers's engagement with questions about artificial intelligence and automated reasoning positions him as one of the mathematicians most actively involved in thinking about the future relationship between human mathematical creativity and machine computation. His public lectures, blog writing, and media appearances have made him one of the most visible mathematicians communicating the nature of mathematical thought to audiences outside the discipline.

As a supervisor, Gowers has trained a generation of combinatorialists and analysts, including Ben Green, David Conlon, and Tom Sanders, each of whom has gone on to make substantial contributions to mathematics.