Timothy Gowers

Last updated

Sir

Timothy Gowers

FRS
Timothy Gowers Washington 2009.jpg
Gowers in 2009
Born
William Timothy Gowers

(1963-11-20) 20 November 1963 (age 60) [1]
Education King's College School, Cambridge
Eton College
Alma mater University of Cambridge (BA, MA, PhD)
Known for
Awards
Scientific career
Institutions University of Cambridge
University College London
Thesis Symmetric Structures in Banach Spaces  (1990)
Doctoral advisor Béla Bollobás [3]
Doctoral students David Conlon
Ben Green
Tom Sanders [3]
Website gowers.wordpress.com
www.dpmms.cam.ac.uk/~wtg10

Sir William Timothy Gowers, FRS ( /ˈɡ.ərz/ ; born 20 November 1963) [1] 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 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics. [3] [4] [5]

Contents

Education

Gowers attended King's College School, Cambridge, as a choirboy in the King's College choir, and then Eton College [1] as a King's Scholar, where he was taught mathematics by Norman Routledge. [6] In 1981, Gowers won a gold medal at the International Mathematical Olympiad with a perfect score. [7] He completed his PhD, with a dissertation on Symmetric Structures in Banach Spaces [8] at Trinity College, Cambridge in 1990, supervised by Béla Bollobás. [8] [3]

Career and research

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 [9] that he would be assuming the title chaire de combinatoire at the College de France beginning in October 2020, though he intends [10] 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. [11] 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. [12]

After this, Gowers turned to combinatorics and combinatorial number theory. In 1997 he proved [13] that the Szemerédi regularity lemma necessarily comes with tower-type bounds.

In 1998, Gowers proved [14] the first effective bounds for Szemerédi's theorem, showing that any subset free of k-term arithmetic progressions has cardinality for an appropriate . 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, [15] analogous to the Szemerédi regularity lemma for graphs.

In 2005, he introduced [16] 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 [17] to other problems such as the P versus NP problem. He has also developed an interest, in joint work with Mohan Ganesalingam, [18] in automated problem solving.

Gowers has an Erdős number of three. [19]

Popularisation work

Gowers has written several works popularising mathematics, including Mathematics: A Very Short Introduction (2002), [20] 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. [21] For his work on this book, he won the 2011 Euler Book Prize of the Mathematical Association of America. [22] In May 2020 he was made a professor at the Collège de France, a historic institution dedicated to popularising science. [23]

Blogging

After asking on his blog whether "massively collaborative mathematics" was possible, [24] he solicited comments on his blog from people who wanted to try to solve mathematical problems collaboratively. [25] 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". [26]

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. [27] Contributors to this Wikipedia-style project, called Tricki.org, include Terence Tao and Ben Green. [28]

Elsevier boycott

In 2012, Gowers posted to his blog to call for a boycott of the publishing house Elsevier. [29] [2] 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. [30] [31]

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. [32]

Awards and honours

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. [33] In 1996, Gowers received the Prize of the European Mathematical Society, and in 1998 the Fields Medal for research on functional analysis and combinatorics. [34] [35] In 1999 he became a Fellow of the Royal Society and a member of the American Philosophical Society in 2010. [36] In 2012 he was knighted by the British monarch for services to mathematics. [37] [38] 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. [2]

Personal life

Timothy Gowers was born on November 20, 1963, in Marlborough, Wiltshire, England. [33]

Gowers's father was Patrick Gowers, a composer; his great-grandfather was Sir Ernest Gowers, a British civil servant who was best known for guides to English usage; and his great-great-grandfather was Sir William Gowers, a neurologist. He has two siblings, the writer Rebecca Gowers, and the violinist Katharine Gowers. He has five children [39] and plays jazz piano. [1]

In November 2012, Gowers opted to undergo catheter ablation to treat a sporadic atrial fibrillation, after performing a mathematical risk–benefit analysis to decide whether to have the treatment. [40]

In 1988, Gowers married Emily Thomas, a classicist and Cambridge academic: they divorced in 2007. Together they had three children. In 2008, he married for a second time, to Julie Barrau, a University Lecturer in British Medieval History at the University of Cambridge. They have two children together. [41]

Publications

Selected research articles

Related Research Articles

<span class="mw-page-title-main">Extremal graph theory</span>

Extremal graph theory is a branch of combinatorics, itself an area of mathematics, that lies at the intersection of extremal combinatorics and graph theory. In essence, extremal graph theory studies how global properties of a graph influence local substructure. Results in extremal graph theory deal with quantitative connections between various graph properties, both global and local, and problems in extremal graph theory can often be formulated as optimization problems: how big or small a parameter of a graph can be, given some constraints that the graph has to satisfy? A graph that is an optimal solution to such an optimization problem is called an extremal graph, and extremal graphs are important objects of study in extremal graph theory.

In arithmetic combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured that every set of integers A with positive natural density contains a k-term arithmetic progression for every k. Endre Szemerédi proved the conjecture in 1975.

<span class="mw-page-title-main">Endre Szemerédi</span> Hungarian-American mathematician

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<span class="mw-page-title-main">Terence Tao</span> Australian–American mathematician (born 1975)

Terence Chi-Shen Tao is an Australian mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. Tao was awarded Fields Medal of 06. His research includes topics in harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, probability theory, compressed sensing and analytic number theory.

<span class="mw-page-title-main">Ben Green (mathematician)</span> British mathematician

Ben Joseph Green FRS is a British mathematician, specialising in combinatorics and number theory. He is the Waynflete Professor of Pure Mathematics at the University of Oxford.

<span class="mw-page-title-main">Szemerédi regularity lemma</span>

Szemerédi's regularity lemma is one of the most powerful tools in extremal graph theory, particularly in the study of large dense graphs. It states that the vertices of every large enough graph can be partitioned into a bounded number of parts so that the edges between different parts behave almost randomly.

Erdős' conjecture on arithmetic progressions, often referred to as the Erdős–Turán conjecture, is a conjecture in arithmetic combinatorics. It states that if the sum of the reciprocals of the members of a set A of positive integers diverges, then A contains arbitrarily long arithmetic progressions.

In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms. The proof is an extension of Szemerédi's theorem. The problem can be traced back to investigations of Lagrange and Waring from around 1770.

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In arithmetic combinatorics, the Erdős–Szemerédi theorem states that for every finite set of integers, at least one of , the set of pairwise sums or , the set of pairwise products form a significantly larger set. More precisely, the Erdős–Szemerédi theorem states that there exist positive constants c and such that for any non-empty set

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In mathematics, in the field of additive combinatorics, a Gowers norm or uniformity norm is a class of norms on functions on a finite group or group-like object which quantify the amount of structure present, or conversely, the amount of randomness. They are used in the study of arithmetic progressions in the group. They are named after Timothy Gowers, who introduced it in his work on Szemerédi's theorem.

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In graph theory, the graph removal lemma states that when a graph contains few copies of a given subgraph, then all of the copies can be eliminated by removing a small number of edges. The special case in which the subgraph is a triangle is known as the triangle removal lemma.

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Roth's theorem on arithmetic progressions is a result in additive combinatorics concerning the existence of arithmetic progressions in subsets of the natural numbers. It was first proven by Klaus Roth in 1953. Roth's theorem is a special case of Szemerédi's theorem for the case .

References

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  3. 1 2 3 4 Timothy Gowers at the Mathematics Genealogy Project OOjs UI icon edit-ltr-progressive.svg
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