# Timothy Gowers

Sir William Timothy Gowers, FRS (/ˈɡərz/; born 20 November 1963) is a British mathematician. He is a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge, where he also holds the Rouse Ball chair, and is a Fellow of Trinity College, Cambridge. In 1998 he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.[3][2][4][5]

Sir Timothy Gowers
Gowers in 2012
Born William Timothy Gowers
20 November 1963 (age 54)[1]
Wiltshire, England, UK
Citizenship British
Alma mater Trinity College, Cambridge
Known for Functional analysis, combinatorics
Awards Fellow of the Royal Society (1999)[1]
Gold Medal, IMO (1981)[2]
Prize of the European Mathematical Society (1996)
Fields Medal (1998)
Knight Bachelor (2012)[1]
De Morgan Medal (2016)
Sylvester Medal (2016)
Website gowers.wordpress.com
www.dpmms.cam.ac.uk/~wtg10
Scientific career
Institutions University of Cambridge
University College London
Thesis Symmetric Structures in Banach Spaces (1990)
Doctoral students David Conlon
Ben Green
Tom Sanders[3]

## Contents

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.

## EducationEdit

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. He completed his PhD, with a dissertation entitled Symmetric Structures in Banach Spaces,[6] at Trinity College, Cambridge in 1990, supervised by Béla Bollobás.[3]

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.[7] 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.[citation needed]

After this, Gowers turned to combinatorics and combinatorial number theory. In 1997 he proved[8] that the Szemerédi regularity lemma necessarily comes with tower-type bounds.

In 1998 he proved[9] the first effective bounds for Szemerédi's theorem, showing that any subset ${\displaystyle A\subset \{1,\dots ,N\}}$  free of k-term arithmetic progressions has cardinality ${\displaystyle O(N(\log \log N)^{-c_{k}})}$  for an appropriate ${\displaystyle c_{k}>0}$ . 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,[10] analogous to the Szemerédi regularity lemma for graphs.

In 2005, he introduced[11] 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[12] to other problems such as the P versus NP problem. He has also developed an interest, in joint work with Mohan Ganesalingam,[13] in automated problem solving.

## HonoursEdit

In 1996 he 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 in 2012 was knighted by the British monarch for services to mathematics.[14][15] He also sits on the selection committee for the Mathematics award, given under the auspices of the Shaw Prize.

## Popularisation workEdit

Gowers has written several works popularising mathematics, including Mathematics: A Very Short Introduction (2002),[16] 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.[17]

## BloggingEdit

After asking on his blog whether "massively collaborative mathematics" was possible,[18] he solicited comments on his blog from people who wanted to try to solve mathematical problems collaboratively.[19] 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 7 weeks, Gowers wrote on his blog that the problem was "probably solved".[20]

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.[21] Contributors to this Wikipedia-style project, called Tricki.org, include Terence Tao and Ben Green.[22]

## Elsevier boycottEdit

In 2012, Gowers posted to his blog to call for a boycott of the publishing house Elsevier.[23][24] 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.[25][26][27]

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.[28]

## Family relations and personal lifeEdit

His father was Patrick Gowers, a composer, and his great-grandfather was Sir Ernest Gowers, a British civil servant who was best known for guides to English usage and who was the son of Sir William Gowers, a neurologist. He has five children[29] and plays jazz piano.[1]

In November 2012 he 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.[30]

## BibliographyEdit

### Selected research articlesEdit

• Gowers, W. T.; Maurey, Bernard (6 May 1992). "The unconditional basic sequence problem". arXiv: [math.FA].
• Gowers, W. T. (2001). "A new proof of Szemerédi's theorem". Geom. Funct. Anal. 11 (3): 465–588. doi:10.1007/s00039-001-0332-9.
• Gowers (2007). "Hypergraph regularity and the multidimensional Szemerédi theorem". arXiv: [math.CO].
• Gowers, W. T. (2007). "Hypergraph regularity and the multidimensional Szemerédi theorem". Ann. of Math. 166 (3): 897–946. doi:10.4007/annals.2007.166.897.
• Gowers, Timothy, ed. (2008). The Princeton Companion to Mathematics. Princeton University Press. ISBN 978-0-691-11880-2.

## ReferencesEdit

1. "GOWERS, Sir (William) Timothy". Who's Who 2013, A & C Black, an imprint of Bloomsbury Publishing plc, 2013; online edn, Oxford University Press.(subscription required)
2. ^ a b
3. ^ a b c d
4. ^
5. ^
6. ^ Gowers, Timothy (1990). Symmetric structures in Banach spaces (PhD thesis). University of Cambridge.
7. ^
8. ^ Gowers, W. Timothy (1997). "A lower bound of tower type for Szemeredi's uniformity lemma". Geometric and Functional Analysis. 7 (2): 322–337. doi:10.1007/PL00001621. MR 1445389.
9. ^ Gowers, W. Timothy (2001). "A new proof of Szemeréi's theorem". Geometric and Functional Analysis. 11 (3): 465–588. doi:10.1007/s00039-001-0332-9. MR 1844079.
10. ^ Gowers, W. Timothy (2007). "Hypergraph regularity and the multidimensional Szemeredi theorem". Annals of Mathematics. 166 (3): 897–946. doi:10.4007/annals.2007.166.897. MR 2373376.
11. ^ Gowers, W.Timothy (2008). "Quasirandom groups". Combinatorics, Probability and Computing. 17 (3): 363–387. arXiv:. doi:10.1017/S0963548307008826. MR 2410393.
12. ^ http://gowers.wordpress.com/2013/10/24/what-i-did-in-my-summer-holidays/
13. ^ Ganesalingam, Mohan; Gowers, W. Timothy (2013). "A fully automatic problem solver with human-style output". arXiv:.
14. ^ "No. 60173". The London Gazette (Supplement). 16 June 2012. p. 1.
15. ^ "Queens Birthday Honors list" (PDF). Archived from the original (PDF) on 6 September 2012. Retrieved 16 June 2012.
16. ^ Gowers, Timothy (2002). Mathematics: A Very Short Introduction. Very Short Introductions. 66. Oxford: Oxford University Press. ISBN 978-0-19-285361-5. MR 2147526.
17. ^ January 2011 Prizes and Awards, American Mathematical Society, retrieved 1 February 2011.
18. ^ Gowers, T.; Nielsen, M. (2009). "Massively collaborative mathematics". Nature. 461 (7266): 879–881. Bibcode:2009Natur.461..879G. doi:10.1038/461879a. PMID 19829354.
19. ^ Gowers, Timothy (27 January 2009). Is massively collaborative mathematics possible?. Gowers's Weblog. Retrieved 30 March 2009.
20. ^ Nielsen, Michael (20 March 2009). "The Polymath project: scope of participation". Retrieved 30 March 2009.
21. ^ Gowers, Timothy (16 April 2009). "Tricki now fully live". Retrieved 16 April 2009.
22. ^ Tao, Terence (16 April 2009). "Tricki now live". What's new. Retrieved 16 April 2009.
23. ^ Whitfield, J. (2012). "Elsevier boycott gathers pace:Rebel academics ponder how to break free of commercial publishers". Nature. doi:10.1038/nature.2012.10010.
24. ^ Brumfiel, G.; Tollefson, J.; Hand, E.; Baker, M.; Cyranoski, D.; Shen, H.; Van Noorden, R.; Nosengo, N.; et al. (2012). "366 days: Nature's 10". Nature. 492 (7429): 335–343. Bibcode:2012Natur.492..335.. doi:10.1038/492335a. PMID 23257862.
25. ^ Grant, Bob (7 February 2012). "Occupy Elsevier?". The Scientist. Retrieved 12 February 2012.
26. ^ Worstall, Tim (28 January 2012). "Elsevier's Publishing Model Might be About to Go Up in Smoke". forbes.com. Retrieved 12 February 2012.
27. ^ Alok Jha (9 April 2012). "Academic spring: how an angry maths blog sparked a scientific revolution". The Guardian.
28. ^ Gowers, Timothy (2015-09-10). "Discrete Analysis — an arXiv overlay journal". Gower's Weblog. Retrieved 2016-03-02.
29. ^ "Status update". Gowers's Weblog. Timothy Gowers. Retrieved 1 December 2010.
30. ^ Mathematics meets real life, by Tim Gowers, 5 November 2012.
31. ^ Gouvêa, Fernando Q. (23 May 2003). "Review of Mathematics: A Very Short Introduction by Timothy Gowers". MAA Reviews, Mathematical Association of America website.