# Timothy Gowers

Sir Timothy Gowers

Gowers in 2012
Born
William Timothy Gowers

20 November 1963 (age 56)[1]
Wiltshire, England, UK
CitizenshipBritish
EducationKing's College School, Cambridge
Eton College
Alma materUniversity of Cambridge (BA, PhD)
Known forFunctional analysis, combinatorics
Awards
Scientific career
InstitutionsUniversity of Cambridge
University College London
ThesisSymmetric Structures in Banach Spaces (1990)
Doctoral studentsDavid Conlon
Ben Green
Tom Sanders[3]
InfluencesNorman Routledge
Websitegowers.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 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][4][5]

## 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] He completed his PhD, with a dissertation on Symmetric Structures in Banach Spaces[7] at Trinity College, Cambridge in 1990, supervised by Béla Bollobás.[7][3] In 1981, Gowers won a gold medal at the International Mathematical Olympiad with a perfect score.[8]

## 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 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 ${\displaystyle A\subset \{1,\dots ,N\}}$ 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,[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, an 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 1996, Gowers received the Prize of the European Mathematical Society, and in 1998 the Fields Medal for research on functional analysis and combinatorics.[33][34] In 1999 he became a Fellow of the Royal Society and in 2012 was knighted by the British monarch for services to mathematics.[35][36] 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

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[37] 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.[38]

In 1988, Gowers married Emily Thomas, a historian and Cambridge academic: they divorced in 2007. Together they had three children. In 2008, he married for a second time, to Julie Barrau. They have two children together.[39]

## Publications

### Selected research articles

• Gowers, W. T.; Maurey, Bernard (6 May 1992). "The unconditional basic sequence problem". arXiv:math/9205204.
• Gowers, W. T. (2001). "A new proof of Szemerédi's theorem". Geom. Funct. Anal. 11 (3): 465–588. CiteSeerX 10.1.1.145.2961. doi:10.1007/s00039-001-0332-9.
• Gowers, W. T. (2007). "Hypergraph regularity and the multidimensional Szemerédi theorem". Ann. of Math. 166 (3): 897–946. arXiv:0710.3032. Bibcode:2007arXiv0710.3032G. 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.

## References

1. Anon (2013). "Gowers, Sir (William) Timothy". Who's Who (online Oxford University Press ed.). A & C Black, an imprint of Bloomsbury Publishing plc. doi:10.1093/ww/9780199540884.013.U17733. (subscription or UK public library membership required) (subscription required)
2. ^ a b c 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.
3. ^ a b c d
4. ^
5. ^
6. ^ Dalyell, Tam (29 May 2013). "Norman Arthur Routledge: Inspirational teacher and mathematician". The Independent. Retrieved 15 April 2020.
7. ^ a b Gowers, William Timothy (1990). Symmetric structures in Banach spaces. cam.ac.uk (PhD thesis). University of Cambridge. doi:10.17863/CAM.16243. OCLC 556577304. EThOS uk.bl.ethos.333263.
8. ^ Mohammed Aassila - Olympiades Internationales de Mathématiques. Ed ellipses, Paris 2003 p. 156
9. ^
10. ^
11. ^
12. ^ Gowers, William Timothy; Maurey, Bernard (1993). "The unconditional basic sequence problem". Journal of the American Mathematical Society. 6 (4): 851–874. arXiv:math/9205204. doi:10.1090/S0894-0347-1993-1201238-0.
13. ^ 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.
14. ^ Gowers, W. Timothy (2001). "A new proof of Szemeréi's theorem". Geometric and Functional Analysis. 11 (3): 465–588. CiteSeerX 10.1.1.145.2961. doi:10.1007/s00039-001-0332-9. MR 1844079.
15. ^ Gowers, W. Timothy (2007). "Hypergraph regularity and the multidimensional Szemeredi theorem". Annals of Mathematics. 166 (3): 897–946. arXiv:0710.3032. doi:10.4007/annals.2007.166.897. MR 2373376.
16. ^ Gowers, W.Timothy (2008). "Quasirandom groups". Combinatorics, Probability and Computing. 17 (3): 363–387. arXiv:0710.3877. doi:10.1017/S0963548307008826. MR 2410393.
17. ^ "What I did in my summer holidays". 24 October 2013.
18. ^ Ganesalingam, Mohan; Gowers, W. Timothy (2013). "A fully automatic problem solver with human-style output". arXiv:1309.4501 [cs.AI].
19. ^ "Mathematical Reviews: Collaboration Distance". mathscinet.ams.org. Retrieved 22 March 2018.
20. ^ Gowers, Timothy (2002). Mathematics: A Very Short Introduction. Very Short Introductions. 66. Oxford: Oxford University Press. ISBN 978-0-19-285361-5. MR 2147526.
21. ^ Roberts, David P. (2009). "Review: The Princeton Companion to Mathematics". Mathematical Association of America. Retrieved 1 July 2020.
22. ^ January 2011 Prizes and Awards, American Mathematical Society, retrieved 1 February 2011.
23. ^
24. ^ Gowers, T.; Nielsen, M. (2009). "Massively collaborative mathematics". Nature. 461 (7266): 879–881. Bibcode:2009Natur.461..879G. doi:10.1038/461879a. PMID 19829354.
25. ^ Gowers, Timothy (27 January 2009). Is massively collaborative mathematics possible?. Gowers's Weblog. Retrieved 30 March 2009.
26. ^ Nielsen, Michael (20 March 2009). "The Polymath project: scope of participation". Retrieved 30 March 2009.
27. ^ Gowers, Timothy (16 April 2009). "Tricki now fully live". Retrieved 16 April 2009.
28. ^ Tao, Terence (16 April 2009). "Tricki now live". What's new. Retrieved 16 April 2009.
29. ^ Whitfield, J. (2012). "Elsevier boycott gathers pace:Rebel academics ponder how to break free of commercial publishers". Nature. doi:10.1038/nature.2012.10010.
30. ^ Grant, Bob (7 February 2012). "Occupy Elsevier?". The Scientist. Retrieved 12 February 2012.
31. ^ Jha, Alok (9 April 2012). "Academic spring: how an angry maths blog sparked a scientific revolution". The Guardian.
32. ^ Gowers, Timothy (10 September 2015). "Discrete Analysis — an arXiv overlay journal". Gower's Weblog. Retrieved 2 March 2016.
33. ^ Lepowsky, James; Lindenstrauss, Joram; Manin, Yuri I.; Milnor, John (January 1999). "The Mathematical Work of the 1998 Fields Medalists" (PDF). Notices of the AMS. 46 (1): 17–26.
34. ^ Gowers, W. T. (1998). "Fourier analysis and Szemerédi's theorem". Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. I. pp. 617–629.
35. ^ "No. 60173". The London Gazette (Supplement). 16 June 2012. p. 1.
36. ^ "Queens Birthday Honors list" (PDF). Archived from the original (PDF) on 6 September 2012. Retrieved 16 June 2012.
37. ^ "Status update". Gowers's Weblog. Timothy Gowers. 30 November 2010. Retrieved 1 December 2010.
38. ^ Mathematics meets real life, by Tim Gowers, 5 November 2012.
39. ^
40. ^ Gouvêa, Fernando Q. (23 May 2003). "Review of Mathematics: A Very Short Introduction by Timothy Gowers". MAA Reviews, Mathematical Association of America website.