William Timothy Gowers
Encyclopedia
William Timothy Gowers FRS (born 20 November 1963, Wiltshire
) is a British
mathematician
. He is a Royal Society
Research Professor at the Department of Pure Mathematics
and Mathematical Statistics
at Cambridge University
, where he also holds the Rouse Ball chair
, and is a Fellow of Trinity College
. In 1998 he received the Fields Medal
for his research connecting the fields of functional analysis
and combinatorics
.
, and at Eton College
where he was a King's Scholar
. He completed his PhD entitled 'Symmetric Structures in Banach Spaces' at the University of Cambridge
(Trinity College) in 1990 under the supervision of Béla Bollobás
.
. In 1996 he received the Prize of the European Mathematical Society
and in 1998 the Fields Medal
for research on functional analysis
and combinatorics
. He used combinatorial tools in proving several of Stefan Banach
's conjectures on Banach space
s and in 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
. Another work which has proved highly influential is his proof of Szemerédi's theorem
by Fourier-analytic methods. He has also made substantial contributions in combinatorics, particularly to the study of regularity for graphs and hypergraphs. In 1999 he was elected Fellow of the Royal Society
.
In addition to scholarly papers on mathematics, Gowers is also the author of several works popularizing mathematics, including the 2002 book Mathematics: A Very Short Introduction which describes modern research mathematics to the layman. He was consulted about the 2005 film Proof
, starring Gwyneth Paltrow
and Anthony Hopkins
. Recently, he has been the editor for The Princeton Companion to Mathematics
, a voluminous book published in 2008 that introduces and traces the development of various branches and concepts of modern mathematics. For his work on the Princeton Companion, Gowers won the 2011 Euler Book Prize
of the Mathematical Association of America
.
collaboratively
.
The initial proposed problem for this project, now called Polymath1 by the Polymath community, was to find a new combinatorial proof to the density version of the Hales–Jewett theorem
. As the project took form, two main threads of discourse emerged. The first thread, which was carried out in the comments of Gowers's blog, would continue with the original goal of finding a combinatorial proof. The second thread, which was carried out in the comments of Terry Tao's
blog, focused on calculating bounds on density Hales-Jewett numbers and Moser numbers for low dimensions.
After 7 weeks, Gowers announced on his blog that the problem was "probably solved", though work would continue on both Gowers's thread and Tao's thread well into May 2009, some three months after the initial announcement. In total over 40 people contributed to the Polymath1 project. Both threads of the Polymath1 project have been successful, producing at least two new papers to be published under the pseudonym D.H.J Polymath.
The success of the Polymath1 project has spawned additional Polymath projects. To date there are 5 official Polymath Projects, and 2 Mini-Polymath Projects. More information on the Polymath1 project can be found on the project wiki. Jason Dyer's A gentle introduction to the Polymath project provides a good explanation of the work of the project for a non-mathematical audience.
-style project collecting methods of mathematical problem solving conceived in 2008 and launched by Gowers, Olof Sisask and Alex Frolkin in March 2009. Terence Tao
and Ben Green are among those to have contributed articles.
, great-grandson of British civil servant Sir Ernest Gowers
and great-great-grandson of neurologist
Sir William Gowers
. He has five children and plays jazz piano. For ten days of every November, Gowers and his five children all have either only odd or only even number ages.
Wiltshire
Wiltshire is a ceremonial county in South West England. It is landlocked and borders the counties of Dorset, Somerset, Hampshire, Gloucestershire, Oxfordshire and Berkshire. It contains the unitary authority of Swindon and covers...
) is a British
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He is a Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
Research Professor at the Department of Pure Mathematics
Pure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...
and Mathematical Statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
at Cambridge University
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
, where he also holds the Rouse Ball chair
Rouse Ball Professor of Mathematics
The Rouse Ball Professorship of Mathematics is one of the senior chairs in the Mathematics Departments at the University of Cambridge and the University of Oxford. The two positions were founded in 1927 by a bequest from the mathematician W. W. Rouse Ball...
, and is a Fellow of Trinity College
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
. In 1998 he received the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
for his research connecting the fields of functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
and combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
.
Education
His early education was at King's College School, Cambridge as a chorister in the Choir of King's College, CambridgeChoir of King's College, Cambridge
The Choir of King's College, Cambridge is one of today's most accomplished and renowned representatives of the great British choral tradition. It was created by King Henry VI, who founded King's College, Cambridge in 1441, to provide daily singing in his Chapel, which remains the main task of the...
, and at Eton College
Eton College
Eton College, often referred to simply as Eton, is a British independent school for boys aged 13 to 18. It was founded in 1440 by King Henry VI as "The King's College of Our Lady of Eton besides Wyndsor"....
where he was a King's Scholar
King's Scholar
A King's Scholar is a foundation scholar of one of certain public schools...
. He completed his PhD entitled 'Symmetric Structures in Banach Spaces' at the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
(Trinity College) in 1990 under the supervision of Béla Bollobás
Béla Bollobás
Béla Bollobás FRS is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory and percolation. As a student, he took part in the first three International Mathematical Olympiads, winning two gold medals...
.
Career
From 1991 to 1995 he was a member of the Department of Mathematics at University College LondonUniversity College London
University College London is a public research university located in London, United Kingdom and the oldest and largest constituent college of the federal University of London...
. In 1996 he received the Prize of the European Mathematical Society
European Mathematical Society
The European Mathematical Society is a European organization dedicated to the development of mathematics in Europe. Its members are different mathematical societies in Europe, academic institutions and individual mathematicians...
and in 1998 the Fields Medal
Fields Medal
The Fields Medal, officially known as International Medal for Outstanding Discoveries in Mathematics, is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union , a meeting that takes place every four...
for research on functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
and combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
. He used combinatorial tools in proving several of Stefan Banach
Stefan Banach
Stefan Banach was a Polish mathematician who worked in interwar Poland and in Soviet Ukraine. He is generally considered to have been one of the 20th century's most important and influential mathematicians....
's conjectures on Banach space
Banach space
In mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every Cauchy sequence in V has a limit in V In mathematics, Banach spaces is the...
s and in 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
Schauder basis
In mathematics, a Schauder basis or countable basis is similar to the usual basis of a vector space; the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums...
. Another work which has proved highly influential is his proof of Szemerédi's theorem
Szemerédi's theorem
In number theory, Szemerédi's theorem is a result that was formerly the Erdős–Turán conjecture...
by Fourier-analytic methods. He has also made substantial contributions in combinatorics, particularly to the study of regularity for graphs and hypergraphs. In 1999 he was elected Fellow of the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
.
In addition to scholarly papers on mathematics, Gowers is also the author of several works popularizing mathematics, including the 2002 book Mathematics: A Very Short Introduction which describes modern research mathematics to the layman. He was consulted about the 2005 film Proof
Proof (2005 film)
Proof is a 2005 American drama film directed by John Madden and starring Anthony Hopkins, Gwyneth Paltrow, Jake Gyllenhaal, and Hope Davis; it was written by Rebecca Miller, based on David Auburn's Pulitzer Prize-winning play of the same title.-Plot:...
, starring Gwyneth Paltrow
Gwyneth Paltrow
Gwyneth Kate Paltrow is an American actress and singer. She made her acting debut on stage in 1990 and started appearing in films in 1991. After appearing in several films throughout the decade, Paltrow gained early notice for her work in films such as Se7en and Emma...
and Anthony Hopkins
Anthony Hopkins
Sir Philip Anthony Hopkins, KBE , best known as Anthony Hopkins, is a Welsh actor of film, stage and television...
. Recently, he has been the editor for The Princeton Companion to Mathematics
The Princeton Companion to Mathematics
The Princeton Companion to Mathematics is a book, edited by Timothy Gowers with associate editors June Barrow-Green and Imre Leader, and published in 2008 by Princeton University Press . It provides an extensive overview of mathematics, and is noted for the high caliber of the contributors...
, a voluminous book published in 2008 that introduces and traces the development of various branches and concepts of modern mathematics. For his work on the Princeton Companion, Gowers won the 2011 Euler Book Prize
Euler Book Prize
The Euler Book Prize is an award named after Leonhard Euler and given annually at the Joint Mathematics Meetings by the Mathematical Association of America to an outstanding book in mathematics that is likely to improve the public view of the field....
of the Mathematical Association of America
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
.
Polymath Project
In a 2009 post on his blog, Gowers asked the provocative question "is massively collaborative mathematics possible?". This post led to his creation of the Polymath Project, using the comment functionality of his blog to produce mathematicsMathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
collaboratively
Collaboration
Collaboration is working together to achieve a goal. It is a recursive process where two or more people or organizations work together to realize shared goals, — for example, an intriguing endeavor that is creative in nature—by sharing...
.
The initial proposed problem for this project, now called Polymath1 by the Polymath community, was to find a new combinatorial proof to the density version of the Hales–Jewett theorem
Hales–Jewett theorem
In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatorial structure; it is impossible for such objects to be "completely random".An informal geometric statement...
. As the project took form, two main threads of discourse emerged. The first thread, which was carried out in the comments of Gowers's blog, would continue with the original goal of finding a combinatorial proof. The second thread, which was carried out in the comments of Terry Tao's
Terence Tao
Terence Chi-Shen Tao FRS is an Australian mathematician working primarily on harmonic analysis, partial differential equations, combinatorics, analytic number theory and representation theory...
blog, focused on calculating bounds on density Hales-Jewett numbers and Moser numbers for low dimensions.
After 7 weeks, Gowers announced on his blog that the problem was "probably solved", though work would continue on both Gowers's thread and Tao's thread well into May 2009, some three months after the initial announcement. In total over 40 people contributed to the Polymath1 project. Both threads of the Polymath1 project have been successful, producing at least two new papers to be published under the pseudonym D.H.J Polymath.
The success of the Polymath1 project has spawned additional Polymath projects. To date there are 5 official Polymath Projects, and 2 Mini-Polymath Projects. More information on the Polymath1 project can be found on the project wiki. Jason Dyer's A gentle introduction to the Polymath project provides a good explanation of the work of the project for a non-mathematical audience.
Tricki
Tricki.org is a WikipediaWikipedia
Wikipedia is a free, web-based, collaborative, multilingual encyclopedia project supported by the non-profit Wikimedia Foundation. Its 20 million articles have been written collaboratively by volunteers around the world. Almost all of its articles can be edited by anyone with access to the site,...
-style project collecting methods of mathematical problem solving conceived in 2008 and launched by Gowers, Olof Sisask and Alex Frolkin in March 2009. Terence Tao
Terence Tao
Terence Chi-Shen Tao FRS is an Australian mathematician working primarily on harmonic analysis, partial differential equations, combinatorics, analytic number theory and representation theory...
and Ben Green are among those to have contributed articles.
Personal life
He is the son of composer Patrick GowersPatrick Gowers
William Patrick Gowers is an English composer mainly known for his film scores.-Film music:Gowers' works include the following music scores: Comic Act , Forever Green , The Hound of the Baskervilles , The Sign of Four , Whoops Apocalypse , Anna Karenina , Smiley's People , I remember...
, great-grandson of British civil servant Sir Ernest Gowers
Ernest Gowers
Sir Ernest Arthur Gowers GCB GBE Hon. D.Litt Hon. ARIBA was a British civil servant, now best known for work on style guides for writing the English language.-Life:...
and great-great-grandson of neurologist
Neurology
Neurology is a medical specialty dealing with disorders of the nervous system. Specifically, it deals with the diagnosis and treatment of all categories of disease involving the central, peripheral, and autonomic nervous systems, including their coverings, blood vessels, and all effector tissue,...
Sir William Gowers
William Richard Gowers
Sir William Richard Gowers was a British neurologist.The Gowers' tract is named after him....
. He has five children and plays jazz piano. For ten days of every November, Gowers and his five children all have either only odd or only even number ages.
External links
- Timothy Gowers's blog
- Timothy Gowers's web page
- 1998 Fields Medalist William Timothy Gowers from the American Mathematical SocietyAmerican Mathematical SocietyThe American Mathematical Society is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, which it does with various publications and conferences as well as annual monetary awards and prizes to mathematicians.The society is one of the...
- Video lectures by Timothy Gowers on Computational Complexity and Quantum Computation
- Timothy Gowers – Faces of Mathematics
- BBC News (1998): British academics Tim Gowers and Richard Borcherds win top maths awards
- "Multiplying and dividing by whole numbers: Why it is more difficult than you might think", lecture by Timothy Gowers at Gresham College, 22 May 2007 (available for download as video and audio files)
- Listen to Timothy Gowers on The Forum, BBC World Service Radio