Ben Green (mathematician)
Encyclopedia
Ben Joseph Green FRS
is a British
mathematician, specializing in combinatorics
and number theory
. He is the Herchel Smith Professor of Pure Mathematics at the University of Cambridge
.
, England
. He studied at local schools of Bristol, Bishop Road Primary School and Fairfield Grammar School
, competing in the International Mathematical Olympiad
in 1994 and 1995. He entered Trinity College
, University of Cambridge
in 1995 and completed his B.A.
in mathematics in 1998. He earned his doctorate under English mathematician Timothy Gowers in 2003, with a thesis entitled Topics in arithmetic combinatorics. He was a research Fellow at Trinity College, Cambridge between 2001 and 2005, before becoming a Professor of Mathematics at the University of Bristol
from January 2005 to September 2006. In September 2006 he returned to Cambridge as the first Herchel Smith Professor of Pure Mathematics. He was also a Research Fellow of the Clay Mathematics Institute
and held various positions at institutes such as Princeton University
, University of British Columbia
, and Massachusetts Institute of Technology
.
and number theory
. These include improving the estimate by Jean Bourgain
of the size of arithmetic progression
s in sumset
s, as well as a proof of the Cameron–Erdős conjecture on sum-free sets of natural number
s.
His work in demonstrating that every set of primes of positive relative upper density
contains an arithmetic progression of length three then led to his breakthrough 2004 work with mathematician Terence Tao
now known as the Green–Tao theorem. This theorem showed that for all n there exist infinitely many arithmetic progressions of length n in the prime number
s.
in 2004 and the Salem Prize
in 2005 for his contributions to combinatorial number theory related to progressions of primes.
In 2007 he was awarded the SASTRA Ramanujan Prize
.
In 2008 he was among the ten recipients of the prestigious EMS
prize awarded every four years only to highly talented young mathematicians who work in Europe.
In 2010 he was elected a Fellow of the Royal Society
, who say "Ben Green is a rising star, and universally acknowledged as one of the best young mathematicians in the world."
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, specializing in 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 ,...
and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. He is the Herchel Smith Professor of Pure Mathematics 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...
.
Early years
Ben Green was born on 27 February 1977 in BristolBristol
Bristol is a city, unitary authority area and ceremonial county in South West England, with an estimated population of 433,100 for the unitary authority in 2009, and a surrounding Larger Urban Zone with an estimated 1,070,000 residents in 2007...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
. He studied at local schools of Bristol, Bishop Road Primary School and Fairfield Grammar School
Fairfield Grammar School
Fairfield Grammar School was a secondary school in Bristol, England, founded in 1898 as Fairfield Secondary and Higher Grade School. It became a grammar school in 1945 and closed in 2000, to be replaced by a new comprehensive, Fairfield High School, at first on the same site, but now located in...
, competing in the International Mathematical Olympiad
International Mathematical Olympiad
The International Mathematical Olympiad is an annual six-problem, 42-point mathematical olympiad for pre-collegiate students and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980...
in 1994 and 1995. He entered 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...
, 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...
in 1995 and completed his B.A.
Bachelor of Arts
A Bachelor of Arts , from the Latin artium baccalaureus, is a bachelor's degree awarded for an undergraduate course or program in either the liberal arts, the sciences, or both...
in mathematics in 1998. He earned his doctorate under English mathematician Timothy Gowers in 2003, with a thesis entitled Topics in arithmetic combinatorics. He was a research Fellow at Trinity College, Cambridge between 2001 and 2005, before becoming a Professor of Mathematics at the University of Bristol
University of Bristol
The University of Bristol is a public research university located in Bristol, United Kingdom. One of the so-called "red brick" universities, it received its Royal Charter in 1909, although its predecessor institution, University College, Bristol, had been in existence since 1876.The University is...
from January 2005 to September 2006. In September 2006 he returned to Cambridge as the first Herchel Smith Professor of Pure Mathematics. He was also a Research Fellow of the Clay Mathematics Institute
Clay Mathematics Institute
The Clay Mathematics Institute is a private, non-profit foundation, based in Cambridge, Massachusetts. The Institute is dedicated to increasing and disseminating mathematical knowledge. It gives out various awards and sponsorships to promising mathematicians. The institute was founded in 1998...
and held various positions at institutes such as Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....
, University of British Columbia
University of British Columbia
The University of British Columbia is a public research university. UBC’s two main campuses are situated in Vancouver and in Kelowna in the Okanagan Valley...
, and Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...
.
Mathematics
Green has published several important results in both combinatoricsCombinatorics
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 ,...
and number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. These include improving the estimate by Jean Bourgain
Jean Bourgain
Jean Bourgain is a Belgian mathematician. He has been a faculty member at the University of Illinois, Urbana-Champaign and, from 1985 until 1995, professor at Institut des Hautes Études Scientifiques at Bures-sur-Yvette in France, and since 1994 at the Institute for Advanced Study in Princeton,...
of the size of arithmetic progression
Arithmetic progression
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant...
s in sumset
Sumset
In additive combinatorics, the sumset of two subsets A and B of an abelian group G is defined to be the set of all sums of an element from A with an element from B...
s, as well as a proof of the Cameron–Erdős conjecture on sum-free sets of natural number
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
s.
His work in demonstrating that every set of primes of positive relative upper density
Natural density
In number theory, asymptotic density is one of the possibilities to measure how large a subset of the set of natural numbers is....
contains an arithmetic progression of length three then led to his breakthrough 2004 work with mathematician 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...
now known as the Green–Tao theorem. This theorem showed that for all n there exist infinitely many arithmetic progressions of length n in the prime number
Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number. For example 5 is prime, as only 1 and 5 divide it, whereas 6 is composite, since it has the divisors 2...
s.
Awards and honors
Green received the Clay Research AwardClay Research Award
The Clay Research Award is given annually by the Clay Mathematics Institute to mathematicians to recognize their achievement in mathematical research...
in 2004 and the Salem Prize
Salem Prize
The Salem Prize, founded by the widow of Raphael Salem, is awarded every year to a young mathematician judged to have done outstanding work in Salem's field of interest, primarily the theory of Fourier series.-Past winners:...
in 2005 for his contributions to combinatorial number theory related to progressions of primes.
In 2007 he was awarded the SASTRA Ramanujan Prize
SASTRA Ramanujan Prize
The SASTRA Ramanujan Prize, founded by Shanmugha Arts, Science, Technology & Research Academy University in Kumbakonam, India, Srinivasa Ramanujan's hometown, is awarded every year to a young mathematician judged to have done outstanding work in Ramanujan's fields of interest...
.
In 2008 he was among the ten recipients of the prestigious EMS
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...
prize awarded every four years only to highly talented young mathematicians who work in Europe.
In 2010 he was elected a 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"...
, who say "Ben Green is a rising star, and universally acknowledged as one of the best young mathematicians in the world."