Richard Taylor (mathematician)
Encyclopedia
Richard Lawrence Taylor (born 19 May 1962) is a British
mathematician
working in the field of number theory
. A former research student of Andrew Wiles
, he returned to Princeton
to help his advisor complete the proof of Fermat's last theorem
.
Taylor received the 2007 Shaw Prize
in Mathematical Sciences for his work on the Langlands program
with Robert Langlands
.
from Clare College, Cambridge
, and his Ph.D.
from Princeton University
in 1988. From 1995 to 1996 he held the Savilian Chair of Geometry at Oxford University and Fellow of New College, Oxford
, and he is currently the Herchel Smith Professor of Mathematics at Harvard University
.
He received the Whitehead Prize
in 1990, the Fermat Prize
, the Ostrowski Prize
in 2001, the Cole Prize
of the American Mathematical Society
in 2002, and the Shaw Prize
for Mathematics in 2007. He was also elected a Fellow of the Royal Society in 1995.
.
In subsequent work, Taylor (along with Michael Harris
) proved the local Langlands conjectures
for GL(n)
over a number field. A simpler proof was suggested almost at the same time by Guy Henniart
.
Taylor, together with Christophe Breuil
, Brian Conrad
, and Fred Diamond
, completed the proof of the Taniyama–Shimura conjecture, by performing quite heavy technical computations in the case of additive reduction.
Recently, Taylor, following the ideas of Michael Harris and building on his joint work with Laurent Clozel, Michael Harris, and Nick Shepherd-Barron, has announced a proof of the Sato–Tate conjecture, for elliptic curve
s with non-integral j-invariant
. This partial proof of the Sato–Tate conjecture uses Wiles's theorem about modularity of semistable elliptic curves.
). They have two children: Jeremy and Chloe. He is also the son of British physicist, John C. Taylor.
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....
working in the field of 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...
. A former research student of Andrew Wiles
Andrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
, he returned to Princeton
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....
to help his advisor complete the proof of Fermat's last theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
.
Taylor received the 2007 Shaw Prize
Shaw Prize
The Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong, it honours living "individuals, regardless of race, nationality and religious belief, who have achieved significant breakthrough in academic and scientific research or...
in Mathematical Sciences for his work on the Langlands program
Langlands program
The Langlands program is a web of far-reaching and influential conjectures that relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. It was proposed by ....
with Robert Langlands
Robert Langlands
Robert Phelan Langlands is a mathematician, best known as the founder of the Langlands program. He is an emeritus professor at the Institute for Advanced Study...
.
Academic career
He received 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...
from Clare College, Cambridge
Clare College, Cambridge
Clare College is a constituent college of the University of Cambridge in Cambridge, England.The college was founded in 1326, making it the second-oldest surviving college of the University after Peterhouse. Clare is famous for its chapel choir and for its gardens on "the Backs"...
, and his Ph.D.
Doctor of Philosophy
Doctor of Philosophy, abbreviated as Ph.D., PhD, D.Phil., or DPhil , in English-speaking countries, is a postgraduate academic degree awarded by universities...
from 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....
in 1988. From 1995 to 1996 he held the Savilian Chair of Geometry at Oxford University and Fellow of New College, Oxford
New College, Oxford
New College is one of the constituent colleges of the University of Oxford in the United Kingdom.- Overview :The College's official name, College of St Mary, is the same as that of the older Oriel College; hence, it has been referred to as the "New College of St Mary", and is now almost always...
, and he is currently the Herchel Smith Professor of Mathematics at Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
.
He received the Whitehead Prize
Whitehead Prize
The Whitehead Prize is awarded yearly by the London Mathematical Society to a mathematician working in the United Kingdom who is at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C...
in 1990, the Fermat Prize
Fermat Prize
The Fermat prize of mathematical research rewards research works in fields where the contributions of Pierre de Fermat have been decisive:* Statements of variational principles* Foundations of probability and analytic geometry* Number theory....
, the Ostrowski Prize
Ostrowski Prize
The Ostrowski Prize is a mathematics award given every other year by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands...
in 2001, the Cole Prize
Cole Prize
The Frank Nelson Cole Prize, or Cole Prize for short, is one of two prizes awarded to mathematicians by the American Mathematical Society, one for an outstanding contribution to algebra, and the other for an outstanding contribution to number theory. The prize is named after Frank Nelson Cole, who...
of the American Mathematical Society
American Mathematical Society
The 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...
in 2002, and the Shaw Prize
Shaw Prize
The Shaw Prize is an annual award first presented by the Shaw Prize Foundation in 2004. Established in 2002 in Hong Kong, it honours living "individuals, regardless of race, nationality and religious belief, who have achieved significant breakthrough in academic and scientific research or...
for Mathematics in 2007. He was also elected a Fellow of the Royal Society in 1995.
Work
One of the two papers containing the published proof of Fermat's Last Theorem is a joint work of Taylor and Andrew WilesAndrew Wiles
Sir Andrew John Wiles KBE FRS is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory...
.
In subsequent work, Taylor (along with Michael Harris
Michael Harris (mathematician)
Michael Howard Harris is an American mathematician. He made notable contributions to the Langlands program, for which he won the 2007 Clay Research Award...
) proved the local Langlands conjectures
Local Langlands conjectures
In mathematics, the local Langlands conjectures, introduced by , are part of the Langlands program. They describe a correspondence between representations of the Weil group of a local field and representations of algebraic groups over the local field, generalizing local class field theory from...
for GL(n)
General linear group
In mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible...
over a number field. A simpler proof was suggested almost at the same time by Guy Henniart
Guy Henniart
Guy Henniart is a French mathematician at Paris-Sud 11 University. He is known for his contributions to the Langlands program, in particular his proof of the local Langlands conjecture for GL over a p-adic local field—independently from Harris and Taylor—in 1998.Henniart attained his doctorate...
.
Taylor, together with Christophe Breuil
Christophe Breuil
Christophe Breuil is a French mathematician, who works in algebraic geometry and number theory.-Academic life:Breuil attended schools in Brive-la-Gaillarde and Toulouse and studied from 1990 to 1992 at the Ecole Polytechnique....
, Brian Conrad
Brian Conrad
Brian Conrad , is an American mathematician and number theorist, working at Stanford University. Previously he was at the University of Michigan....
, and Fred Diamond
Fred Diamond
Fred Diamond is an American mathematician, known for his role in proving the modularity theorem for elliptic curves. His research interest is in modular forms and Galois representations....
, completed the proof of the Taniyama–Shimura conjecture, by performing quite heavy technical computations in the case of additive reduction.
Recently, Taylor, following the ideas of Michael Harris and building on his joint work with Laurent Clozel, Michael Harris, and Nick Shepherd-Barron, has announced a proof of the Sato–Tate conjecture, for elliptic curve
Elliptic curve
In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...
s with non-integral j-invariant
J-invariant
In mathematics, Klein's j-invariant, regarded as a function of a complex variable τ, is a modular function defined on the upper half-plane of complex numbers.We haveThe modular discriminant \Delta is defined as \Delta=g_2^3-27g_3^2...
. This partial proof of the Sato–Tate conjecture uses Wiles's theorem about modularity of semistable elliptic curves.
Personal life
Taylor is married to Christine Taylor (a mathematical biologistMathematical and theoretical biology
Mathematical and theoretical biology is an interdisciplinary scientific research field with a range of applications in biology, medicine and biotechnology...
). They have two children: Jeremy and Chloe. He is also the son of British physicist, John C. Taylor.