Richard Lawrence Taylor (born 19 May 1962) is a British mathematician working in the field of

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

. He is currently the Barbara Kimball Browning Professor in Humanities and Sciences at

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

.Taylor's staff page at Stanford.
/ref> Taylor received the 2015

Breakthrough Prize in Mathematics The Breakthrough Prize in Mathematics is an annual award of the Breakthrough Prize series announced in 2013. It is funded by Yuri Milner and Mark Zuckerberg and others. The annual award comes with a cash gift of $3 million. The Breakthrough Prize ...

"for numerous breakthrough results in the theory of

automorphic form In harmonic analysis and number theory, an automorphic form is a well-behaved function from a topological group ''G'' to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup \Gamma \subset G of ...

s, including the Taniyama–Weil conjecture, the local Langlands conjecture for

general linear group In mathematics, the general linear group of degree ''n'' is the set of invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, ...

s, and the

Sato–Tate conjecture In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves ''Ep'' obtained from an elliptic curve ''E'' over the rational numbers by reduction modulo almost all prime numbers ''p''. Mikio Sato and J ...

." He also received the 2007

Shaw Prize The Shaw Prize is an annual award presented by the Shaw Prize Foundation. Established in 2002 in Hong Kong, it honours "individuals who are currently active in their respective fields and who have recently achieved distinguished and signifi ...

in Mathematical Sciences for his work on the

Langlands program In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by , it seeks to relate Galois groups in algebraic num ...

with

Robert Langlands Robert Phelan Langlands, (; born October 6, 1936) is a Canadian mathematician. He is best known as the founder of the Langlands program, a vast web of conjectures and results connecting representation theory and automorphic forms to the study o ...

. He also served on the Mathematical Sciences jury for the

Infosys Prize The Infosys Prize is an annual award given to scientists, researchers, engineers and social scientists of Indian origin (not necessarily born in India) by the Infosys Science Foundation and ranks among the highest monetary awards in India to re ...

from 2012 to 2014.

Career

He received his

B.A. Bachelor of arts (BA or AB; from the Latin ', ', or ') is a bachelor's degree awarded for an undergraduate program in the arts, or, in some cases, other disciplines. A Bachelor of Arts degree course is generally completed in three or four years ...

from

Clare College, Cambridge Clare College is a constituent college of the University of Cambridge in Cambridge, England. The college was founded in 1326 as University Hall, making it the second-oldest surviving college of the University after Peterhouse. It was refounded ...

.SAVILIAN PROFESSORSHIP OF GEOMETRY in NOTICES, University Gazette 23.3.95 No. 435

During his time at University of Cambridge, Cambridge, he was president of

The Archimedeans The Archimedeans are the mathematical society of the University of Cambridge, founded in 1935. It currently has over 2000 active members, many of them alumni, making it one of the largest student societies in Cambridge. The society hosts regular t ...

in 1981 and 1982, following the resignation of his predecessor. He earned his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

in mathematics from

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

in 1988 after completing a doctoral dissertation, titled "On congruences between

modular forms In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory of ...

", under the supervision of

Andrew Wiles Sir Andrew John Wiles (born 11 April 1953) is an English mathematician and a Royal Society Research Professor at the University of Oxford, specializing in number theory. He is best known for proving Fermat's Last Theorem, for which he was awar ...

. From 1995 to 1996 he held the

Savilian chair of geometry The position of Savilian Professor of Geometry was established at the University of Oxford in 1619. It was founded (at the same time as the Savilian Professorship of Astronomy) by Sir Henry Savile, a mathematician and classical scholar who was ...

Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...

and Fellow of

New College, Oxford New College is one of the constituent colleges of the University of Oxford in the United Kingdom. Founded in 1379 by William of Wykeham in conjunction with Winchester College as its feeder school, New College is one of the oldest colleges at th ...

,'TAYLOR, Prof. Richard Lawrence', Who's Who 2008, A & C Black, 2008; online edn, Oxford University Press, Dec 200
accessed 27 March 2008
/ref> and later became the Herchel Smith Professor of Mathematics at

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...

, and held the Robert and Luisa Fernholz Professorship at the

Institute for Advanced Study The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...

. He is currently the Barbara Kimball Browning Professor in Humanities & Sciences at

. He received the

Whitehead Prize The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whiteh ...

in 1990, the

Fermat Prize The Fermat prize of mathematical research biennially 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 * Numb ...

and the

Ostrowski Prize The Ostrowski Prize is a mathematics award given every odd year for outstanding mathematical achievement judged by an international jury from the universities of Basel, Jerusalem, Waterloo and the academies of Denmark and the Netherlands. Alexand ...

in 2001, the

Cole Prize The Frank Nelson Cole Prize, or Cole Prize for short, is one of twenty-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 ...

of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

in 2002, and the

for Mathematics in 2007. He was also elected a

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

in 1995. In 2012 he became a fellow of the

. In 2015 he was inducted into the

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the Nati ...

. He was elected to the

American Philosophical Society The American Philosophical Society (APS), founded in 1743 in Philadelphia, is a scholarly organization that promotes knowledge in the sciences and humanities through research, professional meetings, publications, library resources, and communit ...

in 2018.

Research

One of the two papers containing the published proof of

Fermat's Last Theorem In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...

is a joint work of Taylor and

. In subsequent work, Taylor (along with Michael Harris) proved the

local Langlands conjectures In mathematics, the local Langlands conjectures, introduced by , are part of the Langlands program. They describe a correspondence between the complex representations of a reductive algebraic group ''G'' over a local field ''F'', and representation ...

for GL(''n'') over a

number field In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension). Thus K is a f ...

. A simpler proof was suggested almost at the same time by Guy Henniart, and ten years later by

Peter Scholze Peter Scholze (; born 11 December 1987) is a German mathematician known for his work in arithmetic geometry. He has been a professor at the University of Bonn since 2012 and director at the Max Planck Institute for Mathematics since 2018. He ha ...

. Taylor, together with

Christophe Breuil Christophe Breuil (; born 1968) is a French people, French mathematician, who works in arithmetic geometry and algebraic number theory. Work With Fred Diamond, Richard Taylor (mathematician), Richard Taylor and Brian Conrad in 1999, he proved th ...

Brian Conrad Brian Conrad (born November 20, 1970) is an American mathematician and number theorist, working at Stanford University. Previously, he taught at the University of Michigan and at Columbia University. Conrad and others proved the modularity theo ...

and

Fred Diamond Fred Irvin Diamond (born November 19, 1964) is a mathematician, known for his role in proving the modularity theorem for elliptic curves. His research interest is in modular forms and Galois representations. Diamond received his B.A. from the ...

, completed the proof of the Taniyama–Shimura conjecture, by performing quite heavy technical computations in the case of additive reduction. In 2008, Taylor, following the ideas of Michael Harris and building on his joint work with Laurent Clozel, Michael Harris, and Nick Shepherd-Barron, announced a proof of the

, for

elliptic curve In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...

s with non-integral

j-invariant In mathematics, Felix Klein's -invariant or function, regarded as a function of a Complex analysis, complex variable , is a modular function of weight zero for defined on the upper half-plane of complex numbers. It is the unique such funct ...

. This partial proof of the Sato–Tate conjecture uses Wiles's theorem about modularity of semistable elliptic curves.

Personal life

Taylor is the son of British physicist John C. Taylor. He is married, and has two children.Taylor, Richar
"The Shaw Prize"
2007

References

External links

His home page at the Institute for Advanced Study
*
Autobiography upon Shaw Prize acceptance
{{DEFAULTSORT:Taylor, Richard 1962 births Alumni of Clare College, Cambridge 20th-century British mathematicians 21st-century British mathematicians Clay Research Award recipients Fellows of New College, Oxford Fellows of the American Academy of Arts and Sciences Fellows of the American Mathematical Society Fellows of the Royal Society Members of the United States National Academy of Sciences Harvard University faculty Institute for Advanced Study faculty Living people Number theorists Princeton University alumni Savilian Professors of Geometry Whitehead Prize winners Fermat's Last Theorem Members of the American Philosophical Society