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Richard 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. May 19 is the 139th day of the year in the Gregorian Calendar (140th in leap years). ...
1962 (MCMLXII) was a common year starting on Monday (the link is to a full 1962 calendar). ...
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Number theory is the branch of pure mathematics concerned with the properties of numbers in general, and integers in particular, as well as the wider classes of problems that arise from their study. ...
Andrew Wiles should not be confused with André Weil, another famous mathematician who, like Wiles, did important work in the area of elliptic curves. ...
Princeton University is a coeducational private university located in Princeton, New Jersey in the United States of America. ...
Pierre de Fermat Problem II.8 in the Arithmetica of Diophantus, annotated with Fermats comment which became Fermats Last Theorem (edition of 1670). ...
Academic career He received his Ph.D. from Princeton University in 1988. From 1995 to 1996 he held the Savilian Chair of Geometry at Oxford University, and he is currently the Herchel Smith Professor of Mathematics at Harvard University. Ph. ...
1988 (MCMLXXXVIII) was a leap year starting on Friday of the Gregorian calendar. ...
1995 (MCMXCV) was a common year starting on Sunday of the Gregorian calendar. ...
1996 (MCMXCVI) was a leap year starting on Monday of the Gregorian calendar, and was designated the International Year for the Eradication of Poverty. ...
The Savilian Chair of Geometry is the position of professor of mathematics at the University of Oxford in England. ...
The University of Oxford, located in the city of Oxford in England, is the oldest university in the English-speaking world. ...
Harvard University (incorporated as The President and Fellows of Harvard College) is a private university in Cambridge, Massachusetts. ...
He received the Cole Prize of the American Mathematical Society in 2002. The Cole Prize 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 American Mathematical Society (AMS) is dedicated to the interests of mathematical research and education, which it does with various publications and conferences as well as annual monetary awards to mathematicians. ...
Work One of the two papers containing the published proof of Fermat's Last Theorem (Ring theoretic properties of certain Hecke algebras. R.Taylor and A.Wiles Annals of Math. 141 (1995) 553-572) is a joint work of Taylor and Wiles.
In subsequent work, Taylor (along with Michael Harris) proved the local Langlands conjectures. In mathematics, the Langlands program is a web of far-reaching and influential conjectures that connect number theory and the representation theory of certain groups. ...
Taylor, along with Christophe Breuil, Brian Conrad, and Fred Diamond, completed the proof of the Taniyama-Shimura conjecture. Brian Conrad is a renowned mathematician and number theorist currently working at the University of Michigan. ...
Fred Diamond (born November 19, 1964) is an American mathematician. ...
The Taniyama-Shimura theorem establishes an important connection between elliptic curves, which are objects from algebraic geometry, and modular forms, which are certain periodic holomorphic functions investigated in number theory. ...
Very recently, Taylor, building on his own work and that of Laurent Clozel, Michael Harris, and Nick Shepherd-Barron, has announced a proof of the Sato-Tate conjecture, for elliptic curves with non-integral j-invariant. This partial proof of the Sato-Tate conjecture follows from a modularity result, generalizing Wiles's result for elliptic curves. Nicholas Ian Shepherd-Barron is a professor of mathematics at Cambridge University who works on algebraic geometry. ...
In mathematics, the Sato-Tate conjecture is a statistical statement about the family of elliptic curves Ep over the finite field with p elements, with p a prime number, obtained from an elliptic curve E over the rational number field, by the process of reduction modulo a prime for almost...
In mathematics, an elliptic curve is a plane curve defined by an equation of the form y2 = x3 + a x + b, which is non-singular; that is, its graph has no cusps or self-intersections. ...
Real part of the j-invariant as a function of the nome q on the unit disk In mathematics, Kleins j-invariant, regarded as a function of a complex variable Ï„, is a modular function defined on the upper half-plane of complex numbers. ...
Some expert opinion now predicts that the removal of the technical condition, and the full Sato-Tate conjecture, will follow from the stabilization of the Selberg trace formula. That is, Sato-Tate is rumoured now to be subject to a conditional proof. In mathematics, the Selberg trace formula is a central result, or area of research, in non-commutative harmonic analysis. ...
Conditional proof is a proof that takes the form of asserting a conditional, and proving that the premise or antecedent of the conditional necessarily leads to the conclusion. ...
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