Richard Taylor (mathematician)

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For other persons named Richard Taylor, see Richard Taylor (disambiguation).

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.

[edit] 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.

He received the Cole Prize of the American Mathematical Society in 2002.

[edit] 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.

Taylor, along with Christophe Breuil, Brian Conrad, and Fred Diamond, completed the proof of the Taniyama-Shimura conjecture.

Very recently, Taylor, building on his own work and that of Laurent Clozel, 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.

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.