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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.

Taylor received the 2007 Shaw Prize in Mathematical Sciences for his work on the Langlands program with Robert Langlands.

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 Fermat Prize in 2001, the Ostrowski Prize 2001 and the Cole Prize of the American Mathematical Society in 2002.

One of the two papers containing the published proof of Fermat's Last Theorem is a joint work of Taylor and Andrew Wiles.^[1]

In subsequent work, Taylor (along with Michael Harris) proved the local Langlands conjectures for GL(n) over a number field.^[2]

Taylor, along with Christophe Breuil, Brian Conrad, and Fred Diamond, completed the proof of the Taniyama-Shimura conjecture.^[3]

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.^[4]

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.

Taylor is married to Christina Taylor (born and raised in China). They have two children: Jeremy and Chloe.

• His home page at Harvard
• Undated PDF talk summary apparently by Taylor

1. ^ R. Taylor and A. Wiles, Ring theoretic properties of certain Hecke algebras, Ann. of Math. 141 (1995), no. 3, pp. 553-572 (subscription required to view article)
2. ^ M. Harris and R. Taylor, The geometry and cohomology of some simple Shimura varieties, Annals of Mathematics Studies, no. 151, Princeton University Press, 2001. ISBN 0-691-09090-4
3. ^ C. Breuil, B. Conrad, F. Diamond and R. Taylor, On the modularity of elliptic curves over Q : wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, pp. 843-939
4. ^ R. Taylor, Automorphy for some l-adic lifts of automorphic mod l representations. II, preprint available at his website].

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