Richard Taylor

Richard Lawrence Taylor (born 19 May 1962) is a British-American mathematician specialising in number theory. He is currently the Barbara Kimball Browning Professor in Humanities and Sciences at Stanford University in California.

Taylor received the 2002 Cole Prize, the 2007 Shaw Prize with Robert Langlands, and the 2015 Breakthrough Prize in Mathematics.

Career He received his Bachelor of Arts (B.A.) degree from the Clare College of the University of Cambridge. He earned his Ph.D. degree in mathematics from Princeton University in the United States in 1988, after completing a doctoral dissertation, titled "On congruences between modular forms", under the supervision of Andrew Wiles.

He was an assistant lecturer, lecturer, and then reader at the University of Cambridge from 1988 to 1995. From 1995 to 1996 he held the Savilian chair of geometry He was a professor of mathematics at Harvard University from 1996 to 2012, at one point becoming the Herchel Smith Professor of Pure Mathematics. This ring theoretic result essentially completed the proof of the semistable case of Taniyama-Shimura, which Wiles expounded in the same issue of the Annals of Mathematics. This proof strategy has been dubbed "Taylor-Wiles patching".

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, and ten years later by Peter Scholze.

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.

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 Sato–Tate conjecture, for elliptic curves with non-integral j-invariant. This partial proof of the Sato–Tate conjecture uses Wiles's theorem about modularity of semistable elliptic curves.

Awards and honors He received the Whitehead Prize in 1990, the Fermat Prize and 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 elected a Fellow of the Royal Society in 1995. In 2015 he was inducted into the National Academy of Sciences. He was elected to the American Philosophical Society in 2018.

Personal life Taylor is the son of British physicist John C. Taylor. He is married and has two children.