1. Early Life and Education
Richard Lawrence Taylor was born on 19 May 1962. He is the son of the British physicist John C. Taylor.
Taylor pursued his undergraduate studies at the University of Cambridge, where he received his Bachelor of Arts degree from Clare College, Cambridge. During his time at Cambridge, he served as the president of The Archimedeans, a mathematical society, in 1981 and 1982, following the resignation of his predecessor. He then moved to the United States to continue his education, earning his Ph.D. in mathematics from Princeton University in 1988. His doctoral dissertation, titled "On congruences between modular forms," was completed under the supervision of the distinguished mathematician Andrew Wiles.
2. Academic Career
Taylor's academic career spans several of the world's leading mathematical institutions, marked by a progression through various professorial and research positions.
He began his career at the University of Cambridge, serving as an assistant lecturer, lecturer, and then reader from 1988 to 1995. During this period, he also held an IHÉS exchange fellowship from 1988 to 1989. In 1992, he was a visiting assistant professor at the California Institute of Technology. He also held a visiting professorship at Harvard University in 1994.
From 1995 to 1996, Taylor held the prestigious Savilian chair of geometry at Oxford University and was a Fellow of New College, Oxford. Following his tenure at Oxford, he joined Harvard University as a professor of mathematics in 1996, where he remained until 2012. During his time at Harvard, he was appointed the Herchel Smith Professor of Pure Mathematics. He also served as a visiting professor at the University of California, Berkeley in 1999 and as a distinguished visiting professor at Princeton University from 2010 to 2011.
In 2012, Taylor moved to the Institute for Advanced Study in Princeton, New Jersey, where he held the Robert and Luisa Fernholz Professorship until 2019. Since 2018, he has been the Barbara Kimball Browning Professor in Humanities and Sciences at Stanford University.
3. Mathematical Research
Richard Taylor's research has profoundly impacted the field of number theory, particularly through his work on automorphic forms and their connections to elliptic curves and Galois representations. His contributions have been instrumental in proving several long-standing conjectures.
3.1. Fermat's Last Theorem
Taylor played a crucial and collaborative role with his former supervisor, Andrew Wiles, in completing the proof of Fermat's Last Theorem. Wiles's initial proof, announced in 1993, contained a gap. Taylor joined Wiles in refining and completing the proof, leading to the publication of two papers in 1995. One of these papers, titled "Ring theoretic properties of certain Hecke algebras," was a joint work by Taylor and Wiles, which addressed and resolved the critical issues in the original argument, thus solidifying the proof of this historic theorem.
3.2. Taniyama-Shimura Conjecture
Taylor was a key participant in the proof of the modularity theorem (originally known as the Taniyama-Shimura conjecture or Taniyama-Weil conjecture), which states that every elliptic curve over the rational numbers is modular. Andrew Wiles's work proved the modularity for semistable elliptic curves, which was sufficient for Fermat's Last Theorem. Taylor, along with collaborators Christophe Breuil, Brian Conrad, and Fred Diamond, completed the proof of the full Taniyama-Shimura conjecture. Their work involved performing complex technical computations, particularly addressing the case of additive reduction, thereby extending the modularity result to all elliptic curves over the rational numbers.
3.3. Local Langlands Conjectures
Taylor made significant achievements in the Langlands program, specifically in proving the local Langlands conjectures for GL(n) over a number field. This groundbreaking work was conducted jointly with Michael Harris, resulting in their book "The geometry and cohomology of some simple Shimura varieties" (2001). Their proof provided a crucial step in understanding the deep connections between Galois representations and automorphic forms. Simpler proofs for these conjectures were later proposed by Guy Henniart and, a decade later, by Peter Scholze.
3.4. Sato-Tate Conjecture
Richard Taylor's research also contributed to the partial proof of the Sato-Tate conjecture for elliptic curves. This conjecture concerns the distribution of the angles of the Frobenius endomorphisms associated with elliptic curves. Following the ideas of Michael Harris and building on his joint work with Laurent Clozel, Michael Harris, and Nicholas Shepherd-Barron, Taylor announced a proof of the Sato-Tate conjecture for elliptic curves with non-integral j-invariant. This partial proof notably utilized Wiles's theorem concerning the modularity of semistable elliptic curves. His work in this area was published in "Automorphy for some l-adic lifts of automorphic mod l representations. II" (2008).
3.5. Other Number Theory Research
Beyond these landmark achievements, Taylor's broader research contributions in number theory encompass a wide range of topics. His work consistently explores the intricate relationships between modular forms, automorphic forms, and Galois representations. He has made significant advancements in various areas of advanced theoretical mathematics, deepening the understanding of fundamental structures in number theory.
4. Awards and Honors
Richard Taylor has received numerous prestigious awards, prizes, fellowships, and memberships, recognizing his profound impact on the mathematical community and his groundbreaking research.
- 1990: Whitehead Prize
- 1992: Franco-Britannic Prize from the French Academy of Sciences
- 1995: Elected a Fellow of the Royal Society
- 2001: Fermat Prize (jointly with Wendelin Werner)
- 2001: Ostrowski Prize (jointly with Henri Iwaniec and Peter Sarnak)
- 2002: Delivered a plenary lecture at the ICM in Beijing
- 2002: Cole Prize in Number Theory from the American Mathematical Society (jointly with Henri Iwaniec)
- 2002: Guggenheim Fellowship
- 2003: Guggenheim Fellowship
- 2005: Danny Heineman Prize from the Göttingen Academy of Sciences
- 2007: Clay Research Award
- 2007: Shaw Prize for Mathematics (jointly with Robert Langlands)
- 2012: Elected a Fellow of the American Mathematical Society
- 2012: Elected a member of the American Academy of Arts and Sciences
- 2014: Breakthrough Prize in Mathematics "for numerous breakthrough results in the theory of automorphic forms, including the Taniyama-Weil conjecture, the local Langlands conjecture for general linear groups, and the Sato-Tate conjecture."
- 2015: Inducted into the National Academy of Sciences
- 2018: Elected to the American Philosophical Society
5. Personal Life
Richard Taylor is the son of the distinguished British physicist John C. Taylor. He is married and has two children.