Andrew Wiles — LLMpedia

Andrew Wiles
"copyright C. J. Mozzochi, Princeton N.J" · Attribution · source
Name	Andrew Wiles
Birth date	1953-04-11
Birth place	Cambridge, United Kingdom
Nationality	British
Alma mater	Merton College, Oxford, King's College London, Princeton University
Known for	Proof of Fermat's Last Theorem
Field	Mathematics
Doctoral advisor	John Coates

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Andrew Wiles

Sir Andrew John Wiles (born 11 April 1953) is a British mathematician renowned for his proof of Fermat's Last Theorem and for contributions to number theory, arithmetic geometry, and the theory of elliptic curves. His work connects concepts from modular forms, Galois representations, and the Taniyama–Shimura–Weil conjecture (now often called the Modularity theorem), influencing research at institutions such as Princeton University, University of Cambridge, and Harvard University.

Early life and education

Wiles was born in Cambridge and grew up in Yorkshire; he attended King's College London and Merton College, Oxford before pursuing doctoral studies at Trinity College, Cambridge and Princeton University under John Coates. As a youth he read Sophie Germain-related accounts of Pierre de Fermat and visited the Bodleian Library to study early sources on Diophantine equations and the history surrounding Fermat's Last Theorem. His formative influences included mathematicians such as G. H. Hardy, André Weil, and Barry Mazur, and he trained in environments connected to the Royal Society and the British Mathematical Society.

Wiles held junior and senior academic posts at institutions including University of Oxford, Imperial College London, Princeton University, and University of Cambridge. He has been affiliated with colleges such as Merton College, Oxford and departments tied to King's College London and Harvard University. Wiles delivered lectures at venues like the International Congress of Mathematicians and participated in collaborations with researchers from École Normale Supérieure, Institut des Hautes Études Scientifiques, and the Max Planck Institute for Mathematics. His career intersects with funding and oversight bodies such as the European Research Council and the National Science Foundation.

Wiles pursued a program linking the Taniyama–Shimura–Weil conjecture to Fermat's Last Theorem by proving modularity for a class of elliptic curves, building on work by Gerhard Frey, Ken Ribet, Jean-Pierre Serre, and Goro Shimura. He announced a proof in 1993 at a lecture series at Cambridge and Princeton University, presenting arguments that combined techniques from Iwasawa theory, Hida theory, and the theory of motives. A gap in the original argument was identified in the work of referees and colleagues such as Richard Taylor; Wiles, aided by Taylor, repaired the proof in 1994 by introducing new ideas concerning Euler systems and deformation theory of Galois representations. The completed proof established cases of the Modularity theorem sufficient to imply Fermat's Last Theorem, resolving a conjecture that had influenced figures from Pierre de Fermat to Andrew Selberg and reshaping study at centers like Cambridge and Princeton.

Beyond the landmark proof, Wiles made lasting contributions to the study of elliptic curves, Galois representations, and modular forms, affecting subsequent work by mathematicians such as Richard Taylor, Barry Mazur, Ken Ribet, Jean-Pierre Serre, and Gerd Faltings. His methods influenced research programs at institutions including IHÉS, Princeton University, Harvard University, University of Oxford, and research groups supported by the Simons Foundation. Wiles's approach integrated ideas from algebraic number theory traditions associated with Emmy Noether, Ernst Kummer, and Carl Friedrich Gauss, and inspired new directions involving automorphic forms, Shimura varieties, and the Langlands program. His legacy is reflected in graduate training at departments such as Cambridge, Oxford, and Princeton, and in prizes, conferences, and publications hosted by organizations like the American Mathematical Society and the London Mathematical Society.

Wiles has received numerous distinctions including the Abel Prize, the Royal Medal, knighthood from the United Kingdom, the Wolf Prize in Mathematics, and election to bodies such as the Royal Society and the National Academy of Sciences. He received honorary degrees from universities including Cambridge, Oxford, Harvard University, and Princeton University, and delivered named lectures like those at the International Congress of Mathematicians and the Newton Institute. His awards join those given to peers such as Pierre Deligne, Andrew Selberg, Gerd Faltings, Jean-Pierre Serre, and John G. Thompson.