Andrew Wiles

For the French mathematician known for work in the area of elliptic curves, see André Weil.

Sir Andrew Wiles
Wiles at the 61st Birthday conference for P. Deligne (Institute for Advanced Study, 2005).
Born	11 April 1953 (1953-04-11) Cambridge, England
Nationality	British
Fields	Mathematics
Institutions	University of Oxford Princeton University
Alma mater	University of Oxford University of Cambridge
Doctoral advisor	John Coates
Doctoral students	Manjul Bhargava Brian Conrad Fred Diamond Karl Rubin Christopher Skinner Richard Taylor
Known for	Proving the Taniyama-Shimura Conjecture for semistable elliptic curves, and thereby proving Fermat's Last Theorem
Notable awards	Fermat Prize (1995) Wolf Prize (1995/6) Royal Medal (1996) IMU Silver Plaque (1998) King Faisal International Prize in Science (1998) Shaw Prize (2005)

Sir Andrew John Wiles, KBE, FRS (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at Oxford University, specializing in number theory. He is most famous for proving Fermat's Last Theorem.

Early life and education

Wiles is the son of Maurice Frank Wiles (1923–2005), the Regius Professor of Divinity at the University of Oxford and Patricia Wiles (née Mowll). His father worked as the Chaplain at Ridley Hall, Cambridge, for the years 1952–55. Wiles was born in Cambridge, England, in 1953, and he attended King's College School, Cambridge, and The Leys School, Cambridge.

Wiles discovered Fermat's Last Theorem on his way home from school when he was 10 years old. He stopped by his local library where he found a book about the theorem. Puzzled by the fact that the statement of the theorem was so easy that he, a ten-year old, could understand it, he decided to be the first person to prove it. However, he soon realized that his knowledge of mathematics was too small, so he abandoned his childhood dream, until 1986, when he heard that Ribet had proved Serre's ε-conjecture and therefore established a link between Fermat's Last Theorem and the Taniyama-Shimura conjecture.

Wiles earned his bachelor's degree in mathematics in 1974 after his study at Merton College, Oxford, and a Ph.D. in 1980, after his research at Clare College, Cambridge.

After a stay at the Institute for Advanced Study in New Jersey in 1981, Wiles became a professor at Princeton University. In 1985–86, Wiles was a Guggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to 1990, Wiles was a Royal Society Research Professor at Oxford University, and then he returned to Princeton.

In October 2009 it was announced that Wiles would again become a Royal Society Research Professor at Oxford in 2011.

Mathematical career

Wiles's graduate research was guided by John Coates beginning in the summer of 1975. Together these colleagues worked on the arithmetic of elliptic curves with complex multiplication by the methods of Iwasawa theory. He further worked with Barry Mazur on the main conjecture of Iwasawa theory over the rational numbers, and soon afterward, he generalized this result to totally real fields.

The proof of Fermat's Last Theorem

Main article: Wiles' proof of Fermat's Last Theorem

Starting in the summer of 1986, based on successive progress of the previous few years of Gerhard Frey, Jean-Pierre Serre and Ken Ribet, Wiles realised that a proof of a limited form of the modularity theorem might then be in reach. He dedicated all of his research time to this problem in relative secrecy. In 1993, he presented his proof to the public for the first time at a conference in Cambridge. In August 1993, however, it turned out that the proof contained a gap. In desperation, Wiles tried to fill in this gap, but found out that the error he had made was a very fundamental one. According to Wiles, the crucial idea for circumventing, rather than closing this gap, came to him on 19 September 1994. Together with his former student Richard Taylor, he published a second paper which circumvented the gap and thus completed the proof. Both papers were published in 1995 in a special volume of the Annals of Mathematics.

Recognition by the media

His proof of Fermat's Last Theorem has stood up to the scrutiny of the world's mathematical experts. Wiles was interviewed for an episode of the BBC documentary series Horizon that focused on Fermat's Last Theorem. This was renamed "The Proof", and it was made an episode of the Public Broadcasting Service's science television series Nova. He is a foreign member of the United States National Academy of Sciences since 1996. He remains a citizen of the United Kingdom.

Family

Wiles is married to Nada Canaan Wiles, who earned her Ph.D. in microbiology from Princeton University in New Jersey, and they have three daughters: Clare, Kate and Olivia. He lives in Oxford.

Awards

Wiles has been awarded several major prizes in mathematics and science:

• Junior Whitehead Prize of the LMS (1988)
• Fellow of the Royal Society (1989)
• Schock Prize (1995)
• Fermat Prize (1995)
• Wolf Prize (1995/6)
• NAS Award in Mathematics from the National Academy of Sciences (1996)
• Royal Medal (1996)
• Ostrowski Prize (1996)
• Cole Prize (1997)
• Wolfskehl Prize (1997) – see Paul Wolfskehl
• A silver plaque from the International Mathematical Union (1998) recognizing his achievements, in place of the Fields Medal, which is restricted to those under 40 (Wiles was born in 1953 and proved the theorem in 1994)
• King Faisal Prize (1998)
• Clay Research Award (1999)
• Pythagoras Award (Croton, 2004)
• Shaw Prize (2005)

Public honours

• The asteroid 9999 Wiles was named for Wiles in 1999.
• Wiles was appointed to the rank of Knight Commander of the Order of the British Empire in the United Kingdom in 2000.

In popular culture

• Wiles was mentioned in an episode of Star Trek: Deep Space Nine for his proof of Fermat's Last Theorem.
• He was also mentioned in Stieg Larsson's second book of the Millennium trilogy The Girl Who Played With Fire, and also the third, The Girl Who Kicked the Hornets' Nest. Wiles was credited with solving Fermat's Last Theorem when the female protagonist Lisbeth Salander attempted to solve it.
• Tom Lehrer updated the lyrics to his song That's Mathematics, to mention that Wiles "confirms what Fermat / Jotted down in that margin / Which could've used some enlargin'."
• Rock band Bats have a song named after Wiles which describes his career.
• Wiles and his achievement are also mentioned in Yoko Ogawa's novel 'The Housekeeper and the Professor'.

External links

• Andrew Wiles at the Mathematics Genealogy Project.
• O'Connor, John J.; Robertson, Edmund F., "Andrew Wiles", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Wiles.html .
• Wiles's bibliography
• Works by or about Andrew Wiles in libraries (WorldCat catalog)