Andrew Wiles
Wiles at the 61st Birthday conference for P. Deligne (Institute for Advanced Study, 2005).
Born	) 11 April 1953 (age 60) Cambridge, England
Nationality	British
Fields	Mathematics
Institutions	University of Oxford Princeton University
Alma mater	University of Oxford University of Cambridge
Thesis	Reciprocity Laws and the Conjecture of Birch and Swinnerton-Dyer (1979)
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, thereby proving Fermat's Last Theorem Proving the main conjecture of Iwasawa theory
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)^[1] 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.

Contents 1 Early life and education 2 Mathematical career 3 The proof of Fermat's Last Theorem 4 Recognition by the media 5 Awards 6 Public honours 7 In popular culture 8 Notes 9 External links

Early life and education []

Wiles is the son of Maurice Frank Wiles (1923–2005), the Regius Professor of Divinity at the University of Oxford^[2] 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.^[3] 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. He rejoined Oxford in 2011 as Royal Society Research Professor.

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 []

Starting in the summer of 1986, based on successive progress of the previous few years of Gerhard Frey, Jean-Pierre Serre and Ken Ribet, it became clear that Fermat's Last Theorem could be proven as a corollary of a limited form of the modularity theorem (unproven at the time and then known as the "Taniyama–Shimura-Weil conjecture"). The modularity theorem involved elliptic curves, which was also Wiles' own specialist area.

The conjecture was seen by contemporary mathematicians as important, but extraordinarily difficult or perhaps inaccessible to proof.^{[4]:203-205, 223, 226} For example, Wiles' ex-supervisor John Coates states that it seemed "impossible to actually prove",^[4]:226 and Ken Ribet considered himself "one of the vast majority of people who believed [it] was completely inaccessible", adding that "Andrew Wiles was probably one of the few people on earth who had the audacity to dream that you can actually go and prove [it]." ^[4]:223

Despite this, Wiles, who had a childhood fascination with Fermat's Last Theorem - decided to undertake the challenge of proving the conjecture - at least to the extent needed for Frey's curve - as the conjecture itself was also a professionally "worthwhile" and significant research area.^[4]:226 He dedicated all of his research time to this problem for over 6 years in near-total secrecy, covering up his efforts by releasing prior work in small segments as separate papers and confiding only in his wife.^[4]:229-230 In 1993, he presented his proof to the public for the first time at a conference in Cambridge.^[5] In August 1993 it turned out that the proof contained a flaw in one area. Wiles tried and failed for over a year to repair his proof. According to Wiles, the crucial idea for circumventing, rather than closing this area, came to him on 19 September 1994 when he was on the verge of giving up. Together with his former student Richard Taylor, he published a second paper which circumvented the problem 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.^[6] He has been a foreign member of the U.S. National Academy of Sciences since 1996. He remains a citizen of the United Kingdom.^[1]

Awards []

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

• Junior Whitehead Prize of the LMS (1988)^[1]
• Fellow of the Royal Society (1989)^[1]
• Schock Prize (1995)
• Fermat Prize (1995)
• Wolf Prize (1995/6)
• NAS Award in Mathematics from the National Academy of Sciences (1996)^[7][8]
• Royal Medal (1996)
• Ostrowski Prize (1996)^[9][10]
• Cole Prize (1997)^[11]
• Wolfskehl Prize (1997)^[12] – 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)^[13][14]
• King Faisal Prize (1998)^[15]
• Clay Research Award (1999)
• Pythagoras Award (Croton, 2004)^[16]
• Shaw Prize (2005)^[17]

Public honours []

• The asteroid 9999 Wiles was named for Wiles in 1999.^[18]
• Wiles was appointed to the rank of Knight Commander of the Order of the British Empire in the United Kingdom in 2000.^[19]

In popular culture []

• An episode of Star Trek: The Next Generation, filmed while Wiles was researching the proof, asserted that Fermat's Last Theorem remains unproven in the 24th century. An episode of Star Trek: Deep Space Nine mentioned Wiles's proof.
• 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.
• Wiles' 1993 presentation in Cambridge is mentioned in the novel The Oxford Murders by Guillermo Martínez, which was adapted into a film of the same title.

Notes []

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.
• Wiles's bibliography