Sir Andrew John Wiles, KBE, FRS (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at Oxford University, specializing innumber theory. He is most notable 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 states that he came across 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. Fascinated by the existence of a theorem that was so easy to state that he, a ten-year old, could understand it, but nobody had proven it, he decided to be the first person to prove it. However, he soon realized that his knowledge was too small, so he abandoned his childhood dream, until it was brought back to his attention at the age of 33 by Ken Ribet’s 1986 proof of the epsilon conjecture, which Gerhard Frey had previously linked to Fermat’s famous equation.
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 aGuggenheim Fellow at the Institut des Hautes Études Scientifiques near Paris and at the École Normale Supérieure. From 1988 to 1990, Wiles was a Royal SocietyResearch Professor at Oxford University, and then he returned to Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor.
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 withcomplex 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 thatFermat’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. For example, Wiles’ ex-supervisor John Coates states that it seemed “impossible to actually prove”, 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].”
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. 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. In 1993, he presented his proof to the public for the first time at a conference in Cambridge. 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.
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 has been a foreign member of the U.S. National Academy of Sciences since 1996. He remains a citizen of the United Kingdom.
Wiles has been awarded several major prizes in mathematics and science: