Sir Andrew John Wiles (born 11 April 1953) is a British mathematician and a Royal Society
Research Professor at the University of Oxford, specialising in number theory.
He is best known for proving Fermat's Last Theorem, for which he was awarded the 2016
Abel Prize and the 2017 Copley Medal by the Royal Society.
He was appointed Knight Commander of the Order of the British Empire in 2000, and in 2018
was appointed as the first Regius Professor of Mathematics at Oxford.
== Education and early life == Wiles was born on 11 April 1953 in Cambridge,
England, 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 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 at 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 that no one had proven, he decided to be the first person to prove
it.
However, he soon realised that his knowledge was too limited, 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.
== Career and research == Wiles earned his bachelor's degree in mathematics
in 1974 at Merton College, Oxford, and a PhD in 1980 as a graduate student of Clare College,
Cambridge.
After a stay at the Institute for Advanced Study in Princeton, New Jersey in 1981, Wiles
became a Professor of Mathematics 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 the University of Oxford,
and then he returned to Princeton.
From 1994 - 2009, Wiles was a Eugene Higgins Professor at Princeton.
He rejoined Oxford in 2011 as Royal Society Research Professor.
In May 2018 he was appointed Regius Professor of Mathematics at Oxford, the first in the
university's history.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 generalised this result to totally real fields.His biographical
page at Princeton University's website states that "Andrew has few equals in terms of his
impact on modern number theory.
Many of the world’s very best young number theorists received their Ph.D.’s under Andrew
... and many of these are today leaders and professors at top institutions around the
world".
=== Proof of Fermat's Last Theorem ===
Starting in mid-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's own specialist area.The
conjecture was seen by contemporary mathematicians as important, but extraordinarily difficult
or perhaps impossible to prove.
For example, Wiles's 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, with his from-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.
He dedicated all of his research time to this problem for over six 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 June 1993, he presented his proof to the public for the
first time at a conference in Cambridge.
He gave a lecture a day on Monday, Tuesday and Wednesday with the title 'Modular Forms,
Elliptic Curves and Galois Representations.'
There was no hint in the title that Fermat's last theorem would be discussed, Dr. Ribet
said.
... Finally, at the end of his third lecture, Dr. Wiles concluded that he had proved a general
case of the Taniyama conjecture.
Then, seemingly as an afterthought, he noted that that meant that Fermat's last theorem
was true.
Q.E.D.
In August 1993, it was discovered 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 May 1995 in a dedicated volume of the Annals of Mathematics.
=== Awards and honours ===
Wiles's proof of Fermat's Last Theorem has stood up to the scrutiny of the world's other
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 US Public Broadcasting Service's
science television series Nova.
His work and life are also described in great detail in Simon Singh's popular book Fermat's
Last Theorem.
Wiles has been awarded a number of major prizes in mathematics and science:
Junior Whitehead Prize of the London Mathematical Society (1988)
Elected a Fellow of the Royal Society (FRS) in 1989
Schock Prize (1995) Fermat Prize (1995)
Wolf Prize in Mathematics (1995/6) NAS Award in Mathematics from the National
Academy of Sciences (1996) Royal Medal (1996)
Ostrowski Prize (1996) Cole Prize (1997)
MacArthur Fellowhip (1997) Wolfskehl Prize (1997) – see Paul Wolfskehl
A silver plaque from the International Mathematical Union (1998) recognising his achievements,
in place of the Fields Medal, which is restricted to those under 40 (Wiles was 41 when he proved
the theorem in 1994) King Faisal Prize (1998)
Clay Research Award (1999) Pythagoras Award (Croton, 2004)
Shaw Prize (2005) The asteroid 9999 Wiles was named after Wiles
in 1999.
Knight Commander of the Order of the British Empire (2000)
The building at the University of Oxford housing the Mathematical Institute is named after
Wiles.
Abel Prize (2016) Copley Medal (2017)Wiles's 1987 certificate
of election to the Royal Society reads:
Andrew Wiles is almost unique amongst number-theorists in his ability to bring to bear new tools
and new ideas on some of the most intractable problems of number theory.
His finest achievement to date has been his proof, in joint work with Mazur, of the "main
conjecture" of Iwasawa theory for cyclotomic extensions of the rational field.
This work settles many of the basic problems on cyclotomic fields which go back to Kummer,
and is unquestionably one of the major advances in number theory in our times.
Earlier he did deep work on the conjecture of Birch and Swinnerton-Dyer for elliptic
curves with complex multiplication – one offshoot of this was his proof of an unexpected
and beautiful generalisation of the classical explicit reciprocity laws of Artin–Hasse–Iwasawa.
Most recently, he has made new progress on the construction of l-adic representations
attached to Hilbert modular forms, and has applied these to prove the "main conjecture"
for cyclotomic extensions of totally real fields – again a remarkable result since
none of the classical tools of cyclotomic fields applied to these problems.
== References ==
== External links == Quotations related to Andrew Wiles at Wikiquote
Media related to Andrew Wiles at Wikimedia Commons