Sir Andrew John Wiles (born 11 April 1953)
is an English mathematician and a
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
Research Professor at the
University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
, specializing in
number theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
. He is best known for
proving Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...
, for which he was awarded the 2016
Abel Prize
The Abel Prize ( ; no, Abelprisen ) is awarded annually by the King of Norway to one or more outstanding mathematicians. It is named after the Norwegian mathematician Niels Henrik Abel (1802–1829) and directly modeled after the Nobel Prizes. ...
and the 2017
Copley Medal
The Copley Medal is an award given by the Royal Society, for "outstanding achievements in research in any branch of science". It alternates between the physical sciences or mathematics and the biological sciences. Given every year, the medal is t ...
by the Royal Society.
He was appointed
Knight Commander of the Order of the British Empire
The Most Excellent Order of the British Empire is a British order of chivalry, rewarding contributions to the arts and sciences, work with charitable and welfare organisations,
and public service outside the civil service. It was established ...
in 2000, and in 2018, was appointed the first
Regius Professor
A Regius Professor
is a university Professor (highest academic rank), professor who has, or originally had, Monarchy of the United Kingdom, royal patronage or appointment. They are a unique feature of academia in the United Kingdom and Republic ...
of Mathematics at Oxford.
Wiles is also a
1997 MacArthur Fellow.
Education and early life
Wiles was born on 11 April 1953 in
Cambridge
Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge bec ...
, England, the son of
Maurice Frank Wiles (1923–2005) and Patricia Wiles (née Mowll). From 1952-1955, his father worked as the chaplain at
Ridley Hall, Cambridge
Ridley Hall is a theological college located on the corner of Sidgwick Avenue and Ridley Hall Road in Cambridge (United Kingdom), which trains men and women intending to take Holy Orders as deacon or priest of the Church of England, and member ...
, and later became the
Regius Professor of Divinity at the University of Oxford.
Wiles attended
King's College School, Cambridge
King's College School is a coeducational independent preparatory school for children aged 4 to 13 in Cambridge, England, situated on West Road off Grange Road, west of the city centre. It was founded to educate the choristers in the King's ...
, and
The Leys School, Cambridge
The Leys School is a co-educational independent school in Cambridge, England. It is a day and boarding school for about 574 pupils between the ages of eleven and eighteen, and a member of the Headmasters' and Headmistresses' Conference.
Histo ...
.
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 ''The Last Problem'', by Eric Temple Bell, 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
Kenneth Alan Ribet (; born June 28, 1948) is an American mathematician working in algebraic number theory and algebraic geometry. He is known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's ...
's 1986 proof of the epsilon conjecture
Epsilon (, ; uppercase , lowercase or lunate ; el, έψιλον) is the fifth letter of the Greek alphabet, corresponding phonetically to a mid front unrounded vowel or . In the system of Greek numerals it also has the value five. It was der ...
, which Gerhard Frey
Gerhard Frey (; born 1 June 1944) is a German mathematician, known for his work in number theory. Following an original idea of Hellegouarch, he developed the notion of Frey–Hellegouarch curves, a construction of an elliptic curve from a pur ...
had previously linked to Fermat's famous equation.
Career and research
In 1974, Wiles earned his bachelor's degree
A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six ...
in mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
at Merton College, Oxford
Merton College (in full: The House or College of Scholars of Merton in the University of Oxford) is one of the Colleges of Oxford University, constituent colleges of the University of Oxford in England. Its foundation can be traced back to the ...
. Wiles's graduate research was guided by John Coates, beginning in the summer of 1975. Together they worked on the arithmetic of elliptic curve
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point . An elliptic curve is defined over a field and describes points in , the Cartesian product of with itself. If ...
s with complex multiplication
In mathematics, complex multiplication (CM) is the theory of elliptic curves ''E'' that have an endomorphism ring larger than the integers. Put another way, it contains the theory of elliptic functions with extra symmetries, such as are visible wh ...
by the methods of Iwasawa theory
In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by (), as part of the theory of cyclotomic fields. In the ea ...
. He further worked with Barry Mazur on the main conjecture of Iwasawa theory
In mathematics, the main conjecture of Iwasawa theory is a deep relationship between ''p''-adic ''L''-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes satisfying the Kummer–Vandiver conjecture and ...
over the rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all ration ...
s, and soon afterward, he generalized this result to totally real field
In number theory, a number field ''F'' is called totally real if for each embedding of ''F'' into the complex numbers the image lies inside the real numbers. Equivalent conditions are that ''F'' is generated over Q by one root of an integer polyno ...
s.
In 1980, Wiles earned a PhD while at Clare College, Cambridge
Clare College is a constituent college of the University of Cambridge in Cambridge, England. The college was founded in 1326 as University Hall, making it the second-oldest surviving college of the University after Peterhouse. It was refounded ...
. After a stay at the Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
in Princeton, New Jersey
Princeton is a municipality with a borough form of government in Mercer County, in the U.S. state of New Jersey. It was established on January 1, 2013, through the consolidation of the Borough of Princeton and Princeton Township, both of whi ...
, in 1981, Wiles became a Professor of Mathematics
Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin as a "person who professes". Professors ...
at Princeton University
Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
.
In 1985–86, Wiles was a Guggenheim Fellow
Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...
at the Institut des Hautes Études Scientifiques
The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French research institute supporting advanced research in mathematics and theoretical physics. It is located in Bures-sur-Yvette, just ...
near Paris and at the École Normale Supérieure
École may refer to:
* an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée)
* École (river), a tributary of the Seine flowing in région Île-de-France
* École, Savoi ...
.
From 1988 to 1990, Wiles was a Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
Research Professor at the University of Oxford
, mottoeng = The Lord is my light
, established =
, endowment = £6.1 billion (including colleges) (2019)
, budget = £2.145 billion (2019–20)
, chancellor ...
, and then he returned to Princeton.
From 1994 to 2009, Wiles was a Eugene Higgins Professor at Princeton. He rejoined Oxford in 2011 as Royal Society Research Professor.[
In May 2018, Wiles was appointed ]Regius Professor
A Regius Professor
is a university Professor (highest academic rank), professor who has, or originally had, Monarchy of the United Kingdom, royal patronage or appointment. They are a unique feature of academia in the United Kingdom and Republic ...
of Mathematics at Oxford, the first in the university's history.
Proof of Fermat's Last Theorem
Starting in mid-1986, based on successive progress of the previous few years of Gerhard Frey
Gerhard Frey (; born 1 June 1944) is a German mathematician, known for his work in number theory. Following an original idea of Hellegouarch, he developed the notion of Frey–Hellegouarch curves, a construction of an elliptic curve from a pur ...
, Jean-Pierre Serre
Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the ina ...
and Ken Ribet
Kenneth Alan Ribet (; born June 28, 1948) is an American mathematician working in algebraic number theory and algebraic geometry. He is known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's ...
, it became clear that Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ...
could be proven as a corollary
In mathematics and logic, a corollary ( , ) is a theorem of less importance which can be readily deduced from a previous, more notable statement. A corollary could, for instance, be a proposition which is incidentally proved while proving another ...
of a limited form of the modularity theorem
The modularity theorem (formerly called the Taniyama–Shimura conjecture, Taniyama-Weil conjecture or modularity conjecture for elliptic curves) states that elliptic curves over the field of rational numbers are related to modular forms. And ...
(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.Simon Singh
Simon Lehna Singh, (born 19 September 1964) is a British popular science author, theoretical and particle physicist. His written works include ''Fermat's Last Theorem'' (in the United States titled ''Fermat's Enigma: The Epic Quest to Solve th ...
(1997). ''Fermat's Last Theorem''. For example, Wiles's ex-supervisor John Coates stated that it seemed "impossible to actually prove", and Ken Ribet
Kenneth Alan Ribet (; born June 28, 1948) is an American mathematician working in algebraic number theory and algebraic geometry. He is known for the Herbrand–Ribet theorem and Ribet's theorem, which were key ingredients in the proof of Fermat's ...
considered himself "one of the vast majority of people who believed twas 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 t"
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.
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 issue of the ''Annals of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
History
The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the ...
.''
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 #REDIRECT BBC #REDIRECT BBC
Here i going to introduce about the best teacher of my life b BALAJI sir. He is the precious gift that I got befor 2yrs . How has helped and thought all the concept and made my success in the 10th board exam. ...
...
about Fermat's Last Theorem. This was broadcast as an episode of the PBS science television series ''
'' with the title "The Proof".
''.
Wiles has been awarded a number of major prizes in mathematics and science:
* Junior