At ten, Andrew Wiles found a book about Fermat’s Last Theorem in his local library and became fascinated by a problem he could understand but no one had solved. Decades later, after years of private work, he announced a proof. A flaw emerged; with his former student Richard Taylor, Wiles found a way through it. The completed work did more than settle a famous question: it connected areas of mathematics and became one of the defining achievements of his career.
A Cambridge childhood and an Oxford education
Wiles was born in Cambridge on 11 April 1953, the son of theologian Maurice Frank Wiles and Patricia Wiles. He spent much of his childhood in Nigeria, where his father worked as a chaplain, and began his formal schooling there. He later attended King’s College School and The Leys School in Cambridge. As a ten-year-old, he encountered Fermat’s Last Theorem in Eric Temple Bell’s book The Last Problem, found in a local library on his way home from school. Its simple statement and elusive proof caught his imagination. He eventually set aside the ambition to solve it, recognising that he first needed to learn much more mathematics.
Wiles studied mathematics at Merton College, Oxford, graduating in 1974. His graduate research began under John Coates, with whom he worked on elliptic curves using methods from Iwasawa theory. He earned his PhD at Clare College, Cambridge, in 1980. His research extended beyond the problem that had captivated him as a child: he worked on the main conjecture of Iwasawa theory and on mathematical structures that would later prove central to his attack on Fermat’s question.
After a period at the Institute for Advanced Study in Princeton, Wiles became a professor of mathematics at Princeton University in 1981. He held appointments at Oxford and Princeton during his career, and returned to Oxford in 2011 as a Royal Society Research Professor. His professional life therefore joined a British mathematical education and later Oxford work with a long period of research in the United States.
Why Fermat’s problem could be approached
Fermat’s Last Theorem concerns the equation an + bn = cn. It says that no positive whole numbers a, b and c satisfy it when the whole-number exponent n is greater than two. Pierre de Fermat wrote a claim about the result in the margin of a book in the seventeenth century, but left no proof. The statement was accessible enough to invite generations of attempts, while its proof proved exceptionally difficult.
The route Wiles pursued depended on a connection between the theorem and the modularity of elliptic curves. Work by Gerhard Frey, Jean-Pierre Serre and Ken Ribet helped establish that proving a particular case of the modularity conjecture would imply Fermat’s Last Theorem. Ribet’s 1986 work showed that a counterexample to Fermat’s equation would lead to a curve incompatible with that case of modularity. Wiles, whose own research concerned elliptic curves and related number theory, saw a way to turn that implication into a proof.
He devoted his research effort to the challenge for more than six years, working in near-total secrecy and telling almost no one beyond his wife. The method drew together elliptic curves, modular forms and Galois representations. Rather than trying to attack Fermat’s equation directly, Wiles set out to prove the necessary modularity result for semistable elliptic curves. That result, combined with Ribet’s work, would rule out the counterexample that a failure of Fermat’s Last Theorem would require.
An announcement, a flaw and a completed proof
In June 1993, Wiles presented his work in a series of lectures at a Cambridge conference. The titles did not advertise Fermat’s Last Theorem; the implication became clear as the lectures progressed. The announcement drew intense attention, but scrutiny of the proof uncovered a flaw, identified in August. It concerned the mathematical argument needed to complete the modularity result. The early announcement was therefore not the end of the work.
Wiles spent more than a year trying to repair the gap. On 19 September 1994, he had an insight that allowed him to circumvent the difficulty. Working with Richard Taylor, his former student, he completed the argument. Their papers were published in a dedicated issue of Annals of Mathematics in May 1995. The proof established the required modularity result for semistable elliptic curves and, through its connection to Fermat’s equation, proved the theorem.
The correction was an essential part of the achievement, not an incidental postscript. Wiles’s initial proof did not withstand examination, and the final result depended on further work with Taylor. The episode also shows how a major proof is tested: a striking announcement can bring a result into view, but mathematical confidence depends on resolving the details and publishing an argument that other specialists can scrutinise.
Work beyond the theorem
Fermat’s Last Theorem is the result for which Wiles is best known, but his mathematical work was wider. He proved the main conjecture of Iwasawa theory for the rational numbers and later generalised the result to totally real fields. His research brought together techniques and ideas from different parts of number theory. Mathematicians building on his work, including Taylor, Brian Conrad, Fred Diamond and Christophe Breuil, proved the full modularity theorem by 2000.
Wiles’s proof also mattered because it supplied tools and methods that other mathematicians could use. In 2016, when he received the Abel Prize, he described the work as opening a new way into the Langlands programme, a broad effort to connect different areas of mathematics. This is a more precise account of its reach than claims that the proof directly transformed fields such as cryptography or algorithm design: its documented influence lies in mathematics, where its methods helped advance related results and research programmes.
His honours include the Royal Society’s Royal Medal, the Wolf Prize, the Shaw Prize and the Abel Prize. He was elected a Fellow of the Royal Society in 1989 and appointed Knight Commander of the Order of the British Empire in 2000. In 2018 he became the first Regius Professor of Mathematics at Oxford. These recognitions reflect both the resolution of the famous problem and the continuing significance of his broader mathematical contributions.
Why Andrew Wiles deserves a place in British Legacy
Wiles’s place in British Legacy rests on a specific achievement and a clear institutional connection. Born in Cambridge, educated at Merton College, Oxford, and later a research professor and Regius Professor at Oxford, he is an English mathematician whose career has been closely linked to British universities. His proof of Fermat’s Last Theorem was not a simple flash of inspiration: it grew from years of work in number theory and from a chain of results connecting elliptic curves, modular forms and the equation Fermat had left unresolved. By proving the relevant case of the modularity conjecture, Wiles supplied the missing step that made the theorem follow.
The importance of that work extends beyond the satisfaction of answering a centuries-old question. Wiles developed techniques that other mathematicians could build on, and the work of Taylor, Conrad, Diamond and Breuil subsequently established the full modularity theorem. Wiles himself placed the achievement within the larger ambition of the Langlands programme, which seeks connections between branches of mathematics. His career also offers a valuable account of how difficult research proceeds: a proof announced in 1993 contained a flaw, and the completed argument emerged through sustained effort and collaboration before publication in 1995. That combination of deep mathematical contribution, lasting influence and documented British academic service makes his story a substantive part of the country’s intellectual history.
Sources
Andrew Wiles — Wikipedia revision 1377966997
Adapted in part from Andrew Wiles by Wikipedia contributors, under CC BY-SA 4.0. Text has been edited and combined with the existing article; this adapted text is shared under the same licence. Contributor history.