Andrew Wiles

Andrew John Wiles was born on April 11, 1953, in Cambridge, England. His father, Maurice Wiles, was an Anglican theologian who later held the Regius Professorship of Divinity at Oxford, so the boy grew up in an academic household where scholarship was ordinary dinner-table matter ^[1].

The defining moment of any Andrew Wiles biography comes early. At the age of ten, browsing in his local library in Cambridge, he found a book describing Fermat's Last Theorem: the claim, jotted by Pierre de Fermat in a book margin around 1637, that no three positive whole numbers can satisfy the equation a^n + b^n = c^n for any exponent n greater than 2. Fermat wrote that he had a marvelous proof the margin was too small to contain, and for over three centuries nobody could reconstruct one. Wiles later recalled that a problem simple enough for a schoolboy to understand, yet unsolved by the greatest mathematicians, seized his imagination and never let go ^[2].

He attended The Leys School in Cambridge before reading mathematics at Merton College, Oxford, where he took his bachelor's degree in 1974. He then returned to Cambridge for doctoral work at Clare College ^[1].

At Cambridge, Wiles studied under the Australian-born number theorist John Coates. Together they worked on the arithmetic of elliptic curves, the smooth cubic equations that would later prove central to his life's work, and made early progress on the Birch and Swinnerton-Dyer conjecture for a class of curves with complex multiplication ^[3]. Wiles completed his PhD in 1980.

His early career moved quickly through elite institutions: a junior research fellowship at Clare College, a period at Harvard as a Benjamin Peirce Assistant Professor, and time at the Institute for Advanced Study in Princeton. In 1982 he was appointed professor of mathematics at Princeton University, where he would spend most of his career ^[1].

During the 1980s Wiles built a formidable reputation in the theory of numbers. With Barry Mazur he proved the main conjecture of Iwasawa theory for rational numbers in 1984, a deep result about the behavior of arithmetic objects in towers of number fields ^[3]. To colleagues he was a first-rate specialist. Nothing yet suggested that he was quietly preparing an assault on the most famous open problem in mathematics.

The opening Wiles needed came in 1986. Ken Ribet, building on an idea of Gerhard Frey and work of Jean-Pierre Serre, proved that Fermat's Last Theorem would follow from a special case of the Taniyama-Shimura conjecture, which asserts that every elliptic curve over the rational numbers is modular, meaning it can be tied to a highly symmetric object called a modular form ^[2]. Suddenly the childhood dream connected to the mainstream machinery Wiles knew best.

He made an unusual decision: he would work on the problem alone and tell almost no one. For seven years, from 1986 to 1993, Wiles worked in his attic study at home in Princeton, publishing small papers from earlier research to avoid arousing suspicion, and confiding in only a few people, including his wife and, near the end, his colleague Nicholas Katz, who helped check the argument under the cover of a graduate course ^[2].

On June 23, 1993, at the Isaac Newton Institute in Cambridge, Wiles ended a series of three lectures by writing Fermat's Last Theorem on the board and remarking that he would stop there. The room erupted, and the story ran on front pages worldwide, including The New York Times under the headline 'At Last, Shout of Eureka in Age-Old Math Mystery' ^[4].

Triumph turned to crisis within months. During refereeing, Katz found a gap in a key step involving a technique known as the Euler system bound. Wiles spent over a year trying to close it, under intense public attention, and by late 1994 was close to conceding defeat. Then, on September 19, 1994, while examining why the flawed approach failed, he saw that it could be combined with an earlier method he had abandoned, based on Iwasawa theory. He later described that morning as the most important moment of his working life ^[2].

The repaired proof, completed with the help of his former student Richard Taylor, appeared in 1995 in the Annals of Mathematics as two papers: Wiles's 'Modular elliptic curves and Fermat's Last Theorem' and a joint Wiles-Taylor paper supplying the corrected step ^[5]. Among Andrew Wiles achievements, this ranks first by any measure: a 358-year-old problem was finally settled, and the semistable case of the Taniyama-Shimura conjecture was established along the way.

The honors that followed were extensive. Wiles received the Wolf Prize in 1995/96, the Royal Society's Copley Medal in 2017, and, because he was just past the age limit of forty for the Fields Medal, a special silver plaque from the International Mathematical Union in 1998 ^[1]. In 2016 the Norwegian Academy of Science and Letters awarded him the Abel Prize, often described as mathematics' equivalent of the Nobel, 'for his stunning proof of Fermat's Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory' ^[6]. He was appointed Knight Commander of the Order of the British Empire in 2000 ^[1].

For anyone asking who was Andrew Wiles beyond the theorem, the answer is a private, soft-spoken academic rather than a public performer. He married Nada Canaan, a molecular biologist, in 1988, and the couple have three daughters. Wiles has said that he told his wife about his secret project during their honeymoon, and that the birth of their children punctuated the years of hidden work ^[2].

Colleagues and interviewers consistently describe his patience and his tolerance for being stuck. In interviews around the Abel Prize, Wiles argued that the experience of being stuck is not failure but the normal state of doing research mathematics, and that accepting it is the main psychological hurdle for young mathematicians ^[7].

His story reached an unusually wide audience. The 1996 BBC Horizon documentary about the proof, directed by Simon Singh and John Lynch, showed Wiles moved to tears while recalling the 1994 breakthrough, and Singh's accompanying book Fermat's Last Theorem became an international bestseller ^[2].

Wiles remained at Princeton after the proof, serving as Eugene Higgins Professor of Mathematics and chairing the department for a period. In 2011 he returned to England to take up a Royal Society Research Professorship at the University of Oxford, joining Merton College, where he had been an undergraduate four decades earlier ^[1].

Oxford marked the connection publicly. In 2013 the university opened the Andrew Wiles Building, the home of its Mathematical Institute, and in 2018 Wiles was appointed the first Regius Professor of Mathematics at Oxford, a chair created to mark Queen Elizabeth II's ninetieth birthday ^[8].

He continues to work on the problems that framed his career, including the Birch and Swinnerton-Dyer conjecture, one of the Clay Mathematics Institute's Millennium Prize Problems, a list Wiles himself helped launch in 2000 ^[7].

The proof of Fermat's Last Theorem closed one chapter and opened several others. The techniques Wiles developed, particularly the modularity lifting methods refined with Taylor, became standard tools and led directly to the full proof of the modularity theorem for all elliptic curves over the rationals by Breuil, Conrad, Diamond, and Taylor in 2001, and to later advances such as the proof of the Sato-Tate conjecture ^[3].

Beyond the mathematics, the basic Andrew Wiles facts carry cultural weight: a child's ambition sustained for thirty years, seven years of solitary work, a public collapse of the proof, and a recovery that completed it. Few episodes in modern science have been retold as often, in documentaries, popular books, and even a musical sketch, and the story is regularly cited as an argument for long-horizon, curiosity-driven research ^[2].

Wiles himself has been careful to frame the theorem as a doorway rather than a destination. The equation Fermat scribbled has no known practical use; what mattered, he has said, is that pursuing it forced the creation of whole fields of mathematics, from Kummer's ideal numbers in the nineteenth century to the modularity machinery of the twentieth ^[6]. That view, of famous problems as engines for building theory, may be his most durable lesson ^[7].