Andrew Wiles

1953-

British Mathematician

Andrew Wiles, born in 1953 in Cambridge, England, is perhaps the most celebrated living mathematician. He became an instant celebrity when he announced in 1993 that he had proven Fermat's Last Theorem. The proof of this theorem, one of the most famous unsolved problems in the history of mathematics, had eluded mathematicians for over three centuries.

Fermat's last theorem states that the equation xⁿ+ yⁿ = zⁿ has no whole number solutions for any values of equation n greater than 2. In other words, equation x²+ y² = z² has whole number solutions (such as x=3, y=4, z=5), but x³+ y³= z³, x⁴+ y⁴= z⁴, etc., have no whole number solutions. The French mathematician Pierre Fermat (1601-1665) wrote in the margin of a book that he had discovered a remarkable proof for this theorem, but the margin was to small to contain it. For the next 350 years, many of the best mathematicians in the world attempted to find a solution to this problem.

Andrew Wiles first encountered the theorem that would be so important in his life when he was only ten years old. As a boy who had already taken an interest in mathematics, he could easily understand Fermat's Last Theorem. Later, as a teenager contemplating mathematics as a career, Wiles actually spent some time trying to prove it.

Wiles did become a mathematician, but his dream to prove Fermat's Last Theorem was pushed into the background while he attended to more immediate and attainable goals in mathematics. Wiles attended Oxford University, where he received a B.A. in 1974. He then received a Ph.D. from Cambridge University in 1980. In 1981 he came to the United States, where he spent a year at the Institute for Advanced Study at Princeton. In 1982 he was appointed professor of mathematics at Princeton. During this time Wiles was establishing himself as a young mathematician with a promising future. Although his research had seemingly led him away from Fermat's Last Theorem, it was actually preparing him for the great work that lay ahead.

Andrew Wiles's interest in the famous problem was rekindled when he heard that the American mathematician Ken Ribet had shown that there was a link between Fermat's Last Theorem and the Taniyama-Shimura conjecture, which had been proposed by two Japanese mathematicians, Yutaka Taniyama and Goro Shimura, in the 1950s. Ribet showed that if this conjecture were proven to be true, then Fermat's Last Theorem must also be true. Suddenly, Wiles had a legitimate reason to turn his interests to the problem that had captured his imagination as a youth. Interestingly, the Taniyama-Shimura conjecture involved the theory of elliptic curves, Wiles's research specialty since his days as a graduate student at Cambridge. The stage was set for one of the most unusual quests in the history of mathematics.

What made Wiles's eventual success so unusual was that he worked on the problem in almost total isolation for seven years. He was concerned that any announcement that he was working on Fermat's last theorem would result in much unwanted publicity. He preferred to work alone, usually at home, not even sharing with his colleagues at Princeton the true nature of his ongoing research.

Finally, in the summer of 1993 Wiles was ready to share his completed proof with the world. He chose to unveil his work at a conference at the Isaac Newton Institute in Cambridge. In a dramatic series of lectures, Wiles stunned the mathematical world with the solution to the most famous problem in the history of mathematics. The quest for a proof of Fermat's Last Theorem appeared to be over. All that remained was for the proof to pass the scrutiny of Wiles's peers.

Unfortunately, a section of Wiles's work did not stand up to this intense scrutiny. An error was found in one part of the long and difficult proof. At first Wiles was confident that he would be able to fix the error and save the proof, but as time went on the "correction" became more and more difficult. Wiles even asked for help from one of his former students, Richard Taylor. After a year of work, Wiles and Taylor appeared to be no closer to correcting the error in the proof. Remarkably, just as Wiles was about to give up, a sudden inspiration helped him to find the new approach that was needed to finish the proof.

The proof of Fermat's Last Theorem brought with it many honors for Andrew Wiles. He was elected a Fellow of the Royal Society of London and a foreign member of the National Academy of Sciences in the United States. In addition, he has received many other prizes and awards from all over the world. Today, Wiles continues to work as a research mathematician. Although he admits that solving Fermat's problem was a once-in-a-lifetime opportunity, he continues to search for answers to other difficult mathematical riddles.

TODD TIMMONS

HOW DOES A MATHEMATICIAN WORK?

Most people assume that a mathematician works by plugging numbers into formulas. But to create new mathematical knowledge, mathematicians must, of course, be creative. Creativity involves trying all sorts of ideas before finding one that makes sense. (Picture a novelist beginning a new work, with piles of crumpled-up paper on the floor, each representing a failed attempt to find the perfect opening line.) Andrew Wiles has compared his experience in creating mathematics to exploring a dark mansion:

You enter the first room of the mansion and it's completely dark. You stumble around bumping into furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of—and couldn't exist without—the many months of stumbling around in the dark that proceed them.