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Andrew Wiles (Biography)

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Popularity: 0 Vote:	Always try the problem that matters most to you.
Popularity: -1 Vote:	But the best problem I ever found, I found in my local public library.
Popularity: -1 Vote:	But what has made this problem special for amateurs is that there's a tiny possibility that there does exist an elegant 17th-century proof.
Popularity: 0 Vote:	Certainly one thing that I've learned is that it is important to pick a problem based on how much you care about it.
Popularity: 1 Vote:	Fermat couldn't possibly have had this proof. It's 150 pages long. It's a 20th-century proof. It couldn't have been done in the 19th century, let alone the 17th century. The techniques used in this proof just weren't around in Fermat's time.
Popularity: -2 Vote:	Fermat said he had a proof.
Popularity: 2 Vote:	Fermat was a 17th-century mathematician who wrote a note in the margin of his book stating a particular proposition and claiming to have proved it.
Popularity: -1 Vote:	Here was a problem, that I, a ten year old, could understand and I knew from that moment that I would never let it go. I had to solve it.
Popularity: 1 Vote:	However impenetrable it seems, if you don't try it, then you can never do it.
Popularity: 0 Vote:	I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.
Popularity: 1 Vote:	I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.
Popularity: 1 Vote:	I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream.
Popularity: 1 Vote:	I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.
Popularity: 0 Vote:	I knew that moment that the course of my life was changing because this meant that to prove Fermat's Last Theorem all I had to do was to prove the Taniyama-Shimura conjecture.
Popularity: -1 Vote:	I know it's a rare privilege, but if one can really tackle something in adult life that means that much to you, then it's more rewarding than anything I can imagine.
Popularity: 2 Vote:	I loved doing problems in school.
Popularity: -3 Vote:	I realized that anything to do with Fermat's Last Theorem generates too much interest.
Popularity: -3 Vote:	I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.
Popularity: -2 Vote:	I tried to fit it in with some previous broad conceptual understanding of some part of mathematics that would clarify the particular problem I was thinking about.
Popularity: -1 Vote:	I was just browsing through the section of math books and I found this one book, which was all about one particular problem - Fermat's Last Theorem.
Popularity: -2 Vote:	I was so obsessed by this problem that I was thinking about it all the time - when I woke up in the morning, when I went to sleep at night - and that went on for eight years.
Popularity: -1 Vote:	I'd always have a pencil and paper ready and, if I really had an idea, I'd sit down at a bench and I'd start scribbling away.
Popularity: 0 Vote:	I've read letters in the early 19th century which said that it was an embarrassment to mathematics that the Last Theorem had not been solved.
Popularity: 0 Vote:	If the proof we write down is really rigorous, then nobody can ever prove it wrong.
Popularity: 2 Vote:	In a mathematical proof you have a line of reasoning consisting of many, many steps, that are almost self-evident.
Popularity: -4 Vote:	In my early teens I tried to tackle the problem as I thought Fermat might have tried it. I reckoned that he wouldn't have known much more math than I knew as a teenager.
Popularity: 0 Vote:	It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.
Popularity: -1 Vote:	Just because we can't find a solution it doesn't mean that there isn't one.
Popularity: 0 Vote:	Mathematicians aren't satisfied because they know there are no solutions up to four million or four billion, they really want to know that there are no solutions up to infinity.
Popularity: -1 Vote:	My wife had heard of Fermat's Last Theorem, but at that time she had no idea of the romantic significance it had for mathematicians, that it had been such a thorn in our flesh for so many years.
Popularity: 2 Vote:	My wife's only known me while I've been working on Fermat.
Popularity: -1 Vote:	Nobody had any idea how to approach Taniyama-Shimura but at least it was mainstream mathematics.
Popularity: 0 Vote:	Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion.
Popularity: 0 Vote:	Perhaps the methods I needed to complete the proof would not be invented for a hundred years. So even if I was on the right track, I could be living in the wrong century.
Popularity: -1 Vote:	Pure mathematicians just love to try unsolved problems - they love a challenge.
Popularity: 2 Vote:	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.
Popularity: -2 Vote:	So the romance of Fermat, which had held me all my life, was now combined with a problem that was professionally acceptable.
Popularity: 0 Vote:	That particular odyssey is now over. My mind is now at rest.
Popularity: -1 Vote:	The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
Popularity: -1 Vote:	The greatest problem for mathematicians now is probably the Riemann Hypothesis. But it's not a problem that can be simply stated.
Popularity: 2 Vote:	The problem with working on Fermat was that you could spend years getting nowhere.
Popularity: 1 Vote:	There are proofs that date back to the Greeks that are still valid today.
Popularity: 3 Vote:	There's no other problem in mathematics that could hold me the way that this one did.
Popularity: 1 Vote:	There's no problem that will mean the same to me. Fermat was my childhood passion. There's nothing to replace it.
Popularity: -2 Vote:	Walking has a very good effect in that you're in this state of relaxation, but at the same time you're allowing the sub-conscious to work on you.
Popularity: -2 Vote:	We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention.
Popularity: 2 Vote:	Well, some mathematics problems look simple, and you try them for a year or so, and then you try them for a hundred years, and it turns out that they're extremely hard to solve.
Popularity: 0 Vote:	When I got stuck and I didn't know what to do next, I would go out for a walk. I'd often walk down by the lake.
Popularity: 1 Vote:	You can't really focus yourself for years unless you have undivided concentration, which too many spectators would have destroyed.
Popularity: 1 Vote:	Young children simply aren't interested in Fermat. They just want to hear a story and they're not going to let you do anything else.

Biography

Andrew John Wiles (born April 11, 1953) is a British mathematician living in the United States. In 1974, he received his bachelor's degree from the University of Oxford. He then completed his Ph.D. at the University of Cambridge in 1979 and is currently a Professor at Princeton University. In one of the great success stories in the history of mathematics, Wiles (with help from Richard Taylor) proved Fermat's Last Theorem in 1994.

Andrew Wiles should not be confused with André Weil, another famous mathematician who, like Wiles, has done important work in elliptic curves.

Before this result, Andrew Wiles had done outstanding work in number theory. In work with John Coates he obtained some of the first results on the famous Birch and Swinnerton-Dyer conjecture, and he also did important work on the main conjecture of Iwasawa theory.

Fermat's Last Theorem (FLT) asserts that there are no positive integers x, y, and z such that

in which n is a natural number greater than 2.

Wiles had been inspired by the problem as a child when he encountered it in E.T. Bell's book, The Last Problem. His odyssey towards the final proof began in 1985 when Ken Ribet, inspired by ideas of Jean-Pierre Serre and Gerhard Frey, proved that FLT would follow from another conjecture of Taniyama, Shimura and Weil, to the effect that every elliptic curve can be parametrized by modular forms. Though less familiar than Fermat's Last Theorem, the Taniyama-Shimura theorem is the more significant of the two, because it touches on truly deep currents in number theory. No one had any idea how to prove it. Working in absolute secrecy, and sharing his ideas and progress only with Nicholas Katz, another professor of mathematics at Princeton, Wiles eventually developed a proof of the Taniyama-Shimura-Weil conjecture, and hence of FLT. The proof is a tour de force introducing many new ideas.

Wiles was uncharacteristically dramatic in revealing the proof. He arranged to give three lectures at the Newton Institute, Cambridge England, in June of 1993. He did not announce the topic of the lectures in advance, and as the audience and the world became aware of where the lectures were headed, the audience swelled so that the third lecture was to an overpacked room. At the end of the third lecture, he announced "(...) this proves Fermat's Last Theorem. I'll stop here", and received a standing ovation.

In the following months, the manuscript of the proof was circulated only to a small number of mathematicians while the world awaited. The first version of the proof depended on the construction of an object called an Euler system, and this aspect proved problematical, a flaw emerged during peer review of the subtle and complex mathematics involved. For almost a year it began to seem that Wiles' proof was destined like so many others to be fatally flawed, and that although he had made many important discoveries, the ultimate goal had eluded him. Wiles was on the point of giving up finally, when he decided to have one last try at solving the last remaining problem in his proof in collaboration with Richard Taylor, one of his former PhD students in 1994. He commented:
The final version of Wiles' proof, which therefore differs from his original one, was published in the Annals of Mathematics 141 (1995), p. 443-551, together with another, supporting article by Wiles and Taylor titled "Ring-theoretic properties of certain Hecke algebras" (Annals of Mathematics 141 (1995), p. 553-572) relating to the final step of discovery.

Wiles was awarded several prizes in mathematics: Schock Prize (1995), Royal Medal (1996), Cole Prize (1996), Wolf Prize (1996) and Shaw Prize (2005).