Last modified on 26 August 2009, at 18:27

Talk:Andrew Wiles

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  • 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.
  • 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.
  • I would wake up with it first thing in the morning, I would be thinking about it all day and I would be thinking about it when I went to sleep.
  • 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.
  • I'm sure that some of them will be very hard and I'll have a sense of achievement again, but nothing will mean the same to me - there's no other problem in mathematics that could hold me the way that this one did.
  • 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.
  • If the proof we write down is really rigorous, then nobody can ever prove it wrong.
  • In a mathematical proof you have a line of reasoning consisting of many, many steps, that are almost self-evident.
  • It could be that the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof would not be invented for a hundred years.
  • It mentioned a nineteenth century construction, and I suddenly realised that I should be able to use that to complete the proof.
  • 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.
  • Just because we can't find a solution it doesn't mean that there isn't one.
  • 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.
  • My wife's only known me while I've been working on Fermat.
  • Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion.
  • 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.
  • Pure mathematicians just love to try unsolved problems - they love a challenge.
  • 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.
  • So the romance of Fermat, which had held me all my life, was now combined with a problem that was professionally acceptable.
  • That particular odyssey is now over. My mind is now at rest.
  • The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
  • The greatest problem for mathematicians now is probably the Riemann Hypothesis.
  • The greatest problem for mathematicians now is probably the Riemann Hypothesis. But it's not a problem that can be simply stated.
  • The only way I could relax was when I was with my children.
  • The problem with working on Fermat was that you could spend years getting nowhere.
  • Then when I reached college I realized that many people had thought about the problem during the 18th and 19th centuries and so I studied those methods.
  • There are proofs that date back to the Greeks that are still valid today.
  • There is a sense of melancholy. We've lost something that's been with us for so long, and something that drew a lot of us into mathematics.
  • There's also a sense of freedom. I was so obsessed by this problem that I was thinking about if all the time - when I woke up in the morning, when I went to sleep at night, and that went on for eight years.
  • There's no other problem in mathematics that could hold me the way that this one did.
  • There's no problem that will mean the same to me. Fermat was my childhood passion. There's nothing to replace it.
  • There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. The Last Theorem is the most beautiful example of this.
  • 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.
  • 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.
  • 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.
  • 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.
  • You can't really focus yourself for years unless you have undivided concentration, which too many spectators would have destroyed.