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Vote:   | Always try the problem that matters most to you. |
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Vote: | But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention. |
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Vote: | But the best problem I ever found I found in my local public library. 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. |
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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. |
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Vote: | Fermat couldn't possibly have had this proof. |
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Vote: | Fermat then considered the cubed version of this equation: x3 + y3 = z3. He raised the question, can you find solutions to the cubed equation? |
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Vote: | Fermat was a seventeenth century mathematician who wrote a note in the margin of his book stating a particular proposition and claiming to have proved it. |
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Vote: | Fermat was my childhood passion. |
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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. |
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Vote: | However impenetrable it seems, if you don't try it, then you can never do it. |
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Vote: | I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof. |
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Vote: | I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days. |
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Vote: | I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream. |
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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. |
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Vote: | I loved doing problems in school, I'd take them home and make up knew ones of my own. |
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Vote: | I realised that anything to do with Fermat's Last Theorem generates too much interest. |
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Vote: | I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal. |
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Vote: | 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. |
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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. |
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Vote: | 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. |
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Vote: | I've read letters in the early 19th century which said that it was an embarrassment to mathematics that Last Theorem had not been solved. |
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Vote: | If the proof we write down is really rigorous then nobody can ever prove it wrong. |
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Vote: | In a mathematical proof you have a line of reasoning consisting of a many, many steps, what are almost self-evident. |
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Vote: | In fact, he claimed that for the general family of equations: xn + yn = zn, where n is bigger than 2, it is impossible to find a solution. That's Fermat's Last Theorem. |
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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. |
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Vote: | 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. |
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Vote: | It mentioned a nineteenth century construction, and I suddenly realised that I should be able to use that to complete the proof. |
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Vote: | It's a 20th century proof, it couldn't have been done in the 19th century, let alone the seventeenth century. The techniques used in this proof just weren't around in Fermat's time. |
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Vote: | Just because we can't find a solution it doesn't mean that there isn't one. |
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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. |
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Vote: | My wife's only known me while I've been working on Fermat. |
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Vote: | Nobody had any idea how to approach Taniyama-Shimura but at least it was mainstream mathematics. |
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Vote: | Perhaps I can best describe my experience of doing mathematics in terms of a journey through a dark unexplored mansion. |
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Vote: | Pure mathematicians just love to try unsolved problems - they love a challenge. |
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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. |
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Vote: | So the romance of Fermat, which had held me all my life, was now combined with a problem that was professionally acceptable. |
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Vote: | The definition of a good mathematical problem is the mathematics it generates rather than the problem itself. |
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Vote: | The greatest problem for mathematicians now is probably the Riemann Hypothesis. |
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Vote: | The only way I could relax was when I was with my children. |
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Vote: | The problem with working on Fermat was that you could spend years getting nowhere. |
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Vote: | 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. |
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Vote: | There are proofs that date back to the Greeks that are still valid today. |
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Vote: | 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. |
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Vote: | 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. |
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Vote: | 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. |
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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. |
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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. |
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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. |
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Vote: | You can't really focus yourself for years unless you have undivided concentration, which too many spectators would have destroyed. |
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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. |