 Fermat said he had a proof. |
| 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 realized that anything to do with Fermat's Last Theorem generates too much interest. |
| 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. |
| 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. |
| Always try the problem that matters most to you. |
| There are proofs that date back to the Greeks that are still valid today. |
| 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. |
| 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. |
| 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. |
| I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream. |
| The definition of a good mathematical problem is the mathematics it generates rather than the problem itself. |
| 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. |
| However impenetrable it seems, if you don't try it, then you can never do it. |
| Pure mathematicians just love to try unsolved problems - they love a challenge. |
| 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. |
| But the best problem I ever found, I found in my local public library. |
| The greatest problem for mathematicians now is probably the Riemann Hypothesis. |
| 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. |
| 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. |
