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" 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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" 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. "

Andrew Wiles

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Problems

Lost

" I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal. "

" There are proofs that date back to the Greeks that are still valid today. "

" Fermat said he had a proof. "

Andrew Wiles

Said

Had

" I loved doing problems in school. I'd take them home and make up new ones of my own. 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. "

" That particular odyssey is now over. My mind is now at rest. "

" Always try the problem that matters most to you. "

" I realized that anything to do with Fermat's Last Theorem generates too much interest. "

" 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. "

" The only way I could relax was when I was with my children. "

" 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. "

" I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days. "

" I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream. "

" But the best problem I ever found, I found in my local public library. "

" 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. "

" 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. "

" I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof. "

" However impenetrable it seems, if you don't try it, then you can never do it. "

" Just because we can't find a solution it doesn't mean that there isn't one. "

" The definition of a good mathematical problem is the mathematics it generates rather than the problem itself. "

" 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. "

" Pure mathematicians just love to try unsolved problems - they love a challenge. "

" 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. "

" 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. "