There are proofs that date back to the Greeks that are still valid today.
From Andrew Wiles
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.
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 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.
I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.
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.
I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.
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.
However impenetrable it seems, if you don't try it, then you can never do it.
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