About Andrew Wiles: Sir Andrew John Wiles is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory. He is most notable for proving Fermat's Last Theorem.
However impenetrable it seems, if you don't try it, then you can never do it.
Always try the problem that matters most to you.
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.
That particular odyssey is now over. My mind is now at rest.
The only way I could relax was when I was with my children.
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.
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.
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.
The greatest problem for mathematicians now is probably the Riemann Hypothesis.
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. There's no reason why these problems shouldn't be easy, and yet they turn out ...
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.