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.

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.

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.

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

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 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.

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

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

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.

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.

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

The greatest problem for mathematicians now is probably the Riemann Hypothesis.