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 hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.
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.
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.
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.
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.
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
