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