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.
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.
I realized that anything to do with Fermat's Last Theorem generates too much interest.
There's also a sense of freedom. I was so obsessed by this problem that I was thinking about if 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 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 don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.
Am I really a good mathematician?
As a poet and as a mathematician, he would reason well; as a mere mathematician, he could not have reasoned at all.
Mathematicians are like managers - they want improvement without change.