I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.
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.
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 realized that anything to do with Fermat's Last Theorem generates too much interest.
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.
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.
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.
Here was a problem, that I, a ten year old, could understand and I knew from that moment that I would never let it go. I had to solve it.
I would wake up with it first thing in the morning, I would be thinking about it all day and I would be thinking about it when I went to sleep.