Andrew Wiles

Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost.

The proof uses a very wide array of tools, and that's what makes it so special.

I had this incredible confidence that I was the one to solve it.

It's a bit like going up a mountain. You think you see the top, but when you get there, you see there's another top behind it.

I wanted to solve this problem because it's a problem that looked so simple, and yet all the great mathematicians in history couldn't solve it.

Sometimes you realize that nothing else has ever interested you as much.

The problem is, you can't really force it. You have to be patient and let the ideas come.

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. Without a break, day after day, week after week.

There is a sense of melancholy. You have lost something that has been a part of you for a very long time.

The best mathematics is not just a solution to a problem, it's a new way of thinking.

I knew that if I didn't try, I would always regret it.

It's not just about one person. It's about the whole mathematical community.

You have to have a certain tolerance for ignorance, for being at sea, for being in the dark.

The moment of discovery is very brief. It's a moment, and then it's over.

I don't think many people have the opportunity to experience that kind of sustained focus on one problem.

It's like a piece of art. You have to step back and look at the whole thing.

The beauty of mathematics is that it is eternal.

I made a very conscious decision to focus exclusively on the problem.

The gap in the proof was something that was very hard to accept.

You are always afraid that you might be wasting your time.