Andrew Wiles

Mathematics is a journey of self-discovery, and it can teach you a lot about yourself.

The greatest mathematicians are not just brilliant, but also incredibly persistent.

The proof of Fermat's Last Theorem was a culmination of centuries of mathematical research.

Mathematics is a constant dialogue between intuition and rigor.

The most important thing is to never give up, even when the odds seem insurmountable.

It was the most important moment of my working life. Nothing I ever do again will mean as much.

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.

There's no other problem that will mean the same to me. I had this very rare privilege of being able to pursue in my adult life what had been my childhood dream.

I was so obsessed by this problem that for eight years I was thinking about it all the time—when I woke up in the morning, when I went to sleep at night.

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.

Perhaps the methods needed to take the next step may simply be beyond present day mathematics. Perhaps the methods I needed to complete the proof were just beyond present day mathematics.

You enter the first room of the mansion and it's completely dark. You stumble around bumping into the furniture, but gradually you learn where each piece of furniture is. Finally, after six months or so, you find the light switch, you turn it on, and suddenly it's all illuminated. You can see exactly where you were. Then you move into the next room and spend another six months in the dark. So each of these breakthroughs, while sometimes they're momentary, sometimes over a period of a day or two, they are the culmination of—and couldn't exist without—the many months of stumbling around in the dark that precede them.

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

It was like discovering a hole in the middle of your argument.

There are proofs that date back to the Greeks that are still valid today. They are a permanent part of knowledge.

The greatest problem is mathematics that is not yet understood.

I don't believe Fermat had a proof. I think he fooled himself into thinking he had a proof.

What you have to handle when you start doing mathematics as an older child or as an adult is accepting the state of being stuck. People don't get used to that. They find it very stressful.

The only way I could relax was when I was with my children. Young children simply aren't interested in Fermat. They just want to hear a story and they're not going to let you do anything else.

It's a wonderful feeling, but it's a very humbling feeling as well.