Always try the problem that matters most to you.

I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream.

Pure mathematicians just love to try unsolved problems - they love a challenge.

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.

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

The greatest problem for mathematicians now is probably the Riemann Hypothesis.

Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room...

I never use a computer.

Fermat said he had a proof.

I know it's a rare privilege, but if one can really tackle something in adult life that means that much to you, then it's more rewarding than anything I can imagine.

However impenetrable it seems, if you don't try it, then you can never do it.

I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.

I carried this problem around in my head basically the whole time. 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 distraction I would have the same thing going round and round in my mind.

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. There's no reason why these problems shouldn't be easy, and yet they turn out to be extremely intricate. [Fermat's] Last Theorem is the most beautiful example of this.

Just because we can't find a solution it doesn't mean that there isn't one.

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.

Then when I reached college I realized that many people had thought about the problem during the 18th and 19th centuries and so I studied those methods.

Mathematics... is a bit like discovering oil. ... But mathematics has one great advantage over oil, in that no one has yet ... found a way that you can keep using the same oil forever.

We've lost something that's been with us for so long, and something that drew a lot of us into mathematics. But perhaps that's always the way with math problems, and we just have to find new ones to capture our attention.

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.

There are proofs that date back to the Greeks that are still valid today.

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.

That particular odyssey is now over. My mind is now at rest.

But the best problem I ever found, I found in my local public library.

I loved doing problems in school.

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