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.

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

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.

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.

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.

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

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.

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.

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

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