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.
The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
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.
I never use a computer.
However impenetrable it seems, if you don’t try it, then you can never do it.
The greatest problem for mathematicians now is probably the Riemann Hypothesis.
Fermat said he had a proof.
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.
I grew up in Cambridge in England, and my love of mathematics dates from those early childhood days.
There are proofs that date back to the Greeks that are still valid today.
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.
Just because we can’t find a solution it doesn’t mean that there isn’t one.
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.
I loved doing problems in school.
The only way I could relax was when I was with my children.
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 really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.
But the best problem I ever found, I found in my local public library.
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.