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

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 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.

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.

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.

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

Always try the problem that matters most to you.