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

Always try the problem that matters most to you.

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.

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.

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