The greatest problem for mathematicians now is probably the Riemann Hypothesis.
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.
The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
I hope that seeing the excitement of solving this problem will make young mathematicians realize that there are lots and lots of other problems in mathematics which are going to be just as challenging in the future.
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.
Pure mathematicians just love to try unsolved problems - they love a challenge.
However impenetrable it seems, if you don't try it, then you can never do it.
Always try the problem that matters most to you.
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.
Just because we can't find a solution it doesn't mean that there isn't one.
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