Always try the problem that matters most to you.
I really believed that I was on the right track, but that did not mean that I would necessarily reach my goal.
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.
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.
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.
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.
There are proofs that date back to the Greeks that are still valid today.
I had this rare privilege of being able to pursue in my adult life, what had been my childhood dream.
The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.
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