I like the idea that pure math is pure problem solving, for it's own sake. This quote captures it nicely: It can be of no practical use to know that Pi is irr

I like the idea that pure math is pure problem solving, for it's own sake. This quote captures it nicely: It can be of no practical use to know that Pi is irrational, but if we can know, it surely would be intolerable not to know. But isn't this still somewhat practical? Proving things gives us a mental workout, even if there is not apparent use. (Not the pure mathematicians would say, "Yes, though it's still worth doing in the absence of this.")