[fny]

My point is not that "pure math is ok" since it will eventually become practical. My point is that its not a vacuous waste of time as the OP suggests. Exploring a math problem for fun is not like sitting on your couch and twiddling your thumbs.

Yes, sitting on a couch arguably has value to someone as leisure, but its pretty clear that studying puzzles and exploring the possibilities of rigorous logical thought also happens to be valuable.

This is why we pay and award people to think about these problems rather than sit on couches.