[minblaster]

This falls into the thinking “pure math is ok, since it will often become practical on a long enough time horizon”. Why not “pure math is ok because that’s what people want to do”?

Whether you can get funded for your explorations is a separate question, but no justification is needed for them.

[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.