I'm with @nilesh on this one, and not exactly sure how merely the existence of a solution precludes the advancement of human knowledge. If a problem is "solved" (say, symbolically verified) without any insights gained, it doesn't seem very interesting to the profession.
Navier-Stokes is a bit different (because there's a prize attached, so "scooping" matters), but almost all interesting problems don't have any prizes attached.
Navier-Stokes is a bit different (because there's a prize attached, so "scooping" matters), but almost all interesting problems don't have any prizes attached.