Why such prejudice against "explicitly mathematical goals"? Why on Earth is this a danger? One way or another, people are going to amuse themselves -- via art, sports, sex, or drugs -- so it might as well be via mathematics, which even the most cynically "hard-headed" will concede is sometimes "useful".

Indeed, people will always amuse themselves. But that doesn't mean they deserve an academic field devoted to amusing people within their own little clique. Should there be Monty Python Studies, stocked with academics who (somehow) get paid to do nothing but write commentary on the same Monty Python sketches and performances?

No, because that would be ****ing stupid. Their work would only be useful to the small clique of people who self-select into the field, and who aspire to do nohting but ... teach Monty Python studies. Yet the exact same thing is tolerated with classical music studies, whose advocates always find just the right excuse for why their field isn't refined enough to make itself applicable outside the ivory tower, or to anyone who isn't trying to say, "Look at me, plebes! I'm going to the opera!"

With that said, I agree that this criticism doens't apply to the field of mathematics for the reasons you gave -- that it is likely to find uses that are not obvious now (case in point: the anti-war prime number researcher whose "100% abstract and inapplicable" research later found use in military encryption). So I think you're right about math. But you wouldn't be able to give the same defense of academic art/music fields.