Yes, of course the government can outlaw solving certain math problems. Anything on a computer can be represented by math. "Solving a math problem" can create Bitcoins or hack a computer system or recreate CSAM or recreate copyrighted or patented works or send a threat to someone.

Calculating a hash for Bitcoin and then broadcasting it assumedly has the same level of First Amendment protection as calculating a hash for someone else's password and then broadcasting it.