...Could you not ask this of anyone who works on pure math problems? What on Earth are you talking about??

"Academics are paid paltry salaries, university departments are cash-strapped, why are they studying these abstruse math problems instead of building rockets?"

Successfully advancing fields of math and science is a good thing. Why would they not do it. Why would they not want to prove their increasingly intelligent computers are able to solve unsolved, complex math problems humans have failed to solve for centuries and then release the solutions to the public. What do you want them to do, not try to solve them?