Presumably some combination of marketing existing models and training/improving future models.

My point was about what is and isn't the responsibility of AI labs. Why should they be required to invest more (or fewer) resources into math than they otherwise want to?

(If you ask me, safety and security are what they need to invest more into.)

Simple. Because they are benefiting from output of the math community, in fact they were required for creating these models in the first place.

...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?

They are not advancing the field. At least they didn't in the case of the N-S debacle. The model most likely used the conversation text of a mathematician which had discovered and was pursuing a new avenue towards the goal, then pumped millions upon millions to hurry up ahead to an opaque solution which leaves no-one the wiser, beyond just settling a theoretical question. The only impact on science is to deflate the potential minds who might have been motivated to join the effort.