There's a kind of sticking point in physics combining general relativity with quantum mechanics in a mathematically consistent way. It hasn't been done yet and is mostly maths so your math grinders could have a go. It's maybe the area I'm most interested in with mathematical AI. I've long had a hunch things are stuck there because the math is a bit hard for human brains.

>But what I wonder: can we legitimately grind on Physics or curing cancer?

If we can enable a feedback loop, yes absolutely. But feedback loops for things in the physical world like these are measured in months per cycle usually.