I think you mean specific problems. Hard math problems are extreme outliers in fhe realm of computer science and there are plenty of suitably qualified people in the maths side. That said, less hard problems, more suitable programmers with undergraduate maths, are quite common and a growing area. This may preclude those that are self taught and lacking more advanced, but not highly advanced math.

I don't even think it's that necessary to solve hard problems, at least in most fields.

You can do a lot with general coding knowledge, however, I've found the CS fundamentals to be most useful for optimization.

it depends on what do we define as "hard problems"