Comment by pixl97

>If we run into a real physical problem today, can we just have AI invent the math on the spot to solve the problem without a human having done the theoretical math in the past?

This depends on unanswered questions on what math actually is and it's causal connectivity.

Imagine we have problem A that needs to connect to math solution Z.

The problem is the A -> Z route can only occur in polynomial time in which you need to burn the visible universe to solve. So, that itself is not workable.

As you look at the problem space of A there are a potentially infinite number of paths you could take in the problem topology so again you'd have to brute force the path... mostly unworkable on a lot of problems.

The breakthroughs tend to occur when somewhere in between A and Z there is another mathematical construct M that can link them together. M was very likely discovered something so completely and wildly different you would never link them by brute force. By M existing you narrow the problem space to NP time. M might have sat in the toolbox 100 years unused before that point.