We have AI that can and has produced new mathematics. I don't understand what you think AI is. Machine learning enables computers to make decisions about things without explicit programing, and it is done by learning from data. It is a sort of intelligence, if not to the degree that we want (yet).

I agree with your distinction between AI and AGI. Hasn't ML failed to produce AGI, but been wildly successful in producing AI?

What you call AGI now is what I used to call AI and ML was just ML and statistics to me. But now AI can be everything from hidden markov chains to the computer player in a game as long as it makes a decision or prediction in some kind of of process, no matter how dumb. I gave up arguing about it long ago.