I wonder if AI can come up with mathematical conjectures. As in, they feel it's right but can't prove it. What even happened in Fermat's brain to sense it was true?
It is capable of applying know heuristics and general principles in places where they haven't been applied and in this sense very much capable of generating conjectures in much the same way a person does. It's ability to employ a diversity of techniques coupled with it's computational power differentiate it from a human researcher. It still needs guidance to work well, but I've already changed my daily work flow as a research mathematician to incorporate use of AI.
Right. Once we see AI start delivering on the creative & intuition side of things that's going to be awesome. Until then I guess we'll live with exhaustive exploration of problem spaces by orchestrating swarms of agents...?