I would love to know if an AI model could come up with certain theories of the old like Pythagoras' theorem, Euclid's formulations, Newton's gravity, Einstein's theories if provided and trained with sufficient amount of observable data available at those period of time. If this is possible can unsolved conjectures be proved by AI? Or even better can AI develop new theories or will it fail to come up with even basic mathematical operations by itself?
Some good examples of this are Lipson's work using evolutionary models, and Wu & Tegmark's work on a theory-based life-long learner, and Iten et al.'s work with deep neural networks. There are many, many, other research papers in this area, and there is a lot more work that is ongoing. The endgame for a lot of this work is the hope that we can synthesize new theories automatically.