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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?

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  • $\begingroup$ Welcome to AI.SE. What do you mean by theories? One way to view Newton's laws, gravitation, Pythagoras theorem are just relational functions which given some input provide some specific output. Machine Learning can approximate such a function. But it cannot formalise it. So if you are talking about finding relationship between cause and effect (if it exists) an AI can do that. But it cannot prove that it exists explicitly. $\endgroup$ – DuttaA Mar 9 at 16:46
  • $\begingroup$ @DuttaA I'd argue that Pearl's work handles the cause/effect side pretty well, but if the goal is just to propose theories from data, then we don't need to establish causality. $\endgroup$ – John Doucette Mar 9 at 17:49
  • $\begingroup$ @JohnDoucette the thing about physics (IMO) is that to propose any theory we need a cause and effect. I think the problem with black holes up till recently was that people couldn't observe the physical effect of black holes, but theory (I'm not very sure) suggested it might exist. Now that technology can observe G waves (which has to be due to some physical effect due to G effect) they are probably researching more on this. So what I tried to say this data we generate is due to cause/effect. Our perception is a few electrical signals in our brain due to cause, resulting in effect (perception). $\endgroup$ – DuttaA Mar 9 at 18:37
  • $\begingroup$ @DuttaA Hmm. That's true. Usually the techniques I mentioned in my answer either include a temporal component (which lets you infer the direction of causality for a lot of physical phenomena). Judea Pearl's work actually goes further than that though, and lets you rule out a lot (perhaps all but one) casual story from data without a temporal component. $\endgroup$ – John Doucette Mar 9 at 22:11
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Yes.

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.

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  • $\begingroup$ It depends on what is assumed to be known. For instance Newton had to invent differential calculus along the way. $\endgroup$ – Mathieu Bouville Mar 31 at 16:20

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