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ur-whale • today at 6:36 PM • 0 replies • view on HN

I believe this whole AI vs. mathematicians story is only at the very beginning and that Mathematicians have an extremely narrow view of what's happening.

In particular, for Mathematicians worried about the inscrutability of AI-generated proofs and about the fact that Maths is first and foremost about understanding rather than proving for the sake of proving, they're vastly underestimating what AI will be able to deliver in years to come.

IMO, it's very likely that:

    - AI will not just be able to prove theorems but more importantly *increase* the speed at which we *intuitively* understand the phenomenon under scrutiny. All these AI companies are busy using AIs to prove stuff, none of them has yet tried to point an AI in the direction of making an existing proof more understandable and intuitive to a human. My bet is there will be AIs trying to find the shortest path (where shorter = easier to understand) from an existing body of knowledge to a theorem proof, thereby iteratively slowly but surely "compressing" the whole universe of Mathematical knowledge over time (and making it easier for humans to digest).

    - Same story for "discovering new mathematics", the other many-times-rehashed concern that AI-doing-math will impede that particular endeavor. Who's to say we can't define a bunch of criteria that quantify "interesting", point a bunch of AI's at it and press the button?