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This question regards the new paper "Advancing mathematics by guiding human intuition with AI" by Davies et al. (Nature, 2021) (DOI link in open access) in which researchers at Deepmind collaborated with mathematicians to find new patterns with modern machine learning. (See also a different question about the same paper in a different spirit.)

What other areas or questions in math would be readily amenable to progress with similar techniques?

For example, are there other areas with many computable examples and many invariants whose precise relationships are far from known?

I also welcome more creative proposals to apply these techniques.

(I would suggest making this question community-wiki.)

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    $\begingroup$ See also mathoverflow.net/questions/390174/… and other similar questions that have been asked on MO already $\endgroup$
    – Sam Hopkins
    Commented Dec 6, 2021 at 16:31
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    $\begingroup$ @SamHopkins The new papers gives a clue to where to look that might suggest new answers - it suggests we should look for areas where two invariants are related (specifically, we expect we should be able to compute one in terms of the other) but the exact nature of the relationship is unknown. I don't know if this is enough to merit asking a new question, but I'm inclined to say it is. $\endgroup$
    – Will Sawin
    Commented Dec 6, 2021 at 16:37
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    $\begingroup$ Does this answer your question? What are possible applications of deep learning to research mathematics? $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Dec 6, 2021 at 18:18
  • $\begingroup$ Finding relationships between invariants is pretty much what Graffiti was all about, as I mentioned in my answer to that other question. $\endgroup$
    – Timothy Chow
    Commented Dec 7, 2021 at 16:45
  • $\begingroup$ @TimothyChow True, although not computing one in terms of the other - I think pretty much all of Graffiti's conjectures were one-sided inequalities. $\endgroup$
    – Will Sawin
    Commented Dec 7, 2021 at 18:19

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