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Comment by againstapples

10 hours ago

At this rate AI will be doing all of the mathematics within 5 years, I don’t see why a mathematician would be worried about anything other than that at this point?

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againstapples

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avsegal  9 hours ago

Sure, but who will care?

If no one understands it, it may as well have not happened. There's not much incentive to understand or internalize the results generated by AI. A human operator gives it a prompt and it produces some lean proof no one wants to (maybe can) read.

Without the community of human mathematicians internalizing the proof, simplifying it, and re-communicating it to others we end up losing the main output of mathematics as an institution.

  • againstapples  7 hours ago

    Why would we assume AI will learn to solve millennium prize problems but will struggle with the easy part of doing the explaining? I think it’s too easy to predict that models 5 years from now will have the same limitations as the they do now, I would be amazed if this was true, GPT3 was the best model available 5 years ago.

    • avsegal  7 hours ago

      I'm not sure it's just a matter of explaining... If it's just explaining, than sure, that's something they already do well.

      The questions I have are:

        * is the structure of the generated proof even compressible/elegant to humans in a way that lends itself to being understood?
  * is it possible to transform the proofs to ones that are elegant without redoing all the work?
  * are there incentives to do any of this at scale?

      It's possible that a headline grabbing proof of a Millennium Prize problem generates enough incentive for people to simplify and gain understanding from it, but we run into problems when AI becomes the dominant approach for all of math. Although, maybe this is self-limiting? I guess it's possible we just ignore a bunch of AI generated proofs and only keep the ones people find comprehensible in a useful way.

      You can always hypothesize that at some point in the future (maybe 5 years? maybe later?) the models will be indistinguishable from humans and there will not be any functional difference at all. It's possible, but we're not there yet. And, as they say, past performance does not guarantee future results. Many technologies plateau at some hard ceiling of performance. Moore's law has had an unusually long run, but it's not a universal rule.