3 ms·

This sounds big. Can some mathematicians please weigh in.

kevinventullo 3y ago
Seems to be in the spirit of the “Ramanujan Machine” from a few years ago, which… well here is one prominent mathematician’s take: https://www.galoisrepresentations.com/2019/07/17/the-ramanujan-machine-is-an-intellectual-fraud/ https://www.galoisrepresentations.com/2019/07/17/the-ramanuj... Until they prove a new irrationality result I personally won’t be paying much attention.
- nonrandomstring 3y ago
  Thanks. This is a fascinating rabbit hole in itself regardless of the merit of the claims, because I was unaware of how rapidly advancing experimental mathematics is banging heads with traditional work. I see the problem, which goes deep into issues of ML/AI, that interesting results without "proofs of understanding" are "Idiotic" in the original Greek sense - that they stand alone and separate from the wider corpus - leaving someone else the work of "connecting them up", as it were. Am I even half right?
  - kevinventullo 3y ago
    To be honest, we’re not even to that point. There have been no major mathematical proofs to come out of ML/AI, regardless of understanding. I say “major” because, sure, you can prove something “new” in a constrained framework that lends itself to different types of search techniques, but this is sort of akin to writing down the “undiscovered” mathematical statement that X*Y=Z, where X and Y are some super large numbers whose product has never been explicitly computed. So, if an ML technique came out and proved the Riemann hypothesis or that zeta(5) was irrational, even if the proof was totally inscrutable, that would be absolutely groundbreaking. At the risk of hyperbole, potentially the most important result of my lifetime; not because of the result per se, but because it would signal a shift in how all of mathematics is done.
    - nonrandomstring 3y ago
      Thanks for your reply Kevin. just to share what I was thinking while out walking this morning. I doubt very much we'd see much come out of ML in the capacity of exhaustive search or pattern seeking vis a vis "large models", because maths is to language as intergalactic space is to a teacup. Doesn't feel like there's a generative potential for stumbling upon "proofy-like" things the way it works with natural language. But I imagine AI in a few years being able to train on a great corpus of known proofs. We show it how to do constructive, deconstructive, contradiction, induction, equivalence... And hopefully what it gives us is a meta insight into the nature of proofs themselves, perhaps by finding new techniques, or revealing refutations... that sort of thing. Those would be tools useful to mathematicians, but I think the BIG finds will still be by made humans who think for 10,000 hours about a problem.
bigbacaloa 3y ago
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Seems to be in the spirit of the “Ramanujan Machine” from a few years ago, which… well here is one prominent mathematician’s take: https://www.galoisrepresentations.com/2019/07/17/the-ramanujan-machine-is-an-intellectual-fraud/ https://www.galoisrepresentations.com/2019/07/17/the-ramanuj... Until they prove a new irrationality result I personally won’t be paying much attention.

nonrandomstring 3y ago
Thanks. This is a fascinating rabbit hole in itself regardless of the merit of the claims, because I was unaware of how rapidly advancing experimental mathematics is banging heads with traditional work. I see the problem, which goes deep into issues of ML/AI, that interesting results without "proofs of understanding" are "Idiotic" in the original Greek sense - that they stand alone and separate from the wider corpus - leaving someone else the work of "connecting them up", as it were. Am I even half right?
- kevinventullo 3y ago
  To be honest, we’re not even to that point. There have been no major mathematical proofs to come out of ML/AI, regardless of understanding. I say “major” because, sure, you can prove something “new” in a constrained framework that lends itself to different types of search techniques, but this is sort of akin to writing down the “undiscovered” mathematical statement that X*Y=Z, where X and Y are some super large numbers whose product has never been explicitly computed. So, if an ML technique came out and proved the Riemann hypothesis or that zeta(5) was irrational, even if the proof was totally inscrutable, that would be absolutely groundbreaking. At the risk of hyperbole, potentially the most important result of my lifetime; not because of the result per se, but because it would signal a shift in how all of mathematics is done.
  - nonrandomstring 3y ago
    Thanks for your reply Kevin. just to share what I was thinking while out walking this morning. I doubt very much we'd see much come out of ML in the capacity of exhaustive search or pattern seeking vis a vis "large models", because maths is to language as intergalactic space is to a teacup. Doesn't feel like there's a generative potential for stumbling upon "proofy-like" things the way it works with natural language. But I imagine AI in a few years being able to train on a great corpus of known proofs. We show it how to do constructive, deconstructive, contradiction, induction, equivalence... And hopefully what it gives us is a meta insight into the nature of proofs themselves, perhaps by finding new techniques, or revealing refutations... that sort of thing. Those would be tools useful to mathematicians, but I think the BIG finds will still be by made humans who think for 10,000 hours about a problem.

bigbacaloa 3y ago

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