3 ms·

I'd rather wait for independent seasoned mathematicians to verify such claims first before someone at said AI lab posting a claim about solving a proof online.

• jibal 3mo ago
  It's a counterexample, not a proof. A schoolchild can confirm it.
  • tptacek 3mo ago
    Well, I mean, come on. There aren't that many minors who have taken basic multivariable calculus. But there are a lot of (technical) teenagers who could confirm it!
• tptacek 3mo ago
  It's a Jacobian determinant and three points. You can check this yourself in Sage. The author is a Princeton math doctorate.
  • markasoftware 3mo ago
    playing devil's advocate a little bit, but wikipedia does have a policy against original research. If you published an obviously correct counterexample to wikipedia which is not anywhere else on the internet (or in a book, etc), the rules are clear: the counterexample must be removed. in this case it's not original research, because there's a tweet by someone with a good reputation, and plenty of comments on said tweet corroborating the result. But it's a more sketchy "secondary source" than most wikipedia references and some caution on the part of the editors is not out of place. (saying this as the person who made the original edit to the wikipedia page adding the counterexample)
    • tptacek 3mo ago
      I'm not complaining about Wikipedia here, just noting for the thread: it's a vector of polynomials. It has a nonsingular Jacobian. Provided with it are 3 distinct points it sends to the same point; it can't be invertible. What Wikipedia says about this doesn't matter, does it?
      • bonzini 3mo ago
        Wikipedia does have a rule allowing "routine calculations" https://en.wikipedia.org/wiki/Wikipedia:No_original_research#Routine_calculations https://en.wikipedia.org/wiki/Wikipedia:No_original_research... Of course given the magnitude of the statement a bit of care is warranted, but the rules do allow it.
        • tptacek 3mo ago
          I think Wikipedia has very sane processes. I'm just saying that process isn't useful to this thread. It's like if I found a SHA2 collision. I'd probably have to be an absurdly talented (and lucky) cryptanalyst to do that, but anybody on the thread could trivially confirm my finding.
        • redsocksfan45 3mo ago
          [dead]
    • CamperBob2 3mo ago
      Wikipedia's editors won't be happy until the site has joined Stack Overflow in self-owned oblivion.
    • endgame 3mo ago
      The talk page about the conjecture clarifies WP:RSSELF: https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources#Self-published_sources_(online_and_paper) https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources#Sel... > Self-published expert sources may be considered reliable when produced by an established expert on the subject matter, whose work in the relevant field has previously been published by reliable, independent publications.
• rowbin 3mo ago
  Maybe have a seasoned mathematician check if the counterexample is really bogus before saying people fell for ai psychosis.
  • tptacek 3mo ago
    I'm pretty sure you can just check this for yourself. The Sage POC is like 8 lines.
    • aleph_minus_one 3mo ago
      This assumes that you already have Sage installed, and you have some working knowledge in using Sage.
      • tptacek 3mo ago
        You also have to know how to take a Jacobian, so I can see how this might be a live controversy on HN.
  • Larrikin 3mo ago
    [flagged]
• sciyoshi 3mo ago
  Looks like this has already been formalized: https://github.com/deancureton/jacobian https://github.com/deancureton/jacobian
  • bugufu8f83 3mo ago
    To be clear, this is not the kind of thing where a Lean formalization provides any value at all. It's like formalizing the answer to a high school algebra problem. The counterexample is obviously correct.
    • sciyoshi 3mo ago
      Indeed. I was mainly responding to the comment about waiting for "independent seasoned mathematicians to verify", whereas in this case it is easy enough to convince oneself of the counterexample's correctness.
• urams 3mo ago
  It's a Princeton math PhD who posted. The verification is quite straightforward and was posted by the tweet author. Wolfram would have to also be producing incorrect outputs for the counterexample to be false. The counterexample works as claimed and conjecture has been proven wrong.
• Certhas 3mo ago
  This topic really is a testament to people's willingness to opine on things they have absolutely no clue about. A first year undergraduate can completely check this counterexample in ten minutes. The original post even linked Wolfram alpha for the calculations. And if you genuinely try you can very quickly understand using only high school math and a bit of Wikipedia that this counterexample is vanishingly unlikely to be wrong, even if you don't do the calculations yourself.