4 ms·

I suspect the LLM was able to synthesize a counterexample because of the availability of a lot of prior work: > The Jacobian conjecture is notorious for the la

• tptacek 3mo ago
  How does that work in this case? What do those proofs do to help find this counterexample?
  • hliyan 3mo ago
    In my view, it's theoretically possible for a combination of the author's iterative prompts + evaluation with Wolfram Alpha to activate the weights that encode the language that describes the constraints on these polynomials (from the faulty proofs) in such a way that the author eventually arrives at this: > ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3
    • tptacek 3mo ago
      How is that not like claiming that a "combination of iterative prompts and evaluation with Wolfram Alpha" would produce my Google Mail password? I also have to note that this response abandons the original claim, that the counterexample was found by exhaustively searching prior failed attempts.
      • TOMDM 3mo ago
        I've seen a lot of people claiming that these recent examples are just trivial combinations of existing prior work. I'm yet to see anyone cite the prior work. If it's true I think some credit is due for the authors Fable/Sol are branching from.
        • QuesnayJr 3mo ago
          I haven't seen these claims, but all of the open problems that have been solved so far have been in the category of "humans could have solved them, but didn't". This doesn't diminish the significance of the results, but it does mean there's still work for mathematicians to do other than glorified prompt engineers. This specific counterexample really is trivial. There's nothing to cite. People have wasted hours and hours on a question whose answer you could give as a homework problem in Calc II.
          • snarkconjecture 3mo ago
            Checking the counterexample is a Calc II problem. Finding it was beyond the efforts of the best algebraic geometers for almost a century.
        • tanderson92 3mo ago
          https://xcancel.com/nihilunbounded/status/2079109869739860450 https://xcancel.com/nihilunbounded/status/207910986973986045...
          • TOMDM 3mo ago
            > You’re unable to view this Post because this account owner limits who can view their Posts.
        • snarkconjecture 3mo ago
          It's absolutely not a trivial combination of prior work, or mathematicians would've found it already. This was not an obscure conjecture.
      • jvanderbot 3mo ago
        I can write a program right now that will print your password. It will just take a while.
  • deleted 3mo ago
    [deleted]
• rowbin 3mo ago
  Maybe, maybe not. The "proofs" may not have helped at all with finding a counterexample. Either way, it doesn't matter. A counterexample was found, no one found one before even though clearly a lot of people have tried who also had access to the prior "proofs".
  • ignoramous 3mo ago
    This makes me wonder, what if anyone uses Fable-class LLM and passes of its novel results as their own work? There's no shortage of folks doing that in software, right now.
    • semi-extrinsic 3mo ago
      Currently there seems to be very little anti-AI bias in maths, and more of a "huh, cool new toy, let's see what it can do" vibe.
      • IngoBlechschmid 3mo ago
        Strongly depends on the subbubble of mathematics. In some parts of type theory / formal proofs for instance, there is a rather strong rejection of LLMs (for moral reasons in addition to quality reasons). The proof assistant Agda was even forked for this reason: https://types.pl/@amy/116522250630340534 https://types.pl/@amy/116522250630340534
    • aurareturn 3mo ago
      I think everyone assumes most, if not all of the code written in a piece of new software is done by AI.
  • cornholio 3mo ago
    I think it's becoming harder and harder to argue that LLMs don't really reason and just mimicry human speech. This counterexample is clearly the result of a sequence of steps that build on previous knowledge in context and logically combine it to reach other true statements - to a degree and complexity that rivals the best human minds. For someone that use Claude Code every day, this is obvious, but for some reason many scientists refuse to accept that it's truly reasoning; perhaps not in the human sense, but in a very profound and real sense. These powerful results are devastating to their point of view. I can sympathize, because I too called LLMs "fancy Markov chains" in the GPT 3 era. But there comes a time where you have to update your world view to match reality, or be stranded in fantasy land.
• piombisallow 3mo ago
  I mean yeah, maybe, but this is how everything works