4 ms·

I mean we have no idea what happened exactly, how Fable was used, how many times it was run, whether earlier models were also tried, what was the prompt, how lo

I mean we have no idea what happened exactly, how Fable was used, how many times it was run, whether earlier models were also tried, what was the prompt, how long it run for, etc etc. All we have to go by is a tweet. Why not be skeptical about that?

CamperBob2 3mo ago
What you're asking for is exactly the sort of thing that belongs in, and will appear in, a journal article. There will likely be a preprint on arxiv, so you might keep an eye out for that. In any case, the fact that it was found by a commercial model means that the unfiltered reasoning trace isn't available even to the original author. So there are aspects of the problem-solving process we'll never see. Even if we did get access to the reasoning trace it wouldn't necessarily be definitive, given how these things work. Hopefully it'll be possible to get the same solution from an open-weight model like one of the 3T heavyweights that are said to be coming up for release. If so, the chain of thought can be scrutinized in-depth.
- eru 3mo ago
  The original author works for Anthropic. And even without that, Anthropic might find this important enough to dig up the trace?
- YeGoblynQueenne 3mo ago
  No, I think it works the opposite way. Until there is an article somewhere that describes what happened, if there is one, all we have to go by is that some guy posted a counter-example for the Jacobian on X, with a vague allusion to using Fable and without any further information. Assuming and guessing anything about e.g. the method used at this point is just raising the noise level.
  - CamperBob2 3mo ago
    No one can figure out where you're coming from here. If the human solved a significant open problem without relying on AI, don't you think they'd have claimed the credit for themselves? The suggestion that a human, working at Anthropic or elsewhere, did the hard work needed to disprove the Jacobian Conjecture yet chose to claim falsely that their AI did it, amounts to an extraordinary accusation that requires extraordinary proof.
    - YeGoblynQueenne 3mo ago
      I guess? But I didn't say anything like that. >> No one can figure out where you're coming from here. No, I think it's just you and I think that's because you have preconceived ideas about the only possible positions that people can assume in this debate. I'm sorry, of course, because that's not conducive to productive dialogue, but it's not my fault. I think what I wrote so far is very simple, no technical jargon, no tortured metaphors: all we know is a guy posted a Jacobian conjecture counterexample on X thanking another guy and Fable for it but without explaining what that means, and there's no reason to assume anything else besides that very limited amount of information at all.
      - impendia 3mo ago
        I'm a research mathematician. I can see that you're arguing in good faith, and indeed I have a lot of respect for anyone willing to argue an unpopular position. That said, I do find your suggestion to be completely farfetched. The Jacobian Conjecture was one of the most notorious open problems in algebraic geometry, something that generations of grad students have daydreamed of solving. I've seen more immediate buzz around the Jacobian conjecture than around any other mathematical breakthrough of the last five years, at least. For example Terry Tao, arguably the most famous mathematician in the world, dropped what he was doing to study Alpoge/Fable's counterexample in detail, and wrote this blog post: https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/ https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the... For Alpoge to have solved it on his own, and then falsely claim to have used AI? That's like an athlete winning an Olympic gold medal, and then falsely claiming to have cheated and used illegal steroids. I agree that it's not completely out of the question, but it's beyond the bounds of human behavior that I can reasonably fathom.
        YeGoblynQueenne 3mo ago
        >> For Alpoge to have solved it on his own, and then falsely claim to have used AI? Never said anything like that.
    - viccis 3mo ago

CamperBob2 3mo ago

What you're asking for is exactly the sort of thing that belongs in, and will appear in, a journal article. There will likely be a preprint on arxiv, so you might keep an eye out for that. In any case, the fact that it was found by a commercial model means that the unfiltered reasoning trace isn't available even to the original author. So there are aspects of the problem-solving process we'll never see. Even if we did get access to the reasoning trace it wouldn't necessarily be definitive, given how these things work. Hopefully it'll be possible to get the same solution from an open-weight model like one of the 3T heavyweights that are said to be coming up for release. If so, the chain of thought can be scrutinized in-depth.

eru 3mo ago
The original author works for Anthropic. And even without that, Anthropic might find this important enough to dig up the trace?
YeGoblynQueenne 3mo ago
No, I think it works the opposite way. Until there is an article somewhere that describes what happened, if there is one, all we have to go by is that some guy posted a counter-example for the Jacobian on X, with a vague allusion to using Fable and without any further information. Assuming and guessing anything about e.g. the method used at this point is just raising the noise level.
- CamperBob2 3mo ago
  No one can figure out where you're coming from here. If the human solved a significant open problem without relying on AI, don't you think they'd have claimed the credit for themselves? The suggestion that a human, working at Anthropic or elsewhere, did the hard work needed to disprove the Jacobian Conjecture yet chose to claim falsely that their AI did it, amounts to an extraordinary accusation that requires extraordinary proof.
  - YeGoblynQueenne 3mo ago
    I guess? But I didn't say anything like that. >> No one can figure out where you're coming from here. No, I think it's just you and I think that's because you have preconceived ideas about the only possible positions that people can assume in this debate. I'm sorry, of course, because that's not conducive to productive dialogue, but it's not my fault. I think what I wrote so far is very simple, no technical jargon, no tortured metaphors: all we know is a guy posted a Jacobian conjecture counterexample on X thanking another guy and Fable for it but without explaining what that means, and there's no reason to assume anything else besides that very limited amount of information at all.
    - impendia 3mo ago
      I'm a research mathematician. I can see that you're arguing in good faith, and indeed I have a lot of respect for anyone willing to argue an unpopular position. That said, I do find your suggestion to be completely farfetched. The Jacobian Conjecture was one of the most notorious open problems in algebraic geometry, something that generations of grad students have daydreamed of solving. I've seen more immediate buzz around the Jacobian conjecture than around any other mathematical breakthrough of the last five years, at least. For example Terry Tao, arguably the most famous mathematician in the world, dropped what he was doing to study Alpoge/Fable's counterexample in detail, and wrote this blog post: https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/ https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the... For Alpoge to have solved it on his own, and then falsely claim to have used AI? That's like an athlete winning an Olympic gold medal, and then falsely claiming to have cheated and used illegal steroids. I agree that it's not completely out of the question, but it's beyond the bounds of human behavior that I can reasonably fathom.
      - YeGoblynQueenne 3mo ago
        >> For Alpoge to have solved it on his own, and then falsely claim to have used AI? Never said anything like that.
  - viccis 3mo ago