So many mathematicians over the years tried hard and failed, but now Anthropic just for some PR magically did it? And this after LLMs obtaining different math wins? What is your logic here really escapes my understanding.
Edit: Now the OP is flagged/dead for some reason. You could disagree on their take (calling it a marketing stunt is maybe a bit much), but I think the argument is sound, so flagging seems counterproductive to the discussion.
They got flagged because it is a literal conspiracy theory that assumes bad faith.
The strongest words they used were “marketing stunt”. Calling that a conspiracy theory is quite the stretch.
Of course it would be really interesting how Claude approached this. Probably with some constraints regarding the input. And it would be interesting what these constraints were.
Why not be skeptical about 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.
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.
>> 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.
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...
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.
Never said anything like that.
You'd likely make a lot more money if Anthropic paid you a couple million to release it as a Fable discovery. For that matter, if "I solved it" bragging rights and CV candy is that important, then why not just publish the counterexample without mentioning Fable?
I was initially a bit skeptical, as it seems very convenient that this discovery came from an employee of the company that was able to take credit for it. When I saw no real prompt was published, that was even more suspicious. Some recent mathematical discoveries included the prompt and session [1]. Why not include the prompt? That and the thought the model used could be incredibly valuable information for the field of mathematics.
I'm not even saying Fable didn't do it, and my attitude might be different with other companies, but Anthropic has so much obvious nonsense marketing going on (their AI welfare experts for example), that I think the burden of proof should be expected to be on them here.
1: https://chatgpt.com/share/6a55aa50-b484-83ea-85c0-c7e7b4bda4...
Note that the "they" who published the counterexample on X is some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization. He posted the counterexample in a tweet -- reason enough for "not disclosing the LLM chat session". There's no reason to think that it won't provided if asked for, but it hardly seems relevant.
Why do you trust a random stranger so much? Will you hand over your car keys to a random stranger? Sharing the chat will take 30s of their time.
> There's no reason to think that it won't provided if asked for
But they didn't provide it.
A) Claude really produced this counterexample
B) A mathematician working for Anthropic solved a problem mathematicians have been working on for more than a century, and then credited it to Claude for PR purposes
If you believe B is more likely, why would you then believe a proof in the form of a chat log, when said chat log could itself have been faked by Anthropic way more easily than solving the mathematical problem in the first place?
I don’t believe a mathematician produced the counter example secretly, but how much did they contribute to the result?
AI isn’t magic, so to evaluate the value delta, you need to know the value of the input.
These kinds of results are interesting for LLMs because mathematicians have been working on them for decades. If the result doesn't already exist, there's no way it's in the training data, and if mathematicians have been unsuccessfully tackling the problem for decades, it is believable that the use of a new tool made the result possible, even if guided by a great mathematician.
Are we talking a bicycle, powered by a human stepping on the pedals; or a rocket that will fly to the moon on its own with people inside?
Don't you want to know? I mean, doesn't everyone want to know?
If I am not mistaken, all of the flurry of novel results has come from existing mathematicians. This makes me suspect that the models aren't at the level where just any layman can get results. They require a skilled human in the loop to keep them on the rails and to properly explore the solution space.
Though not everyone who works in the sausage factory still wants to eat sausages.
because they are using the same prompt to try finding other counter-examples. they are milking it
Why do you make false claims and attack strawmen so much?
My guess is that the chat will look similar to a full transcription of a (multi month?) discussion between a few mathematicians. Full of dead ends and stupid errors (bit by the human and Claude) that would be embarrassing. We all know how bad it is, and we prefer to keep it behind the curtain.
Who knows what "rewritten" means, but you can sort of see how it progresses.
Counterexample: 35 + 6.
Trusting AI math is not an issue here. It's as if you had asserted that no primes when divided by 35 produce a remainder of 6 and the model said that 41 is a counterexample and then you complained about not being able to trust AI math.
P.S. As someone else noted, your AI query was malformed ... no prime is divisible by 35, nor is any integer divisible by an integer with a remainder of 6 -- divisibility implies a remainder of 0. So perhaps the AI simply took what you wrote literally.
Both are impressive, of course, but they're hardly comparable.
that's self-contradictory -- what brute force means is doing an exhaustive search of a search space (brute forcing it)
using human-like(?) reasoning means cutting down the search space by having some sort of insight or intuition which allows you to prune branches from the entire tree
>> using human-like(?) reasoning means cutting down the search space by having some sort of insight or intuition which allows you to prune branches from the entire tree
So according to the OP there's a search of a tree and it also uses pruning btw, so I want to know what search they mean. Why are you asking?
Edit: Turns out "implicit search" is actually a thing in the literature, albeit introduced in a single paper I could find that claims Diffusion Modelling does it:
https://arxiv.org/abs/2502.19805
I don't think anyone has picked that term up. One more for the scrapheap then, oh well, next paper.
No mention of pruning though. So what did you, or the other guys mean?
It's an LLM. It can't do that.
A bunch of people on the original thread about the Conjecture were like "we need to wait and see if real mathematicians verify this proof it's probably just LLM psychosis", because they don't understand that the counterexample is a trivial calculation. Checking it isn't hard; any AP calc student can do it quickly. It's finding the counterexample that's the challenge.
It's as if someone presented a SHA-2 collision, which anyone could just feed to `openssl sha256` to see, and then naysayers were like "we need to wait for independent verification because the LLM can't know if that collision was real".
I don't know. Are you doing the thing were you're arguing against something you don't like that the other person never said?
Once you verify (with SymPy or another CAS, like Mathematica) that the given function has the claimed Jacobian determinant (which involves only taking partial derivatives and taking a determinant) and the given inputs map to the same output (which involves only evaluating polynomials with some inputs), you're done.
Besides which you have no idea whether that's how the Jacobian conjecture counterexample was verified. Nobody does because no details were released.