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Claude Fable produced a counterexample to the Jacobian Conjecture

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Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#541

Post by YeGoblynQueenne »

tptacek wrote: post #532
YeGoblynQueenne wrote: post #505

Earlier quoted context omitted.

>> The model was perfectly capable of verifying its correctness. It's an LLM. It can't do that.

Are you doing the "LLMs don't know how many R's are in 'Raspberry'" thing here? 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 counter…

>> Are you doing the "LLMs don't know how many R's are in 'Raspberry'" thing here?

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?

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#542

Post by tptacek »

YeGoblynQueenne wrote: post #538
tptacek wrote: post #531

Earlier quoted context omitted.

Because your question doesn't make sense; this isn't how implicit search works.

"Implicit search" with pruning?

I don't understand why you're scare quoting "implicit search".

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#543

Post by tptacek »

YeGoblynQueenne wrote: post #541
tptacek wrote: post #532

Earlier quoted context omitted.

Are you doing the "LLMs don't know how many R's are in 'Raspberry'" thing here? 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 counter…

>> Are you doing the "LLMs don't know how many R's are in 'Raspberry'" thing here? 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?

The model is very capable of checking this counterexample, was my point.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#544

Post by wmorgan »

YeGoblynQueenne wrote: post #538
tptacek wrote: post #531

Earlier quoted context omitted.

Because your question doesn't make sense; this isn't how implicit search works.

"Implicit search" with pruning?

Why not? Lasker said, “when you see a good move, look for a better one.” That was tree pruning advice for an implicit search.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#545

Post by viccis »

CamperBob2 wrote: post #536
YeGoblynQueenne wrote: post #504

Earlier quoted context omitted.

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.

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 extraor…

> If the human solved a significant open problem without relying on AI, don't you think they'd have claimed the credit for themselves?

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...

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#546

Post by viccis »

gus_massa wrote: post #328
jibal wrote: post #272

Earlier quoted context omitted.

They gave their "logic", such as it is ... and it's utterly irrational. 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 releva…

> There's no reason to think that it won't provided if asked for, but it hardly seems relevant. 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.

Here's an example of one for a major result earlier this year: https://cdn.openai.com/pdf/1625eff6-5ac1-40d8-b1db-5d5cf925d...

Who knows what "rewritten" means, but you can sort of see how it progresses.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#547

Post by thin_carapace »

Lerc wrote: post #530
thin_carapace wrote: post #518

Earlier quoted context omitted.

umm have you considered that you can go to youtube and verify my claim whereas the other interlocutor explicitly refers to unverifiable personal anecdotes? and did you want to verify that I explicitly accused someone of propaganda?

I attempted that. In videos from the last year the only things I could find were some people protesting ICE, A person accusing a mayor of sexual assault, some republican party events with protestors, and a few of people speaking out of turn being walked off by security. Without the specific examples you described I have no idea what you are talking about. It is either sufficiently old that it could be considered an i…

I believe that I have witnessed at least 3 videos of americans being forcibly removed from town halls for speaking out against data centers. you are correct that search engines are not showing anything at all when searching for data centre forced removal. it took me ten minutes to find the most recent example from my memory[0]. something strange is happening, and when I see you act ostensibly in support of the side that is seemingly scrubbing search engine results, this is why I react poorly to your pro AI and pro system stance - the system does not need our good faith, the system already controls the narrative.

[0] https://www.lowellsun.com/2026/07/21/body-camera-footage-sho...

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#548

Post by jibal »

jibal wrote: post #474
aleph_minus_one wrote: post #300

Earlier quoted context omitted.

> The Collatz conjecture is almost certainly not false, so no "clean up" is possible. Many people believed the same about the Jacobian Conjecture.

non sequitur

P.S. Also false -- it simply is not true that many people believed that the Jacobian conjecture was almost certainly not false--why would they? OTOH, the Collatz conjecture has been confirmed for all integers up to 2.36 *10^21, and Terence Tao has proved that it is true for "almost" all numbers: https://www.quantamagazine.org/mathematician-proves-huge-res...

Again, this is all non sequitur, because the context was a statement that most mathematicians believe the CC to be true, in which case there would be no "clean up".

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#549

Post by YeGoblynQueenne »

tptacek wrote: post #542
YeGoblynQueenne wrote: post #538

Earlier quoted context omitted.

"Implicit search" with pruning?

I don't understand why you're scare quoting "implicit search".

It's a direct quotation from your comment, not a "scare quote". How does "implicit search" do pruning? Can you explain?

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?

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#550

Post by YeGoblynQueenne »

tptacek wrote: post #543
YeGoblynQueenne wrote: post #541

Earlier quoted context omitted.

>> Are you doing the "LLMs don't know how many R's are in 'Raspberry'" thing here? 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?

The model is very capable of checking this counterexample, was my point.

Checking, it how? I mean can you describe the mechanism? How does an LLM "check" that something is (or isn't) a counterexample? Does that involve pattern matching, formal verification or model checking, some other approach?
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