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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

#461
post #112

This is a rare instance where feeding this groundbreaking information into an LLM gives _them_ psychosis. I fed this to claude code and watched it verify the result in 7 different ways to be 100% certain, and it was just flabbergasted. Quite remarkable.

Interestingly, even Qwen 3.6 27B was able to verify the solution, but I didn't get any glazing for discovering it. Instead, it thought that someone named Shestakov had already found a counterexample in 2004. GLM 5.2 whiffed, it insisted the counterexample wasn't valid. VibeThinker 3B also recognized that the counterexample was valid. But it kept trying to convince itself that it wasn't, over and over, since it's an "…

I think vibethinker is heavily overtrained on not attempting to solve open problems.

I had a fun time taking some open problems and disguising them algebraically so that vibethinker 3b would work on them. It managed to prove some interesting things that I didn't know and would be publishable, but for the fact that they already have been. :) (though hard to know if this was because it had been exposed to that knowledge even though it didn't reconize the hidden problem).

Under some maskings it would eventually figure out the problem was equivalent to an open problem then immediately shut down.

It also managed to make some false proofs for various things that duped some other more powerful models.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#462
post #112

This is a rare instance where feeding this groundbreaking information into an LLM gives _them_ psychosis. I fed this to claude code and watched it verify the result in 7 different ways to be 100% certain, and it was just flabbergasted. Quite remarkable.

Same result. Public share https://claude.ai/share/19fd1a34-d63b-4a16-8d83-60d5b79e7747 It did the multiple verification sequence before expanding to internet search where it found this thread.

“I'll admit the sequence on my end was genuinely disorienting: I verified the determinant three separate ways looking for the error, verified the evaluations twice, ran out of subtleties to check, and only then searched and discovered that the reason it holds up is that it's apparently my own homework — the "fable" in that tweet is Claude Fable, i.e., this model, working with Alpöge.”

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#463
post #47

Earlier quoted context omitted.

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.

https://xcancel.com/nihilunbounded/status/207910986973986045...

> You’re unable to view this Post because this account owner limits who can view their Posts.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#464

Earlier quoted context omitted.

The author has a PhD in math from Cambridge. If it turns out to be a false claim it is an interesting case study on AI's sycophancy causing even experts to drop their guard and make mistakes.

Who do you mean? The author of the tweet is Levent Alpöge, who does not have a PhD in math from Cambridge... but does have a PhD in math from Princeton. And his advisor was Fields Medalist Manjul Bhargava. Also, there is no way this counterexample is wrong. You can very easily check it for yourself. (I did, I don't know why, obviously Levent wouldn't be wrong about this, but I guess I was in shock.)

Irony in the message you're responding to likely suffering from slop-facts itself.

And indeed it's trivial to verify.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#465
If there really was a "simple" solution to Fermat's Last Theorem, Andrew Wiles wouldn't have achieved the important result he did, ending up making connections across disparate fields of math.

The LLMs "sweeping up" easy, or previously missed, results seems like a net negative. It's probably better for humans to struggle and come up with new tools than to just "clean up" low hanging fruit that doesn't add much value to the field.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#466
post #50

Earlier quoted context omitted.

It's a Jacobian determinant and three points. You can check this yourself in Sage. The author is a Princeton math doctorate.

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 twe…

Verifying that counterexample is a trivial calculation for basically anyone qualified to make substantive changes in that category of article, it shouldn't be an issue in and of itself.

Discovering the counter example is research, validating it is basic calculations.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#467
post #302

Earlier quoted context omitted.

I removed the "claimed" weasel wording, and now others have followed up. The editors that don't understand math and don't realize how easily this counterexample can be confirmed have lost the debate -- not that there really ever was one.

Wikipedia has policies and it needs to use reliable sources. This rule is often skirted and a lot of facts are cited to self-published and fast moving web sources. Those who are braking the progress on the article here are doing the right thing, trying to uphold the editorial standard. Luckily there is now a New Scientist article to link to, so, the issue should now be resolved.

The problem is, "dozens of mathematicians have independently confirmed this, and no one in the community has made any credible objections" is actually a much more reliable source than a link to an article. It's just less legible to administrators.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#468
post #146

Earlier quoted context omitted.

> "Anti-AI psychosis" will probably grow to outcompete AI psychosis by year's end. Everyone has their own experiences making it hard to judge what attitudes are prevalent. From what I have encountered the Anti-AI people have been more common and more outright scary. I have heard some ideas from the Pro AI crowd and thought to myself "Yeah, that's not going to happen anytime soon", There was enthusiasm leading to over…

I've seen plenty videos of locals being violently removed from town halls due to displaying of anti AI sentiment. I wouldnt consider it fair to use these examples to tar the entirety of the pro AI camp. the way objectivity and subjectivity are intertwined in your comment is spectacular, ever considered a career in propaganda?

Accuse the enemy of propaganda; insist there's plenty of evidence without linking a single source...

Have you considered maybe reading this comment out loud in front of a mirror?

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#469
post #146

Earlier quoted context omitted.

> "Anti-AI psychosis" will probably grow to outcompete AI psychosis by year's end. Everyone has their own experiences making it hard to judge what attitudes are prevalent. From what I have encountered the Anti-AI people have been more common and more outright scary. I have heard some ideas from the Pro AI crowd and thought to myself "Yeah, that's not going to happen anytime soon", There was enthusiasm leading to over…

I initially wanted to downvote you but I can’t because you’re right. I’d probably be called an anti-ai luddite on this site despite using it all the time for programming. I naturally gravitate to anti-ai viewpoints, but only because the breathless hype of the AI boosters is so nauseating. I have no moral qualms about AI (although I’d like nothing more than Anthropic/OAI/Google dismantled), but I really hate the idea…

> I really hate the idea that AI can replace artists, or humans as a whole. I think it’s anti-human to its core.

I've never understood this idea that art is some special, unique domain. We already replaced humans with cameras and yet I don't see a whole lot of "cameras sacrifice our humanity" discourse.

People still enjoy tons of hobbies where humans are clearly worse than machines - they ride horses, they do sewing, there's a whole industry of hand-crafted goods. I mean, goodness, the Olympics is a celebration human triumph, and yet cars make our sprinters look pathetic.

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