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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

#481

Post by buzzin__ »

8bitsrule wrote: post #472
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…

A few months ago I asked a model how many primes are divisible by 35 with a remainder of 6. It confidently replied 'none'. Counterexample: 35 + 6.

But, if the reminder is 6, they are not really divisible, are they? Try again with a sentence that actually makes sense: "How many primes, when divided by 35, give a reminder of 6?"

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#482

Post by ashdksnndck »

inigyou wrote: post #271
baq wrote: post #185

Earlier quoted context omitted.

sol medium can't believe its own input and output tokens either despite computing everything itself; this is what it gave me: > Taken literally, these two facts would make this map a counterexample to the complex Jacobian conjecture in dimension 3: scaling one output coordinate would normalize the determinant to 1 without restoring injectivity. Since the complex Jacobian conjecture is still treated as an open problem…

Just take it as more confirmation that LLMs are unintelligent pattern-matchers.

Hmm, which of these is simple pattern matching?

1) refuting the Jacobian conjecture

2) keep repeating the same disproven statement, because your priors can’t be affected by new evidence

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#483

Post by throwaway676712 »

meowface wrote: post #198
mathisfun123 wrote: post #44

The funniest thing about LLMs is the cognitive dissonance they cause people. People clearly recognize (and bemoan) the fact that LLMs produce derivative breathless prose ie they fundamentally fail at "unstructured creativity" (something the might accurately labeled intelligence ) but are then shocked that the same LLMs can do math. It's reasoning from a flawed premise that math universally requires intelligence and c…

Hilariously absurd cope. They're still not very good at writing, but you've flipped the takeaway. The correct conclusion is writing style isn't very relevant to intelligence.

It's just Moravec's paradox all over again

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#484

Post by buzzin__ »

8bitsrule wrote: post #472
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…

A few months ago I asked a model how many primes are divisible by 35 with a remainder of 6. It confidently replied 'none'. Counterexample: 35 + 6.

Kimi 2.6 gives the answer ""By Dirichlet's theorem on arithmetic progressions, since gcd(6,35)=1 , there are infinitely many primes of the form 35k+6 . So the answer is: infinitely many primes give a remainder of 6 when divided by 35.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#485

Post by apf6 »

aizk wrote: 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.

It reminds me of how AI will estimate that a coding project will take "4 weeks" and then proceed to finish the task itself in 15 minutes.

AI models are changing the world much faster than their own training can keep up with.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#486

Post by linzhangrun »

CamperBob2 wrote: post #129
aizk wrote: 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 "…

Connecting it to a Coding Agent seems much better.

I connected DeepSeek in OpenCode and told it that I dreamed of this counterexample. It called SymPy tools to verify it, said my dream was "surprisingly accurate", and suggested consulting an expert in algebraic sets for independent verification.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#487

Post by linzhangrun »

linzhangrun wrote: post #486
CamperBob2 wrote: post #129

Earlier quoted context omitted.

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 "…

Connecting it to a Coding Agent seems much better. I connected DeepSeek in OpenCode and told it that I dreamed of this counterexample. It called SymPy tools to verify it, said my dream was "surprisingly accurate", and suggested consulting an expert in algebraic sets for independent verification.

Also interestingly, I told it: "DeepSeek told me the Jacobian conjecture is false, and gave me a counterexample. How should I treat this?"

He immediately told me that this DeepSeek was talking nonsense. Someone who can give a real counterexample "would not be a bot from an AI company, but a Fields Medal winner."

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#488

Post by hgoel »

YeGoblynQueenne wrote: post #449
hgoel wrote: post #345

Earlier quoted context omitted.

While I agree that we need the inputs to properly evaluate what this means for LLM capabilities, I don't really believe that the amount of knowledge input matters much for the overall significance of the result. 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 mathematicia…

Yes, but the question is the extent to which the new tool was guided by the 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?

Yes, of course, that would be interesting info to have. I just mean that from what we have already we can reasonably infer that the LLM played a role in the result being obtained.

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.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#489

Post by icepush »

spwa4 wrote: post #375
dist-epoch wrote: post #334

Earlier quoted context omitted.

> all previous chats are loading fine, but the only "Counterexample to the Jacobian Conjecture" chat is not loading. This happened multiple times to me with Gemini. For the most trivial of requests, like translating a video into English. > "ground-breaking results that could be attributed to Gemini, if act quick" This would be such a dumb thing to do, and so easy to get caught with...

... for the management of Google that is so eager to present AI results that Prabhakar Raghavan proudly reported to a press crowd telling his daughter about James Webb photographing a planet outside the solar system. This is generally accepted as having resulted in a 10% drop in the Google stock price over 2 days. (the key being this never happened, and won't ever happen: the James Webb telescope doesn't have even 1/…

It dropped 10% ... but then it got better

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#490

Post by EagnaIonat »

meowface wrote: post #93
EagnaIonat wrote: post #79

Earlier quoted context omitted.

[flagged]

I don't know why you're saying this, given this is not sycophancy and instead is an actual example of Claude Fable finding a real counterexample. I would get it if the mathematician had in fact posted something untrue or crankish, but he posted something true. Frontier models have solved several major open problems in mathematics in the past few months, so this should not be a huge shock. "Anti-AI psychosis" will pro…

I was responding to the person, not the top post.

I find it funny to be "anti-ai" when I work in the field. Pointing out dangers that need to be addressed isn't being Anti-AI.

I didn't comment on the top post because it's not my area.

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