Now that is some spicy autocomplete.
Claude Fable produced a counterexample to the Jacobian Conjecture
121–130 of 562 posts
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#122Earlier quoted context omitted.
Looks like this has already been formalized: https://github.com/deancureton/jacobian
To be clear, this is not the kind of thing where a Lean formalization provides any value at all. It's like formalizing the answer to a high school algebra problem. The counterexample is obviously correct.
Indeed. I was mainly responding to the comment about waiting for "independent seasoned mathematicians to verify", whereas in this case it is easy enough to convince oneself of the counterexample's correctness.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#123he just...he tweeted it out
I almost felt bad adding {{Cite tweet ...}} to the wikipedia article
At least it's not {{Cite bridge graffiti}}
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#124the conjecture held for 85 years and the counterexample was announced in a format that expires after seven days
The surprising thing is that the counterexample seems relatively "simple" in that it's low degree, with coefficients that aren't too large. Does anyone more familiar with this know why this _wasn't_ found earlier, when it seems like you could brute-force through some low-order polynomials?
There are still many degree 5 polynomials, up to 35 terms for a single function, then you need to find three of them as well
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#125This 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.
Who knew DOES NOT COMPUTE would be an actual thing?
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#126Interesting announcement on social media rather than publishing somewhere like arXiv.
a short counterexample makes it likely the best medium for such an announcement. would have been inappropriate for a positive proof.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#127Interesting announcement on social media rather than publishing somewhere like arXiv.
You can't please everyone on the internet, if he had posted this on Arxiv then someone else will be complaining that Arxiv is for humans to publish and that llm output should be social media post instead. Also, the proof fits in a tweet. So why blow it up.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#128he just...he tweeted it out
[deleted]
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#129This 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 "unsolved problem." Eventually it just answered "-2."
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#130Earlier 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…
Wikipedia's editors won't be happy until the site has joined Stack Overflow in self-owned oblivion.