Earlier quoted context omitted.
How is that not like claiming that a "combination of iterative prompts and evaluation with Wolfram Alpha" would produce my Google Mail password? I also have to note that this response abandons the original claim, that the counterexample was found by exhaustively searching prior failed attempts.
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.
Claude Fable produced a counterexample to the Jacobian Conjecture
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Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#302Earlier quoted context omitted.
I think the editor themselves misunderstood the conjecture. UPD: The edit got reverted and there's this on the talk page now: https://en.wikipedia.org/wiki/Talk:Jacobian_conjecture#c-DaR... UPD2: There are edit wars happening now: https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu... https://en.wikipedia.org/wiki/Talk:Jacobian_conjecture#c-Sea...
Wikipedia's gonna Wikipedia. Unless there's a material debate over the Jacobian Conjecture itself, there's really no open question here. This isn't a complicated proof; it's a straightforwardly checkable certificate of a solution.
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.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#303Earlier quoted context omitted.
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?
Reading the chain of thought for Fable, it is incredulous as well. It keeps thinking that it must be missing something or that this is a trick, because it can't have just found a counterexample to a famous conjecture. It's just like us! https://cdn.xcancel.com/pic/orig/EA1E99C3DAE99/media%2FHNpQX... https://cdn.xcancel.com/pic/orig/3B5C0B867A7C3/media%2FHNpQU...
No surprise given half HN still does not consider it general intelligence. Models are being toxic shamed into it.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#304A little over 10 years ago I remember meeting a postdoc who believed he had something close to a counterexample to the Jacobian Conjecture. He and another person was bruteforcing polynomials in about 16 variables, something like 80 - 700 terms each, using binary trees for mapping coefficients. They were guessing, at the time, that the lower bound of a counterexample (P, Q) for max(deg(P), deg(Q)) would go up to 200.…
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Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#305The great thing about these mathematical mopping up type operations is that no person will waste their time trying to prove it to be true anymore. If anything that’s a win. It would be great if an LLM could settle the Collatz conjecture next, god knows how many man-years have been burned on that by unsuspecting victims.
I don't think this is how this works. The next step is to determine for what kinds of polynomials the jacobian conjecture is true and for what kinds of polynomials it's false.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#306Maybe not? https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu...
I'd rather wait for independent seasoned mathematicians to verify such claims first before someone at said AI lab posting a claim about solving a proof online. Let this be a lesson to those who fell for such AI psychosis and to not believe everything you see on the internet as real.
It's a counterexample, not a proof. A schoolchild can confirm it.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#307I don't consider myself an open weights supporter, but it's a bit of a bummer that if there's any novel search technique discovered by the model throughout this finding, it's possibly locked behind ant's reasoning summarization.
One wonders if they could turn their mechinterp work into analyzing the "thought processes" of these very special cases that turn into novel research and finally crack the creative thinking barrier.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#308Earlier quoted context omitted.
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.
Which exact model does claude use here?
> the "fable" in that tweet is Claude Fable, i.e., this model
Looks like this was also Fable.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#309Earlier quoted context omitted.
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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.
Those silly advertisers do everything for exposure and if that means digging yourself into a niche alleged mathematical theorem to refute it, it is what needs to be done!
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.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#310Earlier 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…