Is there a site or github repository that aggregates all these non-trivial AI-solved results?
Claude Fable produced a counterexample to the Jacobian Conjecture
151–160 of 562 posts
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#152For all thehubbub, as far as I know, all the math breakthroughs via AI that I've heard about have come from Anthropic and OpenAI, not Chinese models. I could have missed those announcements, but one might think that between close to frontier performance plus cheap tokens, that they'd be leading the way on these things.
"Anthropic and OpenAI" it's basically been all ChatGPT outside of this one.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#153Earlier quoted context omitted.
I'm not complaining about Wikipedia here, just noting for the thread: it's a vector of polynomials. It has a nonsingular Jacobian. Provided with it are 3 distinct points it sends to the same point; it can't be invertible. What Wikipedia says about this doesn't matter, does it?
Wikipedia does have a rule allowing "routine calculations" https://en.wikipedia.org/wiki/Wikipedia:No_original_research... Of course given the magnitude of the statement a bit of care is warranted, but the rules do allow it.
I think Wikipedia has very sane processes. I'm just saying that process isn't useful to this thread. It's like if I found a SHA2 collision. I'd probably have to be an absurdly talented (and lucky) cryptanalyst to do that, but anybody on the thread could trivially confirm my finding.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#154For all thehubbub, as far as I know, all the math breakthroughs via AI that I've heard about have come from Anthropic and OpenAI, not Chinese models. I could have missed those announcements, but one might think that between close to frontier performance plus cheap tokens, that they'd be leading the way on these things.
As with the case with AI and in fact a lot of things in life, sometimes you just need to wait. It will happen, rather soon.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#155But I'm curious—can Fable handle cases where n=2 as well?
Wasn't it proven true in general for n=2 (NGL I wanted to suggest someone to go for the JC using 5.6 after the CDC proof came out, but then on reflection felt I should neither waste people's time NOR contribute to the myth of AI :) My prediction is that the bubble will burst in 2031 Q4, one year after the Riemann Hypothesis is expected to fall (according to Demis) After 2031, I will suggest going for the JC for N=4 b…
>Wasn't it proven true in general for n=2
Assuming you mean C^2 -> C^2, Do you have a link? If so it would be good to add to the wikipedia page. Also I'm not sure, but does the fact that there's a disproof for n=3 imply that it's false in all n>=3, or could there be higher dimensions where it still holds (I'd guess not since you could probably trivially "embed" this in higher dimensions in some way)
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#156For the people saying goalposts have moved etc, whats your endgame?
What does this mean? Fallacious argumentation and deceptive rhetoric is acceptable, if the topic is sensitive enough / there is enough riding on a wrong answer being accepted?
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#157Earlier 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.
It's tedious, but you could literally even do this by hand. I'm pretty sure I've done worse coordinate bash back when I did math competitions in high school.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#158I find it interesting that the counterexample uses C as a field. C is twisted and weird. Maybe the Jacobian Conjecture still holds for reals?
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#159I find it interesting that the counterexample uses C as a field. C is twisted and weird. Maybe the Jacobian Conjecture still holds for reals?
>C is twisted and weird.
Why do you say this? I've admittedly never done a proper complex analysis course but I got the impression that that complex differentiability was a very strong condition that results in holomprhic functions behaving "nicely" in ways that real functions do not
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#160Maybe not? https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu...
This is nonsensical: Properness of the map is equivalent to its being an isomorphism (quick proof: Jacobian invertible implies that the map is etale, and properness would imply that it is finite etale, but affine space doesn't admit non-trivial finite etale covers), so the lack of properness is just another way of verifying that this is indeed a counterexample.
sure it does? two copies of the affine line? (I guess there's no galois group & no connected finite etale things tho)