This is so unreasonable! As @__alpoge__ himself notes this is classic crank graveyard territory and yet the counter example is something a grad student in 1997 could have found w a ~3 day computer search. Wild!
Claude Fable produced a counterexample to the Jacobian Conjecture
141–150 of 562 posts
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#142Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#143This 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.
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Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#144This 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 like how first it's amazed and doesn't believe it, accepts it, then realizes you not only stole it from twitter but that it's its own proof lmao.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#145Earlier 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.
I haven't seen these claims, but all of the open problems that have been solved so far have been in the category of "humans could have solved them, but didn't". This doesn't diminish the significance of the results, but it does mean there's still work for mathematicians to do other than glorified prompt engineers.
This specific counterexample really is trivial. There's nothing to cite. People have wasted hours and hours on a question whose answer you could give as a homework problem in Calc II.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#146Earlier quoted context omitted.
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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…
>"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 overoptimism. A lot of them are going to be disappointed.
The Anti AI crowd, which I distinguish from those who want AI done responsibly, sustainably, and as safe as can be realistically be managed. There are real criticisms to be made on real issues here. The Anti AI crowd I see seem to want to scrub the world of it, they stand in the way of any responsible implementation because it would be accepting it.
Those people scare me, the vitriol and bad faith interpretation of everything as an indicator of the proof of their reality has the tone of the moral righteousness of a true believer. The outright endorsement of violent acts has me concerned that the more radical or emotionally unstable of the group will do some serious harm. It's not the bulk of a radical movement that causes atrocities, most of those involved just create an environment that normalises toxic attitudes. That environment can incubate a few individuals that act, either for phycological reasons, status, or simple the inability to empathise or consider consequences.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#147Earlier quoted context omitted.
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…
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.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#148Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#149Earlier 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…
The talk page about the conjecture clarifies WP:RSSELF:
https://en.wikipedia.org/wiki/Wikipedia:Reliable_sources#Sel...
> Self-published expert sources may be considered reliable when produced by an established expert on the subject matter, whose work in the relevant field has previously been published by reliable, independent publications.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#150Since I actually don't know math, maybe my ELI5 understanding can be helpful (or corrected).
The conjecture says that you can always reverse (a process) to determine the original inputs.
But this proof shows multiple inputs creating the same output - which obviously cannot be reversed to determine the input - thus falsifying the conjecture.