Related & of interest: https://xenaproject.wordpress.com/2026/07/20/human-mathemati...
Claude Fable produced a counterexample to the Jacobian Conjecture
401–410 of 562 posts
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#402Earlier quoted context omitted.
My Claude found a similar description (it phrased it in terms of the natural map from "cubics with a choice of root" to "cubics"). The part that seems not at all simple or obvious is the fact that X is isomorphic to A^3. In your presentation (and more or less similarly in the one my Claude found), X is given as P1 x P2 minus a reducible hypersurface, also I think R itself is reducible since it contains points of the…
yeah I think it's probably correct -- this is actually insanely simple (except for the fact that the codomain as described is not obvious isomorphic to A^3.
I agree.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#403Earlier quoted context omitted.
I don't. I'm retired. I'm also not going to live all that much longer, most likely, so it's kind of annoying I'm not really going to see any upsides to an AI world either. I'm discounting the possibility of our AI overlords figuring out a miracle like reversing aging. But it is really f-ing cool that automated math is now a thing and we are seeing it. Eat your heart out, past me.
> so it's kind of annoying I'm not really going to see any upsides to an AI world either I don't think the "permanent underclass" will see many upsides either. They certainly won't have the money to pay for it. I'm excluding myself in that statement because luckily I have access to large amounts of barbiturates.
The math community was not a global underclass. World wealth is increasing, the actual global underclass is seeing rapidly improving lives.
You may be seeing a loss of privilege due at least in part to the inevitable reversion to the mean of US economic dominance. But on a global scale, things are going well. AI will lead to a much larger pie.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#404Earlier quoted context omitted.
> so it's kind of annoying I'm not really going to see any upsides to an AI world either I don't think the "permanent underclass" will see many upsides either. They certainly won't have the money to pay for it. I'm excluding myself in that statement because luckily I have access to large amounts of barbiturates.
The math community was not a global underclass. World wealth is increasing, the actual global underclass is seeing rapidly improving lives. You may be seeing a loss of privilege due at least in part to the inevitable reversion to the mean of US economic dominance. But on a global scale, things are going well. AI will lead to a much larger pie.
> The math community was not a global underclass.
I never claimed they were. The term "permanent underclass" refers to the preferred world order of AI techbro billionaires[1] where human labour is worthless and in consequence normal people no longer have any leverage. Societies where most of the value is dug out of the ground and where human labour is comparatively worthless already exist and living there is not necessarily fun[2].
> World wealth is increasing, the actual global underclass is seeing rapidly improving lives.
The global underclass has been seeing improving lives well before LLMs were a thing. The question is whether they will _continue_ to see their lives improve if their labour is no longer required.
> You may be seeing a loss of privilege due at least in part to the inevitable reversion to the mean of US economic dominance.
I'm not from the US, I don't live in the US, and in fact I've never been to the US.
> AI will lead to a much larger pie.
Which will only benefit people if their piece of the pie doesn't shrink because they don't have any leverage. There is also more than one pie. The real estate pie for example won't grow, instead every piece of the pie will become even more expensive. Most people only own pieces of the pie that will decrease in value (human labour) not pieces of pies that will increase in value.
[1]: https://www.nytimes.com/2026/04/30/opinion/ai-labor-work-for...
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#405Earlier quoted context omitted.
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.
Well, I mean, come on. There aren't that many minors who have taken basic multivariable calculus. But there are a lot of (technical) teenagers who could confirm it!
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#406Earlier quoted context omitted.
The parent's absolutely nonsensical post highlights how polarized AI (as everything else) is today. I can understand someone being opposed to AI on moral, cost-benefit or productivity grounds. But we're seeing a lot of extremist "AI is good for nothing" posts out there nowadays.
I don't think it is nonsensical at all. The author and his collaborator both appear to be bright people, so there's a good chance they had to offer non-trivial insights to guide the LLM, yet it's clearly in the interest of his employer to downplay whatever personal contribution they provided. Edit: Now the OP is flagged/dead for some reason. You could disagree on their take (calling it a marketing stunt is maybe a bi…
> I think the argument is sound
They got flagged because it is a literal conspiracy theory that assumes bad faith.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#407Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#408> The incredible Yitan Zhang ( https://newyorker.com/magazine/2015/02/02/pursuit-beauty ) worked on proving this conjecture for 7 years. Moh, his advisor, wrote that Zhang "failed miserably" in proving the Jacobian conjecture, "never published any paper on algebraic geometry" after leaving Purdue, and "wasted seven years of his own life and my time". https://x.com/aminkarbasi/status/2079129649830137989 https://en.wik…
Zhang, Yitang’s life at Purdue (Jan 1985-1991) T.T.Moh - https://www.math.purdue.edu/~ttm/ZhangYt.pdf kind of a wild document to exist...
This doc is insane.
Moh repeatedly:
calls Zhang’s words “fake” and his claim “a lie”;
speculates, without demonstrating it, that Zhang “fooled” professors to get admitted;
says Zhang “failed miserably” and “wasted seven years of his own life and my time”;
alleges that Zhang “wanted to be famous all the time”;
publishes an irrelevant and humiliating story about Zhang not attending his father’s funeral;
says he would not touch Zhang “with a five feet pole”;
repeatedly emphasizes his own generosity, influence, mathematical work and supposed sacrifices.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#409A counterexample to the Jacobian Conjecture - and also a counterexample to “AI will never be smarter than humans.” Even the most dyed-in-the-wool AI hater at this point must acknowledge that it is more intelligent than any human. The other day I found out that Fable could read seal script! The small seal, standardized stuff no prob, but I found it even did OK at the hardest you can get, Warring States regional scripts. That’s something maybe 2,000 academics worldwide can do and nobody’s even talking about it because it’s just one more item in a very long list.
It’s a strange feeling, to be overtaken by our own creation. Top dog for millions of years and then in the blink of an eye we go from “how many Rs in strawberry” to this.
Re: Claude Fable produced a counterexample to the Jacobian Conjecture
#410A 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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if you ask the chatbots for "list of top unsolved math problems", the JC comes in at a ranking of around #10 - #20. what, a problem that's been unsolved since 1939 was cracked because anthropic has an underground sweatshop of math Phds cranking out research, just so that they can slap "made by AI" on it? hell, maybe lizard people did it.