Hacker NewsArticle URL: https://xcancel.com/__alpoge__/status/2079028340955197566
Comments URL: https://news.ycombinator.com/item?id=48973869
Points: 763
# Comments: 477
Hacker News 讨论
765 points · 478 comments · 查看原帖
- koito17
A 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. To think that Claude Fable was able to find a counterexample in degree 7 is insane to me. We are truly in a new era.
- z7
> 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.wikipedia.org/wiki/Yitang_Zhang
- aizk
This 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.
- laichzeit0
The 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.
- ibarrajo
I’ve been math-vibe coding a few months now. It’s surprisingly easy to do with AI. The hard part has been manually verifying and validating the results. I took one of the smaller findings (disproving a conjecture) and wrote a paper as my first endeavor into publishing. Because the next few findings i have in the pipeline are substantial in the field of quantum topology and physics im taking some time to publish them with a ton of scrutiny. And verification has taken more time than it did to make the discoveries. Here’s my first piece if anybody is interested in number theory: https://arxiv.org/abs/2607.09793
- unexpectedtrap
Using LLMs to generate piles of code and/or proofs of dubious quality is very questionable thing, and I understand these non-stop debates about it. But in this case, as using plain brute force is already quite a common thing in searching for counterexamples, using LLMs as a sort of more advanced brute force seems to be just the right thing to do, so I struggle to understand so much hostility to this approach.
- tristanj
The poster works at Anthropic, so they likely have internal access to the next generation of Fable. Their internal model is probably an absolute beast at mathematics, and the upcoming benchmark results will likely set a new record for maths performance. I suspect this is what happened, because the poster is coy about sharing the actual prompt / reasoning trace used to reach this result. That would be covered by an NDA until the model is properly released. Exciting times!
- tekacs
Given how small the counterexample is... this feels like a great example of where a lot of interesting results are going to be found: not because they were super difficult, but because intelligence didn't scale, and until computers could do this for us, the number of people who seriously poked at many such things was low. I'm very excited for the impact of this effect in science and medicine and other disciplines too.