Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Claude Fable produced a counterexample to the Jacobian Conjecture

xcancel.com

Post reply on HN
Print view View original

321–330 of 562 posts

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#321

Post by fn-mote »

Xmd5a wrote: post #277
monocasa wrote: post #139

Earlier quoted context omitted.

I've heard about mathematicians going through kind of the same thing when they get a weird proof that ends up being right from some weird source or themselves. Which is fair, they get inundated with kooky proofs from amateurs all the time and odds are incredibly good that there's some major fatal flaw that the amateur doesn't see. Or in the case of themselves, there's a certain blindness that makes it a little more d…

> they get inundated with kooky proofs from amateurs Source?

The citation needed is for the other part, which claims a mathematician got an amateur proof which was correct.

Nobody is reading unsolicited proofs. They are like spam.

Source: personal friend of a “crank”.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#322

Post by aeon_ai »

fn-mote wrote: post #296
j_maffe wrote: post #283

Earlier quoted context omitted.

Cheating how? The proof is in the pudding...

On one hand, yes. The parent wants to be skeptical… nothing wrong with being suspicious of marketing claims, right? I would be a lot less impressed if I found out the session was guided by an expert in the field who already had a good idea of where to look. For example, I don’t believe that the results Terrance Tao gets from an LLM are comparable to what I am going to get. I’m not even saying I’m a skeptic. Just that…

Because AI is only impressive if the average Taco Bell employee can guide it to address niche domain topics?

It seems obvious to me that you’d need someone to point at a thing and say “pay attention to that”, as a baseline, to have any results at all with the current architecture and technology

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#323

Post by dist-epoch »

raxxorraxor wrote: post #309
antirez wrote: post #254

Earlier quoted context omitted.

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.

Author probably doesn't want to show the prompt because they are now trying to find a bunch of other counter-examples with the same prompt

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#324

Post by Davidzheng »

Davidzheng wrote: post #269
pja wrote: post #260

Earlier quoted context omitted.

Some speculation in this Claude chat: https://claude.ai/share/22abed98-d9af-43c5-9881-b19e009a07b0 linked from here: https://x.com/b_shrir/status/2079094004885668003?s=20 Very short version: there’s an existing false counterexample in the literature which holds almost everywhere except at a pole. It looks like Fable used this polynomial as a base & extended it in a way that eliminated the pole whilst preserving the s…

I'm going to paraphrase what GPT told me: Consider the canonical degree 3 (subvariety of the trivial P1 bundle consisting of zeros) cover of the projectivization of homogenous polynomials of degree 3 in 2 variables (so it's a 3fold cover of P^3). The top space is P1 x P2 and if you take a standard affine open of the base and look at the cover over that restricted to a subset where the zero of the cubic is simple you…

here's another version directly from the horse's mouth : "Consider the natural map π: P¹ × Sym²(P¹) → Sym³(P¹), (p, {q,r}) ↦ {p,q,r}. Let R be its ramification divisor and let H ⊂ Sym³(P¹) ≅ P³ be a hyperplane tangent but not osculating to the small diagonal; identify X := (P¹ × Sym²(P¹)) \ (R ∪ π⁻¹(H)) ≅ A³ and Y := Sym³(P¹) \ H ≅ A³. Take π|X: X → Y." This is in fact so simple if correct that someone should have found it after all...

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#326

Post by dist-epoch »

0x1ceb00da wrote: post #284
jibal wrote: post #272

Earlier quoted context omitted.

They gave their "logic", such as it is ... and it's utterly irrational. Note that the "they" who published the counterexample on X is some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization. He posted the counterexample in a tweet -- reason enough for "not disclosing the LLM chat session". There's no reason to think that it won't provided if asked for, but it hardly seems releva…

> some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization Why do you trust a random stranger so much? Will you hand over your car keys to a random stranger? Sharing the chat will take 30s of their time. > There's no reason to think that it won't provided if asked for But they didn't provide it.

> But they didn't provide it.

because they are using the same prompt to try finding other counter-examples. they are milking it

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#327

Post by dist-epoch »

Sophira wrote: post #252
siddboots wrote: post #243

Earlier quoted context omitted.

I fed ChatGPT the map with no other context, just “tell me about this function”. It did a bit of work finding the Jacobean etc and eventually worked out the implications of what it was seeing. It then proceeded to check the arithmetic 4 times, and then decided to do a manual verification using an ad hoc symbolic checker in case its SymPy had been tampered with.

Can you please share the chat log for this? I would absolutely love to see this.

It's easy to reproduce, I've fed the example in GPT-5.6 Sol Max and it started multi-checking it in all kinds of ways, with multiple symbolic packages then manual computation, then it did extensive literature search on the subject, looked at tens of math websites, extensive arxiv research. this was soon after it was posted, it didn't find the original twits with the finding

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#328

Post by gus_massa »

jibal wrote: post #272
antirez wrote: post #254

Earlier quoted context omitted.

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.

They gave their "logic", such as it is ... and it's utterly irrational. Note that the "they" who published the counterexample on X is some rando mathematician (Levent Alpöge) working for Anthropic, not Anthropic the organization. He posted the counterexample in a tweet -- reason enough for "not disclosing the LLM chat session". There's no reason to think that it won't provided if asked for, but it hardly seems releva…

> There's no reason to think that it won't provided if asked for, but it hardly seems relevant.

My guess is that the chat will look similar to a full transcription of a (multi month?) discussion between a few mathematicians. Full of dead ends and stupid errors (bit by the human and Claude) that would be embarrassing. We all know how bad it is, and we prefer to keep it behind the curtain.

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#329

Post by danabramov »

ibarrajo wrote: post #203

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…

How much do you try to understand while doing it? I.e. how many levels of abstraction down in your own understanding do you go vs vibing at the surface level?

Re: Claude Fable produced a counterexample to the Jacobian Conjecture

#330

Post by [deleted] »

eru wrote: post #292
aizk wrote: post #112

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.

Can confirm, Claude is flabbergasted. Gemini just checks the web first it seems, and already references the news. Kimi doesn't quite believe it.

[deleted]
Post reply on HN