Claude Fable produced a counterexample to the Jacobian Conjecture

loubbrad

Context: https://en.wikipedia.org/wiki/Jacobian_conjecture

throw310822

Overhead, without any fuss, the stars were going out.

gammarator

he just...he tweeted it out

toomuchtodo

Related: Open Problems Solved by LLMs? A Survey of Verifiable Mathematical Discovery [pdf] - https://news.ycombinator.com/item?id=48953756 - July 2026 Solving 20 Erdős Problems with 20 Codex Accounts Running in Parallel - https://news.ycombinator.com/item?id=48914646 - July 2026 (110 comments)

Barbing

Thanks for the mirror link OP!

wenc

I just fed this to GPT 5.6 Sol: Counterexample to Jacobian conjecture: ((1+xy)^3 z + y^2 (1+xy) (4+3xy), y + 3 x (1+xy)^2 z + 3 x y^2 (4+3xy), 2 x - 3 x^2 y - x^3 z): \C^3\to \C^3, has jacobian determinant -2, and sends (0, 0, -1/4), (1, -3/2, 13/2), and (-1, 3/2, 13/2) to (-1/4, 0, 0) GPT wrote some SymPy code to check it. The response? "As written, this is an explicit counterexample to the Jacobian conjecture. I checked it using exact symbolic algebra. I do not see an algebraic catch in what you typed. Unless a term or exponent differs from the intended expression, it appears to disprove the conjecture. This deserves serious independent checking rather than casual dismissal." Waiting for someone to write the Lean proof.

luciana1u

the conjecture held for 85 years and the counterexample was announced in a format that expires after seven days

scarmig

"Any idiot could have done this, it's just high school calculus and just a counterexample anyway. Stochastic parrot, spicy autocomplete, AI psychosis. Wake me up when an AI does something real."

hliyan

I suspect the LLM was able to synthesize a counterexample because of the availability of a lot of prior work: > The Jacobian conjecture is notorious for the large number of published and unpublished proofs that turned out to contain subtle errors. https://en.wikipedia.org/wiki/Jacobian_conjecture#cite_note-...

pyuser583

I asked Fable to verify and it absolutely freaked out! I have no idea what any of this stuff even means, but my AI thinks I’m a legend level mathematician!

gnarlouse

Anybody can ELI5?

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.

kmaitreys

Maybe not? https://en.wikipedia.org/w/index.php?title=Jacobian_conjectu...

mathisfun123

The funniest thing about LLMs is the cognitive dissonance they cause people. People clearly recognize (and bemoan) the fact that LLMs produce derivative breathless prose ie they fundamentally fail at "unstructured creativity" (something the might accurately labeled intelligence ) but are then shocked that the same LLMs can do math. It's reasoning from a flawed premise that math universally requires intelligence and creativity. It does not. Anyone that's proved things via "diagram chasing" can affirm that. The conclusion you should draw is that math (at least the kind they excel at) isn't actually a creative endeavor.

jdw64

I've come to understand that while an LLM is a parrot, it's a parrot that's smarter than I am.

jdw64

But I'm curious—can Fable handle cases where n=2 as well?

brcmthrowaway

For the people saying goalposts have moved etc, whats your endgame?

laszlojamf

Apparently ChatGPT-verified: https://xcancel.com/__alpoge__/status/2079045382940573896#m

aizk

I want to see the Collatz Conjecture next!

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.