Claude Fable produced a counterexample to the Jacobian Conjecture

Post by aurareturn » Mon, Jul 20, 2026, 5:34 AM UTC

ignoramous wrote: post #64

rowbin wrote: post #24

Earlier quoted context omitted.

Maybe, maybe not. The "proofs" may not have helped at all with finding a counterexample. Either way, it doesn't matter. A counterexample was found, no one found one before even though clearly a lot of people have tried who also had access to the prior "proofs".

This makes me wonder, what if anyone uses Fable-class LLM and passes of its novel results as their own work? There's no shortage of folks doing that in software, right now.

Post by SubiculumCode » Mon, Jul 20, 2026, 5:37 AM UTC

Post by SubiculumCode » Mon, Jul 20, 2026, 5:38 AM UTC

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.

Post by oliculipolicula » Mon, Jul 20, 2026, 5:40 AM UTC

jdw64 wrote: post #62

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

Post by radokirov » Mon, Jul 20, 2026, 5:41 AM UTC

wenc wrote: post #9

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 ch…