Claude Fable produced a counterexample to the Jacobian Conjecture

Post by bugufu8f83 » Mon, Jul 20, 2026, 5:03 AM UTC

sciyoshi wrote: post #65

rvz wrote: post #48

Earlier 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.

Looks like this has already been formalized: https://github.com/deancureton/jacobian

Post by h-jones » Mon, Jul 20, 2026, 5:05 AM UTC

nullsanity wrote: post #27

krackers wrote: post #13

Earlier quoted context omitted.

The surprising thing is that the counterexample seems relatively "simple" in that it's low degree, with coefficients that aren't too large. Does anyone more familiar with this know why this _wasn't_ found earlier, when it seems like you could brute-force through some low-order polynomials?

Same awnser as much of the LLM Proofs - people cared about other things. There isn't a lot of money in academic math, and the ones that love it don't look for low value findings. Proofs like these are, funnily enough, usually the domain of hobbyists - but over the last few years, the "Monetize everything" mentality and struggling first world economy has pushed people away from interesting academic pursuits on their f…

Post by SubiculumCode » Mon, Jul 20, 2026, 5:10 AM UTC

tptacek wrote: post #56

NitpickLawyer wrote: post #38

Earlier quoted context omitted.

To be fair to the sycophancy tendencies, this was an open conjecture that held for 85 years, and not for lack of trying. So, maybe a bit warranted here? :)

I told GPT5.6 I came up with this walking down the street. "Jesus Christ" was its response.

Post by tyre » Mon, Jul 20, 2026, 5:11 AM UTC

krackers wrote: post #13

luciana1u wrote: post #10

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

The surprising thing is that the counterexample seems relatively "simple" in that it's low degree, with coefficients that aren't too large. Does anyone more familiar with this know why this _wasn't_ found earlier, when it seems like you could brute-force through some low-order polynomials?

Post by s1artibartfast » Mon, Jul 20, 2026, 5:16 AM UTC

tptacek wrote: post #56

NitpickLawyer wrote: post #38

Earlier quoted context omitted.

To be fair to the sycophancy tendencies, this was an open conjecture that held for 85 years, and not for lack of trying. So, maybe a bit warranted here? :)

I told GPT5.6 I came up with this walking down the street. "Jesus Christ" was its response.