Claude Fable produced a counterexample to the Jacobian Conjecture

Post by tptacek » Tue, Jul 21, 2026, 1:50 AM UTC

handoflixue wrote: post #467

kzrdude wrote: post #413

Earlier quoted context omitted.

Wikipedia has policies and it needs to use reliable sources. This rule is often skirted and a lot of facts are cited to self-published and fast moving web sources. Those who are braking the progress on the article here are doing the right thing, trying to uphold the editorial standard. Luckily there is now a New Scientist article to link to, so, the issue should now be resolved.

The problem is, "dozens of mathematicians have independently confirmed this, and no one in the community has made any credible objections" is actually a much more reliable source than a link to an article. It's just less legible to administrators.

Post by jibal » Tue, Jul 21, 2026, 1:56 AM UTC

kzrdude wrote: post #413

jibal wrote: post #302

Earlier quoted context omitted.

I removed the "claimed" weasel wording, and now others have followed up. The editors that don't understand math and don't realize how easily this counterexample can be confirmed have lost the debate -- not that there really ever was one.

Wikipedia has policies and it needs to use reliable sources. This rule is often skirted and a lot of facts are cited to self-published and fast moving web sources. Those who are braking the progress on the article here are doing the right thing, trying to uphold the editorial standard. Luckily there is now a New Scientist article to link to, so, the issue should now be resolved.

Post by jibal » Tue, Jul 21, 2026, 1:58 AM UTC

8bitsrule wrote: post #472

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…

A few months ago I asked a model how many primes are divisible by 35 with a remainder of 6. It confidently replied 'none'. Counterexample: 35 + 6.

Post by I-M-S » Tue, Jul 21, 2026, 2:01 AM UTC

inigyou wrote: post #270

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.

Like the unicorn emoji, but for math? It occurs when the LLM is presented with incontrovertible evidence against something it "deeply believes" to be true.

Post by tristanj » Tue, Jul 21, 2026, 2:19 AM UTC

tristanj wrote: post #439

sailingparrot wrote: post #429

Earlier quoted context omitted.

You are right, I completely missed that, to me internal version of Codex meant the harness, but I was wrong.

Not necessarily, it's plausible that GPT-5.6 Sol could also find this disproof, as neither of us has enough information to make a conclusive case. Public GPT is certainly capable, it was able to reverse-engineer the counterexample into a short proof: https://x.com/davikrehalt/status/2079175065695035442 I still suspect Fable 6 found the counterexample, mostly because Anthropic has been silent about this achievement. T…