LLMs break down in funny ways when told the Jacobian Conjecture counterargument

On Sunday night, Anthropic researcher Levent Alpöge casually tweeted a surprisingly simple counterargument to the Jacobian Conjecture, a mathematics problem that has been unproven for over 80 years. Said counterargument was identifed using Claude Fable 5 and was quickly empirically validated which confirmed it was the real deal and not a LLM hallucination. I won’t explain the proof further as I’m not qualified. Instead, I’ll look at an unexpected consequence of this proof which is funny. On the Hacker News thread about the counterargument, a comment by user aizk caught by eye: 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. User kelseyfrog followed up with a public Claude Fable 5 chat artifact confirming this behavior: Fable at, the least, has a sense of humor about the situation as…