[minimaxir]

I'll have a blog post up tomorrow about it but the Jacobian Conjecture counterexample is a very funny cognitohazard for LLM assistants. It's a paradox for modern LLMs: they have enough math skills such that they can easily compute the Jacobian to formally verify the counterargument, but its own knowledge base is locked prior July 19th 2026 where all it knows is that the Jacobian Conjecture is unsolved and a random chat user providing such a proof is highly unlikely.

[bananaflag]

I wonder whether when the fact that AIs have started solving conjectures will enter the training data, they will become more confident in their abilities.

[applfanboysbgon]

The models are just a reflection of how you prompt them. When I posted the counterexample, in dry language with a dry personality setting, claiming credit for it with search disabled, GPT simply verified that it was correct but noted that it could not ascertain novelty or priority and that external verification was required. "Model reacts in crazy ways when my prompt influences it to" is really, really not interesting.