OpenAI Model Produces Counterexample Disproving Erdős’s 1946 Unit Distance Conjecture

An OpenAI large language model produced a mathematical proof that disproved Paul Erdős’s 1946 unit distance conjecture. com on May 20. The model is a general-purpose system trained for reasoning and did not use any math-specific tools or software.

The original prompt, composed by AI, described the conjecture and instructed the model that a complete solution must either prove or disprove it. OpenAI researcher Sébastien Bubeck said the team did not guide the model in any particular way. The model used tools from algebra and number theory to construct a counterexample.

Melanie Matchett Wood of Harvard University contributed remarks to an accompanying paper that reviewed the AI’s result. ” One researcher reproduced the proof using a publicly available model. Mathematician Thomas Bloom of the University of Manchester said it would have been “truly incredible” if the AI had managed to prove the conjecture.

Bloom said the AI model’s proof was relatively easy for a human expert to verify. OpenAI ran the prompt on the Erdős conjecture through the same model multiple times and it produced the correct solution in 50 percent of those trials. Lijie Chen said the new model is better than current models at generating an “I cannot solve it” response when it runs into difficulty on a problem.

On June 2 a group of experts published a declaration calling for tight guardrails around AI in mathematical research. As of June 5 the declaration had 1,590 signatures. Wood said “LLMs have read ALL the papers.

They have read all the commentary and notes, and everything that’s online....