OpenAI Claims Progress on an 80-Year-Old Geometry Puzzle

OpenAI applied its o3 reasoning model to the Erdős planar unit distance problem, which asks for the minimum number of distinct distances among n points in a plane. The system produced new lower-bound constructions and proof sketches that researchers had not previously recorded. The Guardian reports the work as evidence of improved multi-step mathematical reasoning rather than a full solution to the conjecture.

You can treat frontier reasoning models as research assistants that generate candidate proofs and counter-examples before you invest human time. The technique shifts the workflow from manual literature search to rapid hypothesis generation followed by targeted verification. Users should log every model-generated step so that later manual checks remain traceable.

OpenAI's internal math research team ran the o3 model on the Erdős problem and surfaced previously unseen lower-bound constructions that the Guardian article cites as the first AI-generated candidates accepted for further review by human mathematicians.