A model disproves the Erdos unit distance conjecture
An internal OpenAI model built an infinite family of configurations beating the square grid by a polynomial factor, disproving a conjecture from 1946. Nine external mathematicians checked the proof.
Why it matters
For the first time a prominent open problem central to a subfield of mathematics was solved autonomously by a model neither trained for mathematics nor aimed at that problem.
The publication is dated 20 May 2026. The unit distance problem in the plane was posed by Paul Erdos in 1946: how many pairs among n points can be at distance exactly one. Erdos conjectured an upper bound of n to the power 1 plus a vanishing term, and the best known construction, from a scaled square grid, gave only slightly more than linear growth. The model produced an infinite family of configurations with at least n to the power 1 plus a fixed positive exponent. The original proof gives no explicit exponent, but a refinement by Will Sawin of Princeton showed that 0.014 can be taken. The same day a companion paper appeared on arXiv from nine mathematicians - Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang and Melanie Matchett Wood - presenting a short, human-verified version of the argument. OpenAI published the proof text, the companion paper and an edited version of the model's reasoning.