OpenAI model autonomously solves 80-year Erdős planar unit distance problem
A general-purpose reasoning model from OpenAI solved the planar unit distance problem, overturning the longstanding belief that square grids were optimal—the first autonomous AI solution to a central open problem in discrete geometry.
OpenAI's general-purpose reasoning model has solved the planar unit distance problem, an 80-year-old open question in discrete geometry first posed by Paul Erdős in 1946. The model discovered a new family of constructions that outperforms the square-grid arrangements mathematicians had believed optimal for nearly eight decades. OpenAI published the proof, the model's chain-of-thought reasoning, and companion remarks on May 20, 2026.
The planar unit distance problem asks: what is the maximum number of unit-distance pairs you can form with points in the plane? For decades, the best-known constructions were variants of square lattices. The new result disproves that conjecture by finding configurations that do better. OpenAI calls it "the first time AI has autonomously solved a prominent open problem central to a field of mathematics."