OpenAI Model Disproves 80-Year-Old Erdős Geometry Conjecture

Overview

OpenAI announced that one of its general-purpose reasoning models has solved the planar unit distance problem, a famous open question in discrete geometry first posed by Hungarian mathematician Paul Erdős in 1946. The model was not specifically designed to solve math problems — it arrived at the solution through general-purpose reasoning.

What Was the Problem?

The planar unit distance problem asks: among n points in a plane, what is the maximum number of pairs at unit distance? For nearly 80 years, mathematicians believed that square grid configurations were close to optimal. The OpenAI model found an infinite family of point arrangements producing significantly more unit-distance pairs than any square grid — disproving this long-held belief.

Mathematician Verification

Prominent mathematicians Noga Alon, Melanie Wood, and Thomas Bloom reviewed the proof and authored companion remarks. Bloom previously criticized OpenAI's earlier (false) claim about Erdős problems as "a dramatic misrepresentation." His endorsement this time lends particular credibility to the result.

Why It Matters

OpenAI called this "the first time AI has autonomously solved a prominent open problem central to a field of mathematics." The breakthrough demonstrates that frontier AI models can make original contributions to pure mathematics — not just assist with known techniques, but discover genuinely new constructions. Sam Altman noted: "a general-purpose model solved a major open problem in mathematics. We'll be saying this a lot over the coming years."