On May 20, 2026, OpenAI announced that an internal general-purpose reasoning model disproved Paul Erdős’s 1946 unit distance conjecture — the first time a prominent open problem central to a subfield of mathematics has been solved autonomously by AI.
The model provided an infinite family of examples yielding polynomial improvement over square-grid constructions: at least n^(1+δ) unit-distance pairs for fixed δ > 0. Will Sawin subsequently refined the exponent to δ = 0.014.
Nine external mathematicians including Tim Gowers, Noga Alon, Thomas Bloom, and Will Sawin verified the proof and published a companion paper. The proof uses algebraic number theory tools including infinite class field towers and Golod–Shafarevich theory.
Fields medalist Tim Gowers called the result “a milestone in AI mathematics” and said he would recommend it for the Annals of Mathematics without hesitation.