Disproof of the Erdos planar unit-distance conjecture
An unreleased OpenAI reasoning model disproved the 80-year-old belief that square-grid constructions maximize unit distances, with checking by external mathematicians.
A general-purpose model, not a math-specific system, produced an infinite family with a polynomial improvement over the grid, using algebraic number theory. A group of outside mathematicians checked it and wrote a companion paper. OpenAI calls it the first prominent open problem solved autonomously by AI.
- Date
- Wednesday, 20 May 2026
- Lab
- OpenAI
- Kind
- paper
- Access
- research preview
Fields medalist Tim Gowers calls it "a milestone in AI mathematics" in the companion paper (OpenAI-quoted). "First" is a company claim; The companion paper and external checks not independently opened here.
Sources
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