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OpenAI model disproves Erdős's 1946 unit-distance conjecture

ResearchScienceFrontierUSConfirmed

OpenAI said an internal general-purpose reasoning model, not trained specifically for maths, constructed planar point sets with at least n^(1+δ) unit-distance pairs, refuting the long-standing n^(1+o(1)) conjecture. The argument uses algebraic number theory (class field towers); external mathematicians checked it and wrote a companion paper, and Noga Alon and Tim Gowers praised it publicly.

Why it matters

OpenAI called it the first time a prominent open problem central to a field of mathematics was solved autonomously by AI, and Gowers called it a milestone, shifting AI from solving obscure problems to famous ones.

SourceOpenAICoverage: Quanta MagazineCoverage: The Decoder Checked against the primary source. Independently fact-checked on 7 Oct 2026.

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