OpenAI model disproves a decades-old discrete geometry conjecture

OpenAI's May 20 research announcement is a major science-AI story rather than a product launch. The company says an internal general-purpose reasoning model autonomously disproved a longstanding conjecture in the planar unit distance problem, first posed by Paul Erdős in 1946. The question asks how many pairs of n points in the plane can be exactly distance 1 apart. OpenAI says the model found an infinite family of examples that beat the widely believed n^(1+o(1)) limit, with a polynomial improvement; a refinement by Princeton professor Will Sawin gives delta = 0.014 for infinitely many n. External mathematicians checked the proof and wrote companion remarks, with Tim Gowers calling it a milestone in AI mathematics. The result matters because it suggests models can contribute original research insights, not just assist with known proof search. The watch item is reproducibility and whether similar systems solve problems outside carefully selected evaluations.

Key details: OpenAI, May 20, 2026, unit distance problem, Paul Erdos, 1946, discrete geometry, n^(1+delta), delta = 0.014.

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