An OpenAI model has disproved a central conjecture in discrete geometry
An OpenAI model has successfully disproved a long-standing conjecture in discrete geometry regarding the planar unit distance problem. This breakthrough marks the first time an AI has autonomously solved a prominent open problem in mathematics. The proof has been validated by external mathematicians and highlights the advanced reasoning capabilities of current AI models.
- ▪The planar unit distance problem has been studied for nearly 80 years and was first posed by Paul Erdős in 1946.
- ▪The OpenAI model provided an infinite family of examples that yield a polynomial improvement over previous beliefs about the problem.
- ▪This achievement demonstrates that AI models can generate original ideas and contribute significantly to mathematical research.
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May 20, 2026ResearchMilestoneAn OpenAI model has disproved a central conjecture in discrete geometryRead the proof(opens in a new window)Read the companion remarks(opens in a new window)Loading…ShareFor nearly 80 years, mathematicians have studied a deceptively simple question: if you place nnn points in the plane, how many pairs of points can be exactly distance 111 apart?This is the planar unit distance problem, first posed by Paul Erdős in 1946. It is one of the best-known questions in combinatorial geometry, easy to state and remarkably difficult to resolve.
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