An OpenAI model has disproved a central conjecture in discrete geometry

For nearly 80 years, the unit distance problem—which asks for the maximum number of pairs of points exactly distance one apart in a plane—remained a significant challenge in combinatorial geometry. OpenAI researchers have now utilized an autonomous reasoning model to disprove the long-held conjecture that square grid constructions were optimal. The AI discovered a new family of configurations using sophisticated concepts from algebraic number theory, such as infinite class field towers. This achievement represents a major milestone, as it is the first time an AI has independently resolved a prominent open problem in mathematics, demonstrating that these models can contribute original insights to frontier research.

(Source：OpenAI)