After 80 years, OpenAI has resolved a central problem in discrete geometry using an AI model. The planar unit distance problem, posed by Paul Erdős in 1946, questioned how many pairs of points could be exactly distance 1 apart. Mathematicians widely believed the "square grid" constructions were optimal. OpenAI's model disproved this conjecture, finding configurations with significantly more unit-distance pairs.

The breakthrough constructs point configurations achieving n¹+δ unit-distance pairs for fixed δ>0, improving on previous best constructions. The proof uses sophisticated algebraic number theory concepts including infinite class field towers and Golod-Shafarevich theory. Fields medalist Tim Gowers calls this "a milestone in AI mathematics," demonstrating that current models can develop original mathematical ideas beyond assisting humans.

This marks the first time AI autonomously solved a prominent open problem in mathematics. The unexpected connection between algebraic number theory and discrete geometry reveals new research avenues. Princeton professor Will Sawin refined the proof to show δ=0.014. The result demonstrates advanced reasoning capabilities in AI systems and suggests new collaboration models between human mathematicians and AI assistants.