OpenAI's reasoning model has disproved a central conjecture in discrete geometry after 80 years of study. Mathematicians had long believed square grid constructions were optimal for maximizing unit-distance pairs among n points in the plane. The AI discovered an infinite family of examples yielding a polynomial improvement, verified by external mathematicians.

The solution introduces sophisticated ideas from algebraic number theory to address a fundamental geometric question. The new construction achieves n^(1+δ) unit-distance pairs for fixed δ>0, where previous approaches only achieved n^(1+o(1)). Fields medalist Tim Gowers calls this "a milestone in AI mathematics," showing AI systems can generate original mathematical ideas.

This marks the first time a prominent open problem in mathematics has been solved autonomously by AI. The unexpected connection between algebraic number theory and discrete geometry provides mathematicians new tools for related problems. The result demonstrates AI can contribute meaningfully to frontier research without mathematical specialization.