OpenAI model cracks 80-year-old Erdős geometry problem

OpenAI's general-purpose model has autonomously disproved the Erdős planar unit distance conjecture, a problem first posed in 1946 that stumped mathematicians for nearly eight decades. The model didn't just inch past prior work -- it discovered an entirely new family of geometric constructions rooted in algebraic number theory, producing a solution that outperforms every previously known result. The proof has been independently verified by external mathematicians, clearing the bar that separates a claimed result from an accepted one. That verification step matters: it means this isn't a plausible-sounding output that collapsed under scrutiny, but a mathematically sound contribution to pure mathematics. Essentially: OpenAI produced the first AI system to autonomously resolve a prominent open problem at the core of a pure math discipline. - The Erdős conjecture concerns how many pairs of points in a set of n points in the plane can be exactly unit distance apart -- a deceptively simple question with deep combinatorial consequences. - The AI's use of algebraic number theory to construct the counterexample represents a methodological leap, not just a brute-force search over known solution types. - External mathematician verification was part of the disclosure, setting a precedent for how AI-generated proofs should be credentialed. If this generalizes beyond a single conjecture, the role of human mathematicians in open problem resolution shifts from sole authors to verifiers and collaborators.