An OpenAI general-purpose reasoning model autonomously solved the planar unit distance problem — a discrete geometry conjecture first posed by Paul Erdős in 1946 — by discovering new point arrangements that outperform the longstanding square-grid-based constructions. The proof was independently verified by external mathematicians. OpenAI describes the system as a general-purpose model, not a narrow maths tool, handling long multi-step logical chains without step-by-step human guidance.
Why it matters: This is the first externally verified AI proof of a major open mathematics problem, signalling that frontier reasoning models have crossed a meaningful threshold in autonomous scientific discovery.