An internal OpenAI reasoning model has autonomously disproved Paul Erdos' 1946 unit-distance conjecture, marking the first time an AI has independently cracked a prominent open problem at the center of a mathematical subfield. Given only the problem statement, the model produced the full solution on its own.
The model discovered an infinite family of point configurations using deep algebraic number theory, including Golod-Shafarevich theory and infinite class field towers. The constructions yield a polynomial improvement over the long-assumed near-linear upper bound, achieving n^(1+delta) unit-distance pairs. Princeton mathematician Will Sawin later refined the exponent to delta = 0.014.
The proof was verified by external mathematicians, and Fields medalist Tim Gowers wrote a companion paper describing the result as a milestone in AI mathematics that he would have accepted for the Annals of Mathematics without hesitation. Number theorist Arul Shankar said current AI models now go beyond being helpers and are capable of original ideas carried through to completion.