OpenAI announced that an internal general-purpose reasoning model has autonomously disproved a longstanding conjecture in discrete geometry known as Paul Erdős's planar unit distance problem, which has been open since 1946 and is one of the best-known problems in combinatorial geometry. The proof, verified by external mathematicians including Fields medalist Tim Gowers, uses sophisticated tools from algebraic number theory to construct configurations of n points with more unit-distance pairs than the previously believed optimal “square grid” construction. The result marks the first time a major open mathematical problem central to a subfield has been resolved autonomously by AI, with the model not specifically trained for mathematics or scaffolded to search through proof strategies.
