OpenAI's AI disproves 80-year math conjecture

OpenAI researchers leveraged a cutting-edge large language model to shatter a mathematical puzzle that had endured for 80 years. The unit distance problem, proposed by Paul Erdős in 1946, asked how to arrange dots on a plane to maximize pairs exactly one unit apart. Using only a general-purpose reasoning model with no math-specific tools, OpenAI’s AI generated a counterexample disproving the conjecture by constructing a high-dimensional grid projection—a technique blending algebra and number theory in ways mathematicians hadn’t previously explored.

The discovery, published May 20, has reignited debates about AI’s role in mathematical research. Harvard mathematician Melanie Matchett Wood praised the result as 'beautiful mathematics,' highlighting how AI can bridge disparate fields. However, critics argue the solution relied on exhaustive computation rather than creative insight—with some noting that even publicly available models could replicate the proof. A June 2 declaration signed by 1,590 experts now demands strict guardrails for AI in mathematics, citing concerns about verification, reliability, and the erosion of human-led discovery.