OpenAI announced that a new general-purpose reasoning model produced a proof disproving a geometry conjecture first posed by Paul Erdős in 1946. The proof was generated by a general-purpose reasoning model rather than a system specifically designed to solve math problems or this conjecture. The company published companion remarks supporting the disproof from mathematicians Noga Alon, Melanie Wood, and Thomas Bloom.

"For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better," OpenAI posted on X.

In a separate statement, the company described the result as a milestone for the use of artificial intelligence in mathematical research. "This is the first time AI has autonomously solved a prominent open problem central to a field of mathematics," OpenAI said.

OpenAI said AI systems are now more capable of holding together long, difficult chains of reasoning and connecting ideas across fields in ways researchers may not have previously explored. The conjecture, first posed by Erdős in 1946, had remained unsolved for nearly 80 years before the model produced its proof.

"AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries," Thomas Bloom said. Bloom was among three mathematicians, alongside Noga Alon and Melanie Wood, whose companion remarks OpenAI published in support of the disproof.