OpenAI has unveiled a new general‑purpose reasoning model that it says produced an original proof disproving a long‑standing geometric conjecture first posed by Paul Erdős in 1946. The breakthrough challenges the prevailing belief that the most efficient configurations resemble square grids, introducing a novel family of constructions that outperform the traditional approach.

The claim follows earlier controversy when a former OpenAI executive announced that GPT‑5 had solved several Erdős problems, only to discover the purported solutions already existed in the mathematical literature. After criticism from prominent AI researchers and a swift retraction, OpenAI now presents this latest result as the first instance of an AI system autonomously resolving a major open problem without being tailor‑made for the task.

Supporting the discovery, leading mathematicians including Noga Alon, Melanie Wood and Thomas Bloom—who maintains the Erdős Problems website—have endorsed the proof. The company argues that the model’s ability to maintain long, complex chains of reasoning and synthesize ideas across disparate fields could have far‑reaching implications for disciplines such as biology, physics, engineering and medicine.

“AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries,” Bloom said, adding that the achievement may reveal further hidden wonders within the mathematical landscape.