OpenAI says its new reasoning model has produced an original mathematical proof disproving a famous unsolved geometry conjecture first posed by Paul Erdős in 1946. If your eyebrows just shot up, you're not alone - this isn't the first time OpenAI has made such a bold claim. Seven months ago, former VP Kevil Weil posted on X that "GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others." Spoiler: GPT-5 didn't actually solve them; it just rediscovered existing solutions already in the literature. Taunts from rivals like Yann LeCun and Google DeepMind CEO Demis Hassabis followed, and Weil promptly deleted his premature post.
This time, OpenAI says it didn't repeat the same mistake. Alongside the announcement, the company published companion remarks from mathematicians Noga Alon, Melanie Wood, and Thomas Bloom - who maintains the Erdos Problems website and previously called Weil's post "a dramatic misrepresentation." "For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids," OpenAI posted on X. "An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better."
The company claims this marks "the first time AI has autonomously solved a prominent open problem central to a field of mathematics." The proof came from a new general-purpose reasoning model, not a system specifically designed for math - which OpenAI says is significant because it means AI can now hold together long, difficult chains of reasoning and connect ideas across fields. That reportedly has implications for 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. "What other unseen wonders are waiting in the wings?"