OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946.
If this sounds familiar to you, it’s because this isn’t the first time OpenAI has made such a bold claim. Seven months ago, the AI giant’s former VP Kevin Weil posted on X: “GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others.”
It turns out, GPT-5 didn’t actually solve those problems; it just found solutions that already existed in the literature.
Taunts from rivals like Yann LeCun and Google DeepMind CEO Demis Hassabis followed, and Weil promptly took down his premature post. Today, at least, it seems OpenAI didn’t make the same mistake twice. Alongside the announcement, the company published companion remarks in support of the disproof from mathematicians like 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 said this marks “the first time AI has autonomously solved a prominent open problem central to a field of mathematics.” The proof, per OpenAI, came from a new general-purpose reasoning model, not a system specifically designed to solve math problems or even this problem in particular.
OpenAI says this is significant because it means 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. That 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 in a statement. “What other unseen wonders are waiting in the wings?”
