OpenAI's reasoning model solves 80-year-old Erdős geometry problem

OpenAI has announced that its latest reasoning model, a general-purpose AI not specifically designed for math, autonomously produced an original proof that disproves a long-standing conjecture in geometry. The problem was first posed by the legendary mathematician Paul Erdős in 1946, and for nearly eight decades mathematicians believed the optimal solutions were roughly square grids. The AI discovered a new family of constructions that perform better, overturning that belief. To avoid the embarrassment of a prior false claim—where former VP Kevin Weil incorrectly said GPT-5 solved 10 Erdős problems—OpenAI secured endorsements from respected mathematicians including Noga Alon, Melanie Wood, and Thomas Bloom (who maintains the Erdős Problems website). Bloom called the prior claim “a dramatic misrepresentation” but now says the new result is legitimate.

The company emphasizes that this marks the first time AI has solved a prominent open problem central to a field of mathematics. The model's ability to maintain long, difficult chains of reasoning and connect ideas across domains suggests potential breakthroughs in 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?” While rivals like Yann LeCun and Demis Hassabis previously mocked OpenAI, this verified achievement signals a new capability for AI-driven discovery.