OpenAI says its reasoning model has disproved a famous unsolved conjecture in geometry first posed by Paul Erdős in 1946

OpenAI announced that a new general-purpose reasoning model autonomously solved a prominent open problem in mathematics by discovering an entirely new family of constructions that performs better than solutions mathematicians had believed were optimal for nearly 80 years. The company published companion remarks in support from mathematicians including Noga Alon, Melanie Wood, and Thomas Bloom.

The proof came from a reasoning model not specifically designed to solve math problems or this problem in particular. OpenAI characterized this as significant because it demonstrates AI systems can hold together long, difficult chains of reasoning and connect ideas across fields.

OpenAI stated this marks "the first time AI has autonomously solved a prominent open problem central to a field of mathematics," with potential implications for biology, physics, engineering, and medicine.