OpenAI has announced a groundbreaking achievement, claiming that its advanced reasoning model has produced a novel mathematical proof that disproves a longstanding conjecture in geometry, originally proposed by Paul Erdős in 1946.
This announcement follows a previous claim made by OpenAI about its GPT-5 model, which suggested it had solved ten unsolved Erdős problems. However, it was later revealed that GPT-5 merely identified existing solutions in the literature, prompting skepticism from figures like Yann LeCun and Demis Hassabis of Google DeepMind.
In contrast, OpenAI's latest assertion comes with substantial backing. The organization has published supporting remarks from esteemed mathematicians such as Noga Alon, Melanie Wood, and Thomas Bloom, who have acknowledged the significance of this new proof. Bloom, who maintains the Erdős Problems website, previously criticized the earlier claims as a "dramatic misrepresentation."
OpenAI stated, "For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better." This marks a pivotal moment, as it is the first instance where AI has autonomously solved a prominent open problem within mathematics.
The proof was derived from a general-purpose reasoning model, not one specifically tailored to tackle mathematical challenges. OpenAI emphasizes the importance of this development, suggesting that it indicates AI systems are now capable of managing complex reasoning chains and bridging concepts across various fields, potentially influencing disciplines such as biology, physics, engineering, and medicine.
Reflecting on the implications of AI in mathematics, Bloom remarked, "AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries. What other unseen wonders are waiting in the wings?"