OpenAI Refutes an Erdős Conjecture with Its AI

OpenAI recently claimed that its latest reasoning model produced an original mathematical proof, refuting a famous unresolved conjecture in geometry posed by Paul Erdős in 1946. This announcement marks a turning point in the use of artificial intelligence to solve complex mathematical problems.

A few months ago, OpenAI had already attracted attention with a bold statement. Kevin Weil announced on X that GPT-5 had found solutions to 10 previously unresolved Erdős problems and had made progress on 11 others. However, this claim turned out to be incorrect, as GPT-5 had merely rediscovered solutions already present in the existing literature. In the face of criticism from figures like Yann LeCun and Demis Hassabis, Weil quickly deleted his post.

This time, OpenAI seems to have avoided repeating that mistake. The current announcement is backed by renowned mathematicians such as Noga Alon, Melanie Wood, and Thomas Bloom, who had previously described Weil's post as a "dramatic misrepresentation."

According to OpenAI, for nearly 80 years, mathematicians believed that the best solutions to Erdős's problems resembled square grids. However, OpenAI's model discovered an entirely new family of more efficient constructions. The company stated that this discovery represents the first time an AI has autonomously solved a major open problem in the field of mathematics.

The proof comes from a new general reasoning model, rather than a system specifically designed to solve mathematical problems or this particular problem. OpenAI emphasizes that this demonstrates the ability of AI systems to maintain long and complex chains of reasoning and to connect ideas across different domains, which could have significant implications for biology, physics, engineering, and medicine.

Thomas Bloom expressed his enthusiasm by stating that AI helps us explore more fully the "cathedral of mathematics" we have built over the centuries and wonders what other invisible wonders might still be discovered.