OpenAI claims it solved an 80-year-old math problem — for real this time

OpenAI is making a bold claim: its new reasoning model has produced an original mathematical proof that disproves a famous unsolved conjecture in geometry, first posed by Paul Erdős in 1946. This isn't the first time OpenAI has made such a claim, but the company is taking pains to ensure its latest assertion sticks. Seven months ago, OpenAI's former VP Kevin Weil posted on X that GPT-5 had found solutions to 10 previously unsolved Erdős problems and made progress on 11 others.

However, it turned out that GPT-5 had simply found existing solutions already documented in the literature. The post was quickly taken down after rivals like Yann LeCun and Google DeepMind CEO Demis Hassabis criticized OpenAI for the premature claim. This time, OpenAI is backing up its assertion with a published proof and endorsements from notable mathematicians.

The company's model has reportedly disproved a long-held belief that the best possible solutions to the problem looked like square grids. Instead, the model discovered an entirely new family of constructions that performs better. According to OpenAI, this marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

The proof was produced by a new general-purpose reasoning model, not a system specifically designed to solve math problems or even this particular problem. OpenAI sees this as significant because it demonstrates that AI systems are now capable of holding together long, difficult chains of reasoning and connecting ideas across fields in ways researchers may not have previously explored. This has implications for a range of fields, including biology, physics, engineering, and medicine.

Mathematician Thomas Bloom, who maintains the Erdos Problems website, welcomed OpenAI's achievement. "AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries," he said in a statement. "What other unseen wonders are waiting in the wings?" Bloom had previously expressed skepticism about OpenAI's earlier claim, calling Weil's post "a dramatic misrepresentation." OpenAI's announcement is accompanied by remarks from other mathematicians, including Noga Alon and Melanie Wood, who support the company's claim.

According to OpenAI, the company's model has opened up new possibilities for mathematical exploration. "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."