OpenAI announced that its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry first posed by Paul Erdős in 1946, marking what the company calls the first time AI has autonomously solved a prominent open problem central to a field of mathematics. However, the announcement comes amid lingering skepticism from prominent AI researchers, including Meta AI's Yann LeCun, who previously criticized OpenAI for making similar claims that turned out to be false.

Why Should You Care About OpenAI's Math Claims?

The stakes of this announcement extend beyond pure mathematics. OpenAI says the proof came from a general-purpose reasoning model, not a system specifically designed to solve math problems. If verified, this would suggest 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. The company argues this has implications for biology, physics, engineering, and medicine.

The problem OpenAI claims to have solved concerns optimal geometric constructions. "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".

What Happened the Last Time OpenAI Made This Claim?

This announcement carries particular weight because of OpenAI's recent history with similar claims. Seven months earlier, OpenAI's former VP Kevin Weil posted on X that "GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others." That claim proved false. It turned out GPT-5 had not actually solved those problems; it had simply found solutions that already existed in the literature. Weil promptly deleted the post after facing criticism.

The backlash was swift and public. Yann LeCun, chief AI scientist at Meta, and Demis Hassabis, CEO of Google DeepMind, both taunted OpenAI over the false claim. Thomas Bloom, who maintains the Erdos Problems website, called Weil's original post "a dramatic misrepresentation".

How Does OpenAI Plan to Avoid Another False Claim?

This time, OpenAI appears to have taken steps to verify its claims before announcing them publicly. The company published companion remarks in support of the disproof from mathematicians including Noga Alon, Melanie Wood, and Thomas Bloom, the same researcher who criticized the earlier false claim.

• Third-Party Verification: OpenAI secured endorsements from established mathematicians before making the announcement, a safeguard absent from the earlier GPT-5 claim.
• General-Purpose Model: The proof came from a general reasoning model rather than a system optimized for a specific problem, suggesting broader AI capabilities rather than narrow task-specific performance.
• Original Proof: OpenAI claims the model produced an original mathematical proof, not simply rediscovered existing solutions, addressing the core criticism of the previous claim.

"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?" said Thomas Bloom, who maintains the Erdos Problems website.

Thomas Bloom, Mathematician

The announcement represents a significant moment for OpenAI's credibility in the AI research community. If the proof withstands mathematical scrutiny, it would demonstrate that AI systems can contribute meaningfully to unsolved problems in pure mathematics. However, given the company's previous overstatement of AI capabilities, the research community will likely demand rigorous peer review before accepting the claim as definitive.

The broader implication is that AI's role in mathematical discovery may be shifting from finding existing solutions to generating genuinely novel proofs. Whether this latest claim proves accurate will significantly influence how researchers and the public evaluate future announcements from OpenAI and other AI companies about breakthrough discoveries.