OpenAI Claims Reasoning Model Disproved 80-Year-Old Erdős Conjecture

OpenAI says its new general-purpose reasoning model has produced an original mathematical proof disproving a geometry conjecture first posed by mathematician Paul Erdős in 1946.

According to OpenAI, the model discovered "an entirely new family of constructions" that outperform what mathematicians believed were the best possible solutions for nearly 80 years. The company claims this marks "the first time AI has autonomously solved a prominent open problem central to a field of mathematics."

Verification and Context

Unlike OpenAI's previous claim in October 2025—when former VP Kevin Weil incorrectly stated GPT-5 had solved 10 Erdős problems, only to discover the solutions already existed in literature—the company this time published supporting statements from multiple mathematicians.

Verification came from:

• Noga Alon
• Melanie Wood
• Thomas Bloom, who maintains the Erdős Problems website

Bloom, who previously called Weil's October post "a dramatic misrepresentation," stated: "AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries."

Technical Significance

OpenAI emphasizes the proof came from a general-purpose reasoning model, not a system specifically designed for mathematical problems. The company says this demonstrates AI systems can now "hold together long, difficult chains of reasoning and connect ideas across fields in ways researchers may not have previously explored."

The specific Erdős problem, model name, benchmark performance, and technical details of the proof were not disclosed in the announcement.

What This Means

If verified through peer review, this would represent a significant milestone in AI-assisted mathematical research—moving from pattern matching existing solutions to genuine novel discovery. The claim's credibility is strengthened by mathematician endorsements and OpenAI's apparent caution after last year's embarrassment. However, the lack of technical details, model specifications, and peer-reviewed publication leaves key questions unanswered. The broader implication: general reasoning models may now be capable of autonomous discovery in physics, biology, and engineering, not just mathematics.