OpenAI reasoning model produces original proof for 80-year-old Erdős geometry problem

OpenAI said on Wednesday that one of its general-purpose reasoning models has produced an original proof that settles an 80-year-old geometry problem first posed by mathematician Paul Erdős in 1946, a claim that, if confirmed in full, would mark a notable milestone for artificial intelligence in mathematics. According to TechCrunch, the company says the model did not simply recall a known solution or rely on a special-purpose math system, but instead independently found a new family of constructions that outperforms the long-assumed best approach.

The problem sits in a part of geometry and combinatorics that has attracted decades of attention from mathematicians. OpenAI said the model disproved a belief that the best solutions should resemble square grids, showing instead that a different structure can do better. The company described the result as the first time one of its AI systems has autonomously solved a prominent open problem in mathematics, though that claim will ultimately depend on how the wider math community evaluates the proof.

The announcement comes after earlier, less successful claims from OpenAI about math breakthroughs drew scrutiny. TechCrunch noted that this time the company says the work has been backed by mathematicians who previously criticized its overstatement in an earlier case, suggesting a more cautious reception. The broader significance is not just the specific conjecture, but whether AI systems are beginning to contribute genuinely new ideas rather than only speeding up calculations or checking human work.

There is also a wider context around OpenAI’s public posture as it pushes deeper into high-stakes areas. In a separate Bloomberg report, a judge dismissed Elon Musk’s lawsuit against the company, removing one of the most visible legal challenges facing OpenAI as it moves forward with plans for a Wall Street debut. Together, the legal win and the mathematics announcement underscore a company trying to project momentum both technologically and strategically.

Even so, important questions remain. In mathematics, a result matters only when it can be checked, refined and accepted by experts, and AI-generated proofs often require careful verification. If the proof holds up, it could strengthen the case that advanced models are becoming useful research tools in fields once thought far beyond their reach. If not, it would still add to the debate over how to measure AI’s real progress in science and mathematics.