OpenAI says its reasoning model solved an 80-year-old math problem — this time with proof

OpenAI has announced that its latest reasoning model produced an original mathematical proof disproving a long-standing conjecture in geometry — a problem first posed by mathematician Paul Erdős in 1946. Unlike a similar claim made seven months ago that was later retracted, the company says this achievement has been independently verified by leading mathematicians.

A claim with stronger backing this time

The announcement comes after a notable misstep. In October 2024, OpenAI’s former vice president Kevil Weil posted on X that GPT-5 had found solutions to 10 previously unsolved Erdős problems and made progress on 11 others. That claim was quickly debunked: the model had only rediscovered existing solutions already documented in mathematical literature. Critics including Yann LeCun and Google DeepMind CEO Demis Hassabis publicly questioned the statement, and Weil deleted the post shortly after.

This time, OpenAI appears to have taken greater care. Alongside the announcement, the company published supporting remarks from mathematicians Noga Alon, Melanie Wood, and Thomas Bloom, who maintains the Erdős Problems website. Bloom had previously called Weil’s earlier post “a dramatic misrepresentation.”

What the model actually did

For nearly 80 years, mathematicians believed the best possible solutions to the geometry problem resembled square grids. OpenAI’s model discovered a new family of constructions that outperforms those traditional approaches, effectively disproving that long-held assumption.

OpenAI described the result as “the first time AI has autonomously solved a prominent open problem central to a field of mathematics.” The company emphasized that the proof came from a general-purpose reasoning model, not a system specifically designed for mathematics or for solving this particular problem.

Why this matters beyond mathematics

The significance, according to OpenAI, lies in the model’s ability to maintain long, complex chains of reasoning and to connect ideas across different fields — capabilities that could extend to biology, physics, engineering, and medicine. Thomas Bloom reflected on the broader implications: “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?”

Conclusion

While the field of AI-driven scientific discovery has seen its share of overhyped claims, this verified result marks a genuine step forward. It demonstrates that general-purpose reasoning models can now contribute original insights to longstanding open problems — a milestone that may reshape how researchers approach complex questions across multiple disciplines.

FAQs

Q1: What problem did OpenAI’s model solve?
The model produced a proof disproving a geometry conjecture first posed by mathematician Paul Erdős in 1946, which had remained unsolved for nearly 80 years.

Q2: How is this different from OpenAI’s previous claim about solving Erdős problems?
Seven months ago, a former OpenAI executive claimed GPT-5 solved multiple Erdős problems, but those turned out to be rediscoveries of existing solutions. This time, the proof is original and has been verified by independent mathematicians.

Q3: Could this AI capability be used outside of mathematics?
Yes. OpenAI says the reasoning model is general-purpose, meaning its ability to hold long chains of reasoning and connect ideas across fields could be applied to biology, physics, engineering, and medicine.