OpenAI has announced that its latest reasoning model has generated an original mathematical proof, successfully disproving a prominent unsolved conjecture in geometry initially proposed by Paul Erdős in 1946.
This assertion may resonate as familiar, given that it is not OpenAI's inaugural grand claim of this nature. Just seven months prior, Kevil Weil, then a VP at the AI powerhouse, posted on X: “GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others.”
However, it was subsequently revealed that GPT-5 had not, in fact, solved these problems, but rather identified pre-existing solutions already documented within academic literature.
This incident drew swift criticism and taunts from industry rivals, including Yann LeCun and Google DeepMind CEO Demis Hassabis, prompting Weil to quickly retract his earlier post. This time, it appears OpenAI has avoided a similar misstep. The company accompanied its latest announcement with corroborating remarks from esteemed mathematicians such as Noga Alon, Melanie Wood, and Thomas Bloom, the latter of whom curates the Erdos Problems website and had previously characterized Weil’s earlier claim as “a dramatic misrepresentation.”
On X, OpenAI elaborated: “For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids.” The company continued, stating, “An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better.”
The company emphasized that this achievement represents “the first time AI has autonomously solved a prominent open problem central to a field of mathematics.” According to OpenAI, this groundbreaking proof originated from a novel general-purpose reasoning model, rather than a system engineered specifically for mathematical problem-solving or this particular conjecture.
OpenAI highlights the significance of this development, suggesting it indicates AI systems are now more adept at sustaining extensive and complex chains of reasoning, and at forging interdisciplinary connections that researchers might not have previously considered. This capability holds profound implications across diverse fields, including biology, physics, engineering, and medicine.
In a statement, Bloom remarked, “AI is helping us to more fully explore the cathedral of mathematics we have built over the centuries.” He then posed an intriguing question: “What other unseen wonders are waiting in the wings?”
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