OpenAI announced that a new general-purpose reasoning model produced an original mathematical proof disproving a famous unsolved geometry conjecture first posed by Paul Erdős in 1946. OpenAI claims the proof discovered an entirely new family of constructions that performs better than the square-grid-like solutions mathematicians believed were best for nearly 80 years. The company says this is the first time AI autonomously solved a prominent open problem central to a field of mathematics. OpenAI attributes the result to the model’s ability to hold together long, difficult chains of reasoning and connect ideas across fields. The company suggests implications for biology, physics, engineering, and medicine.
"For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better."
"The company said this marks "the first time AI has autonomously solved a prominent open problem central to a field of mathematics." The proof, per OpenAI, came from a new general-purpose reasoning model, not a system specifically designed to solve math problems or even this problem in particular."
"OpenAI says this is significant because it means AI systems are now more capable of holding together long, difficult chains of reasoning and connecting ideas across fields in ways researchers may not have previously explored. That has implications for biology, physics, engineering, and medicine."
"Alongside the announcement, OpenAI published companion remarks in support of the disproof from mathematicians like Noga Alon, Melanie Wood, and Thomas Bloom, who maintains the Erdos Problems website, and previously called Weil's post "a dramatic misrepresentation.""
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