HomeOpenAI asserts genuine breakthrough in solving decades-old mathematical puzzle
OpenAI asserts that its latest reasoning model has generated an original mathematical proof that disproves a famous unsolved conjecture in geometry, first proposed by Paul Erdős in 1946.
If this sounds familiar, it's because OpenAI has made similar bold claims before. Seven months ago, the company's former VP Kevin Weil posted on X: "GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others."
As it turned out, GPT-5 did not actually solve those problems; it merely rediscovered solutions that were already documented in existing literature.
The announcement drew criticism from rivals like Yann LeCun and Google DeepMind CEO Demis Hassabis, leading Weil to quickly delete his premature post. This time, however, OpenAI appears to have avoided repeating that mistake. Alongside its new claim, the company published supporting statements from mathematicians including Noga Alon, Melanie Wood, and Thomas Bloom—who maintains the Erdos Problems website and had previously described Weil's post as "a dramatic misrepresentation."
"For nearly 80 years, mathematicians believed the best possible solutions resembled something like square grids," OpenAI stated on X. "An OpenAI model has now disproven that belief by discovering a completely new family of constructions that perform better."
The company described this as "the first time AI has autonomously solved a prominent open problem that is central to a field of mathematics." According to OpenAI, the proof originated from a new general-purpose reasoning model, not a system specifically built for solving mathematical problems—or even this particular problem.
OpenAI emphasizes the significance of this achievement, suggesting it demonstrates AI systems' growing ability to maintain long, complex chains of reasoning and to connect ideas across disciplines in ways researchers might not have previously considered. This capability could have important implications for fields such as biology, physics, engineering, and medicine.
"AI is helping us explore the grand cathedral of mathematics that we've built over centuries more thoroughly," Bloom said in a statement. "What other unseen wonders are still waiting to be discovered?"
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OpenAI asserts that its latest reasoning model has generated an original mathematical proof that disproves a famous unsolved conjecture in geometry, first proposed by Paul Erdős in 1946.
If this sounds familiar, it's because OpenAI has made similar bold claims before. Seven months ago, the company's former VP Kevin Weil posted on X: "GPT-5 found solutions to 10 (!) previously unsolved Erdős problems and made progress on 11 others."
As it turned out, GPT-5 did not actually solve those problems; it merely rediscovered solutions that were already documented in existing literature.
The announcement drew criticism from rivals like Yann LeCun and Google DeepMind CEO Demis Hassabis, leading Weil to quickly delete his premature post. This time, however, OpenAI appears to have avoided repeating that mistake. Alongside its new claim, the company published supporting statements from mathematicians including Noga Alon, Melanie Wood, and Thomas Bloom—who maintains the Erdos Problems website and had previously described Weil's post as "a dramatic misrepresentation."
"For nearly 80 years, mathematicians believed the best possible solutions resembled something like square grids," OpenAI stated on X. "An OpenAI model has now disproven that belief by discovering a completely new family of constructions that perform better."
The company described this as "the first time AI has autonomously solved a prominent open problem that is central to a field of mathematics." According to OpenAI, the proof originated from a new general-purpose reasoning model, not a system specifically built for solving mathematical problems—or even this particular problem.
OpenAI emphasizes the significance of this achievement, suggesting it demonstrates AI systems' growing ability to maintain long, complex chains of reasoning and to connect ideas across disciplines in ways researchers might not have previously considered. This capability could have important implications for fields such as biology, physics, engineering, and medicine.
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