OpenAI claims that its new reasoning model has produced a unique mathematical proof that disproves geometry’s famous open conjecture, first posed by Paul Erdos in 1946.
If this sounds familiar, it’s because this isn’t the first time OpenAI has made such a bold claim. Seven months ago, Kevil Weil, former vice president of the AI giant, posted on X: “GPT-5 has found solutions to 10 (!) previously unsolved Erdos problems and has made progress on 11 other problems.”
As it turns out, GPT-5 didn’t actually solve these problems. I just found an existing solution that already exists in the literature.
Weil quickly withdrew his post prematurely following continued abuse from rivals including Yann LeCun and Google DeepMind CEO Demis Hassabis. At least today, it looks like OpenAI didn’t make the same mistake twice. Alongside this announcement, OpenAI released an accompanying comment supporting the disconfirmation by mathematicians Noga Aron, Melanie Wood, and Thomas Bloom, administrator of the Erdos Problem website, which previously called Weil’s post a “dramatic misrepresentation.”
OpenAI posted on X, “For nearly 80 years, mathematicians have believed that the best possible solution resembles a roughly square lattice. OpenAI models have overturned that belief and discovered an entirely new set of structures that perform better.”
The company said this is “the first time that AI has autonomously solved a prominent unsolved problem at the heart of the field of mathematics.” OpenAI says the proof comes from a new general-purpose reasoning model, not a mathematical problem or a system specifically designed to solve this problem.
OpenAI says this is important because it means AI systems are now better able to hold long and difficult chains of inference and connect ideas across disciplines in ways that researchers have not previously explored. It affects biology, physics, engineering, and medicine.
“AI is helping us more fully explore the cathedral of mathematics that we have built over centuries,” Bloom said in a statement. “What other invisible wonders await in the wings?”
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