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"Worrying about AI today is like worrying about overpopulation on Mars."

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An OpenAI reasoning model has disproved a conjecture in combinatorial geometry first posed by Hungarian mathematician Paul Erdős in 1946, known as the planar unit distance problem, which asks how many pairs of points can be placed exactly one unit apart on a flat plane.

An OpenAI reasoning model has disproved a conjecture in combinatorial geometry first posed by Hungarian mathematician Paul Erdős in 1946, known as the planar unit distance problem, which asks how many pairs of points can be placed exactly one unit apart on a flat plane.

For nearly 80 years, mathematicians believed square-grid arrangements offered the best possible solution to the problem. The AI model identified an infinite family of point configurations that outperform those classical constructions, with Princeton mathematician Will Sawin later refining the result to show a fixed improvement exponent of 0.014.

For nearly 80 years, mathematicians believed square-grid arrangements offered the best possible solution to the problem. The AI model identified an infinite family of point configurations that outperform those classical constructions, with Princeton mathematician Will Sawin later refining the result to show a fixed improvement exponent of 0.014.

The proof drew on algebraic number theory, using tools such as infinite class field towers and Golod-Shafarevich theory to construct high-dimensional lattices with special symmetries, which were then mapped down to two dimensions. Experts noted the mathematical tools used were not novel, but their application to this geometric problem was unexpected.

The proof drew on algebraic number theory, using tools such as infinite class field towers and Golod-Shafarevich theory to construct high-dimensional lattices with special symmetries, which were then mapped down to two dimensions. Experts noted the mathematical tools used were not novel, but their application to this geometric problem was unexpected.

OpenAI said the proof came from a general-purpose reasoning model not specifically trained for mathematics or the unit distance problem. Cambridge mathematician Tim Gowers wrote that the result is "a milestone in AI mathematics" and that no previous AI-generated proof had come close to meriting publication in a top mathematics journal.

OpenAI said the proof came from a general-purpose reasoning model not specifically trained for mathematics or the unit distance problem. Cambridge mathematician Tim Gowers wrote that the result is "a milestone in AI mathematics" and that no previous AI-generated proof had come close to meriting publication in a top mathematics journal.

The announcement drew comparisons to a prior OpenAI claim, made seven months earlier, in which a former company executive said GPT-5 had solved 10 previously unsolved Erdős problems. Mathematicians later determined the model had reproduced solutions already existing in the literature, and the post was deleted.

The announcement drew comparisons to a prior OpenAI claim, made seven months earlier, in which a former company executive said GPT-5 had solved 10 previously unsolved Erdős problems. Mathematicians later determined the model had reproduced solutions already existing in the literature, and the post was deleted.

This time, OpenAI released a companion paper co-authored by external mathematicians, including Thomas Bloom, who had previously criticized the earlier GPT-5 claims. Bloom wrote that while the AI proof was valid, it "was significantly improved by the human researchers at OpenAI and the many other mathematicians involved in the present paper."

This time, OpenAI released a companion paper co-authored by external mathematicians, including Thomas Bloom, who had previously criticized the earlier GPT-5 claims. Bloom wrote that while the AI proof was valid, it "was significantly improved by the human researchers at OpenAI and the many other mathematicians involved in the present paper."

OpenAI AI Cracks 78-Year-Old Math Conjecture

OpenAI makesAI breakthroughCracks on 8078-yearYear-oldOld mathsMath problemConjecture

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OpenAI AI Cracks 78-Year-Old Math Conjecture

OpenAI makesAI breakthroughCracks on 8078-yearYear-oldOld mathsMath problemConjecture

The Controversies

Andreessen

Ng

LeCun

Mitchell

Li

Bengio

Musk

Altman

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Amodei

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Bengio

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Amodei

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Maslej

Martinez

Delangue

Altman

Allred

Kantrowitz

Rusch

Piper

Toberoff

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