OpenAI Just Solved an 80-Year-Old Math Problem. Nobody Decided It Should Own the Answer.

In January 2026, Lijie Chen — an assistant professor of electrical engineering and computer science at UC Berkeley — joined OpenAI full time. His mandate was mathematical reasoning. Six months later, a proof he helped generate using an internal OpenAI model landed in the offices of the Annals of Mathematics.

The proof settles the Erdős unit distance conjecture, a problem first posed by Paul Erdős in 1946: if you place n points on a plane, how many pairs can sit exactly one unit apart? Erdős believed the answer grew at most like n to the power of one plus a tiny fractional term. The best human mathematicians had spent 80 years trying to confirm or refute that bound. The best they could prove was that the answer was somewhere between linear and n to the four-thirds power — a wide and unsatisfactory range. OpenAI blog post

An internal model at OpenAI closed that gap. It produced a construction showing that for some fixed exponent delta greater than zero, infinitely many point sets can achieve at least n to the one-plus-delta unit distances. The result is a genuine disproof of Erdős's conjecture, not a partial result or a reformulation. It was reviewed and verified by a group of eight external mathematicians including Noga Alon of Princeton, Fields medalist Timothy Gowers of Cambridge, Arul Shankar of Toronto, and Jacob Tsimerman of Toronto. Their verdict was uniform: the proof holds. Companion paper

Gowers wrote that if a human mathematician had submitted the same paper to the Annals, he would have recommended acceptance without hesitation. "No previous AI-generated proof has come close to that," he said. Misha Rudnev at the University of Bristol, who was not involved in verifying the work, called it "a bomb" — and said he had not expected to see the problem solved in his lifetime. New Scientist The construction relies on techniques from algebraic number theory, specifically infinite unramified towers of totally real number fields, that the mathematicians who reviewed the proof said they had not anticipated. Companion paper

The model that produced the argument was not a system built or trained specifically for mathematics. It was a general-purpose reasoning model — unnamed in the public announcement — evaluated as part of a broader effort to test whether advanced models can contribute to frontier research. The proof was generated in a single pass, without the scaffolding that specialized theorem-proving systems typically require. Chen and colleagues Mark Sellke and Mehtaab Sawhney then verified its correctness. Gil Kalai blog Will Sawin of Princeton later strengthened the result by computing an explicit value for the exponent delta: 0.014, meaning the construction achieves roughly n to the 1.014 power unit distances. Gil Kalai blog

The companion paper by the verifying mathematicians — posted simultaneously with the announcement — describes the result as a milestone in AI mathematics. They note that the AI's chain of thought included an observation about algebraic number fields that they credit with unlocking the proof: that the degree and height of an algebraic realization, which had always been treated as an inconvenience, might itself be a source of counterexamples rather than a hindrance. "Number fields deserve a closer look," the model wrote. It was correct. Companion paper

What makes this different from prior AI math results is the combination of three things: the problem is a genuine open conjecture with an 80-year history, the solution required bringing sophisticated machinery from one area of mathematics to bear on a problem in another, and the mathematicians who reviewed it say the approach surprised them. This is not a case of a system being trained to win a competition. It is a case of a model producing an argument that the people best equipped to evaluate it had not produced themselves.

The question this raises is not whether the proof is correct. On that point, the eight mathematicians who reviewed it have spoken clearly. The question is what it means that the proof now belongs to OpenAI.

The Annals of Mathematics is not a trade publication. It is the most selective pure-mathematics journal in the world, and having a result in it is the currency of record for fundamental mathematical knowledge. If the paper is accepted — and Gowers's endorsement suggests it will be — the academic literature will cite an OpenAI internal model as the originator of one of the most significant combinatorial geometry results of the past half-century. The discoverers are a private company and a professor who works for that company. No mathematics department signed off. No grant funded it. No academic searchlight illuminated the path.

This is the part of the story the wire summaries are skipping. The unit distance problem is a genuine mathematical result, but it is also evidence that the infrastructure of fundamental knowledge — peer review, journal prestige, academic tenure built on the currency of original results — is being entered by actors who did not ask permission. Chen retains his Berkeley faculty position. The university where he holds tenure is now adjacent to a discovery that will appear under a corporate byline in the world's foremost mathematics journal. Nobody has a policy for what happens when those two facts sit in the same room.

The AI labs know this is the game. OpenAI has been explicit that one of its goals is building systems that can do original scientific research. Anthropic, DeepMind, and Google have said the same. The proof of the Erdős conjecture is the most concrete evidence yet that this is not a distant aspiration. Whether the institutions that have historically governed the production of mathematical knowledge are prepared for what is coming is a different question — and one that nobody at any of those labs appears to have asked.