OpenAI's secret Yang-Mills proof: Nobel laureate's panel sets date for first release

What's going on

On October 26, 2026, OpenAI made one of the boldest claims in the history of AI research: the company says its internal, unreleased AI models have proven the mathematical existence of Yang-Mills theory. This theory from particle physics describes, among other things, the strong nuclear force. That's the force that holds quarks together, and quarks are the building blocks of protons and neutrons. Putting the theory on rigorous mathematical footing is part of one of the seven Millennium Prize Problems set by the Clay Mathematics Institute. Each one carries a $1 million prize.

So far, though, nobody outside OpenAI has seen the proof, apart from a specially appointed panel of five well-known physicists. On November 3, that panel released its second interim report and gave a timeline for the first time. A first release is due in November, and according to the French magazine Numerama, "if possible next week." The panel says it will announce any release of AI-generated material a full day in advance.

Three breakthroughs at once, according to OpenAI

The Yang-Mills proof is just one of three results OpenAI presented on October 26:

The mathematics result is about the wave equation. Roughly speaking, the conjecture says focused waves can't stay extremely concentrated for long. According to a Japanese blog on note.com, the two-dimensional case had been solved since 2019. The new proof would also imply the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The AI reportedly produced the proof on October 18, and the Lean formalization followed the next day.

In computer science, OpenAI claims to have refuted the Exponential Time Hypothesis. The ETH was proposed in 1999 and says the logic problem 3-SAT fundamentally can't be solved in "subexponential" time. Subexponential means the running time grows more slowly than an exponential function as you add variables. Hundreds of papers in graph theory, bioinformatics, databases and geometry assume the ETH as a premise. OpenAI says the model found the refutation on October 16 and formalized it in Lean on October 17. It's being reviewed by Russell Impagliazzo and Ramamohan Paturi (UC San Diego), who proposed the ETH in 1999 together with Francis Zane, and by Ryan Williams of MIT. In an open letter, the three write:

"Our involvement should not be taken as an endorsement of the claim. A result of this magnitude demands careful, independent scrutiny."

Williams stresses that the group hasn't signed any non-disclosure agreements and isn't being paid. OpenAI has promised to release all raw data and to fund a conference on the implications. The note.com author also points to something else worth noting: an internal Claude research model at Anthropic reportedly found a similar refutation independently, also on October 16. It reportedly used 14 million output tokens and needed no human input. According to the author, it's unclear who got there first and whether the two results have been checked against each other.

The physics claim is the most ambitious. The model is said to have delivered a mathematically rigorous existence proof for interacting quantum field theories in four spacetime dimensions, with gauge fields (which carry forces) and fermions (matter particles like electrons and quarks). This covers quantum chromodynamics and an extension of the Standard Model. OpenAI says the approach builds on Thaddeus Balaban's constructive field theory. According to mezha.ua, the AI wrote the Yang-Mills proof on September 9 and the quantum chromodynamics proof on September 18. The Lean formalization of the first was finished on October 16.

What the Gross panel is checking

On October 16, OpenAI asked David Gross, who won the 2004 Nobel Prize in Physics, to chair the review panel. The other members are Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, all heavyweights in mathematical physics. On where things stand, the panel writes:

"We are currently focused on reviewing the Lean proof of the existence of pure Yang-Mills theory. We are paying particular attention to making sure that the definitions and problem statements match what is standard in physics and mathematics, and that the formalization matches the informal write-up."

This is the crucial point. Lean is a programming language in which a computer checks every single step of a proof. But the computer only checks the claim you give it. If a definition in the code differs even slightly from what physicists actually mean by Yang-Mills, a formally correct proof can still prove the wrong thing. Think of a notary who checks a contract without knowing whether it covers the right property. The panel says the work is going well and it hopes to finish "very soon."

The first release will cover only pure Yang-Mills theory, the version without quarks, even though OpenAI says it has also handled the case with quarks. The panel plans to publish the 1,147 pages the AI wrote later, along with its own assessment, and only once it's convinced they're correct. It attached its working rules to the interim report.

No million-dollar prize, and criticism of the process

One thing matters for context: the Millennium Problem has two parts. First, you have to show the theory exists mathematically. Second, you have to prove the so-called mass gap, meaning the lightest particles in the theory have a mass greater than zero. The second part is still open. As aiweekly.co points out, citing a fact check by MindStudio, the current claim wouldn't trigger the prize money.

Not everyone is happy with the pace. In late October, nine mathematicians from AGMAI, a volunteer group that advises OpenAI on math, called for the proofs to be published "immediately." AGMAI had generally advised against giving results to hand-picked people first. It named three problems with that approach: unequal access, borrowed credibility and selection bias. It recommended releasing results to the research community instead.

The backstory explains why people are touchy. According to mezha.ua, OpenAI published 722 math papers from its unreleased model in early October. Some of them hadn't been formally checked and may have contained errors. An earlier claim about the Navier-Stokes problem had sparked a fight over methods and possible breaches of academic norms. This time, OpenAI is relying on outside "shepherds" to oversee the results. The company names four principles: transparency, no claim to academic credit, proper attribution of contributions, and independence. It says taking part is voluntary and unpaid. OpenAI also donated $5 million to the Simons Foundation for workshops and conferences on AI-generated research. The company admits it doesn't "yet" know which of the three release approaches works best.

The bottom line

If even some of these claims hold up, it would be a historic moment: AI systems would have solved decades-old foundational problems in mathematics, computer science and physics. So far, though, none of it has been confirmed. A Lean proof only guarantees logical correctness within the chosen definitions. It doesn't guarantee that the famous problem was actually solved. The Yang-Mills claim is the most spectacular, and it's also the least transparent because everything is being withheld. That's why mathematicians are pushing back. The Gross panel, for its part, apparently wants to keep 1,147 unreviewed pages from causing confusion.

Even a confirmed ETH refutation wouldn't make hard computational problems easy overnight. But researchers would have to rethink a lot of assumptions about how fast algorithms can be. The hint of a similar result at Anthropic is intriguing too. The coming weeks should show whether AI math is having its breakthrough moment or whether the claims turn out to be overblown.