OpenAI recruits experts to verify AI-generated math and physics proofs

The three major results

OpenAI recently announced that its internal models produced three distinct results in the fields of mathematics, computer science, and physics. The company describes these outputs as raw research data that currently require human interpretation to be fully understood. Because of this complexity, OpenAI is enlisting outside experts to serve as 'shepherds' for the findings.

The computer science result involves the Exponential Time Hypothesis (ETH). This hypothesis suggests that certain problems, like the Boolean satisfiability problem (SAT), have no shortcuts and require time that grows exponentially as variables are added. OpenAI claims its system has proved that the ETH is actually false, which could impact hundreds of papers in fields like computational biology and graph theory.

In mathematics, the AI reportedly proved the local smoothing conjecture for waves in every dimension. This conjecture suggests that waves behave more smoothly over time than extreme concentrations might suggest. Because this is a foundational result, it also automatically proves two other major conjectures: the Kakeya conjecture from geometry and Stein's restriction conjecture from Fourier analysis.

Physics and the mass gap

The third result concerns quantum field theory, which is the primary framework for describing elementary particles and forces. While the theory is highly accurate, it currently lacks an exact mathematical basis and relies on approximations. OpenAI claims its AI proved that certain quantum field theories exist mathematically in four dimensions, specifically for theories where particles interact.

One of the specific theories covered is Yang-Mills theory, which describes gluons. This theory is tied to one of the seven Millennium Prize Problems, which offer a $1 million prize from the Clay Mathematics Institute. OpenAI clarified that they have only solved the 'existence' part of the problem, not the 'mass gap' puzzle, which explains why the strong force acts over tiny distances.

The proof also extends to quantum chromodynamics (QCD), which adds quarks to the description of the strong force. Because the strong force gets weaker as particles get closer—a property called asymptotic freedom—the math remains manageable. If the proof holds, it would provide a rigorous mathematical foundation for these fundamental descriptions of nature without changing current physical predictions.

Verification using Lean

To help the scientific community verify these complex proofs, OpenAI translated the math and computer science results into Lean. Lean is a programming language designed to let a computer check every individual step of a mathematical proof. This process ensures that the proof establishes the statement as it was written in the code.

However, using Lean does not guarantee that the final result is entirely error-free. It only confirms that the logic follows the rules of the language. Human experts must still determine if the specific statement written in Lean actually captures the intended original problem correctly. This distinction is why human oversight remains a critical component of the verification process.

The company is handling each of the three results differently based on expert advice. For the math result, they published the proof text and the Lean code directly so researchers can check it independently. For the physics result, a group led by Nobel laureate David Gross is holding back the materials to write up the results themselves before public release.

The path to peer review

OpenAI is navigating a complex review process that involves significant trade-offs regarding who gets to see the data first. The company admits that the choice of who acts as the first 'shepherd' determines who gets involved in the research earliest. They have pledged $5 million to the Simons Foundation to fund workshops and conferences to help the community interpret these results.

The company stated that it is not claiming scientific credit for these discoveries. Instead, they believe the credit belongs to the groups of scientists who eventually explain and validate the results. This approach appears to be a response to previous criticisms regarding how the company handles and presents its AI-generated research outputs.

Independent researchers are also calling for a broader debate on the implications of these findings. They are raising questions about how to verify AI-driven breakthroughs, who should have access to the raw data, and how credit should be distributed. OpenAI has committed to publishing all raw data, including written and Lean proofs, to facilitate this ongoing discussion.