Academic researchers will examine work on wave behavior, the limits of computation and the mathematical foundations of particle physics
OpenAI says its models have produced three research results spanning mathematics, computer science and physics, including a proof about how waves concentrate and a disproof of a longstanding assumption about the time computers need to solve certain problems.
The company is working with academic researchers to examine and explain the findings. It has released the mathematics and computer science materials publicly, while an external physics group will determine how to release that work.
Katrina Mulligan, Head of National Security Partnerships at OpenAI for Government, discussed the results on LinkedIn, outlining research into Sogge’s local smoothing conjecture, the Exponential Time Hypothesis and quantum chromodynamics.
Understanding how waves concentrate
The mathematics result concerns Sogge’s local smoothing conjecture, which describes how waves become concentrated. Its central idea is that the most intense concentrations cannot persist for long.
Mulligan wrote: “Our models produced a proof of Sogge’s local smoothing conjecture, which concerns how waves concentrate over time. The result also has implications for the Kakeya conjecture in all dimensions.”
OpenAI says the proof covers every dimension and also resolves the Kakeya and Stein restriction conjectures, two connected mathematical problems.
The company has published an explanatory manuscript and a formal proof in Lean, software that checks mathematical arguments against precise logical rules. This gives researchers both a written account to study and a computer-checkable version of the reasoning.
Reconsidering the limits of computation
The computer science result challenges the Exponential Time Hypothesis, an assumption about how difficult a problem called 3-SAT is to solve.
In 3-SAT, a computer must determine whether a collection of logical conditions can all be satisfied at once. Each condition contains three terms that can be true or false. The hypothesis holds that, in the worst case, the time needed to solve the problem grows exponentially with the number of variables.
Mulligan wrote: “Our models produced a disproof of the Exponential Time Hypothesis, a longstanding assumption about the time needed to solve 3-SAT.”
A group led by Russell Impagliazzo and Ramamohan Paturi at the University of California San Diego, and Ryan Williams at the Massachusetts Institute of Technology, will examine the work.
The result concerns theoretical limits on computation. Developing practical algorithms from it will require further research.
Strengthening the foundations of particle physics
The physics work concerns quantum chromodynamics, or QCD, the theory of the strong force, and a unified completion of the Standard Model.
Mulligan explained: “Our models produced mathematical existence results for quantum chromodynamics, the theory of the strong force, and a unified completion of the Standard Model. The work also addresses part of the Yang–Mills Millennium Prize problem.”
An existence proof establishes that a theory can be constructed as a mathematically consistent object. The Yang–Mills Millennium Prize problem also requires establishing a “mass gap,” a property concerning the minimum energy of an excited state above the vacuum. The reported existence result addresses one component of that wider challenge.
David Gross will lead the physics group, alongside Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov.
The collaborations come alongside wider support for researchers adapting to AI-generated discoveries. The Simons Foundation, Anthropic and OpenAI have committed a combined $15 million in funding and resources to help the mathematics community evaluate results, use new tools and develop shared standards.
OpenAI says: “We continue to invite feedback on the best way to disclose results and engage with scientists to accelerate discovery.”
