OpenAI releases AI claims in maths, computer science
OpenAI has shared new research results produced by its AI models in mathematics and computer science. It has also formed a partnership with outside researchers to review a separate result in physics. If confirmed, the findings could solve long-standing problems in all three fields.
This marks a change in how OpenAI shares scientific results created by its models. The company has chosen different ways to release findings in each subject and has asked outside researchers to help explain and organise the work. These researchers will not have to sign non-disclosure agreements, will not be paid and can publish their own conclusions freely.
In mathematics, OpenAI said its models had proved the local smoothing conjecture in every dimension. The company said this result would also settle the Kakeya conjecture and Stein's restriction conjecture in every dimension. The proof uses a new supporting partial differential equation, which is a type of mathematical equation.
OpenAI has published both a proof written in ordinary language by its models and a formal version written in Lean, a computer language used to check mathematical proofs. The company chose to publish the mathematics material directly and let researchers organise their own work to explain the result.
The local smoothing conjecture is part of a field called harmonic analysis. It concerns how waves behave as they become focused. Earlier progress included a 2019 proof for two spatial dimensions by Larry Guth, Hong Wang and Ruixiang Zhang. In 2025, Wang and Joshua Zahl proved the Kakeya conjecture in three dimensions.
Computer science
In computer science, OpenAI said its system had proved that the Exponential Time Hypothesis, or ETH, is false. For a long time, researchers in theoretical computer science have used this hypothesis to support conditional results about how difficult certain problems are to solve. These include Boolean satisfiability, which asks whether a set of logical conditions can all be true at once, and related problems.
An outside team will check and explain this claim. It is led by Russell Impagliazzo of the University of California San Diego, Ramamohan Paturi of the University of California San Diego and Ryan Williams of the Massachusetts Institute of Technology. OpenAI has also published the disproof in ordinary language and its formal Lean version so that the public can examine them.
The team asked OpenAI to make all raw data linked to the result public so that the wider research community can check the work independently. OpenAI has also agreed to fund a conference about what the result could mean for the field, but it has not shared further details.
Impagliazzo, Paturi and Francis Zane first proposed the ETH. For about 30 years, it has played an important role in complexity theory and related fields, including graph theory, databases, computational biology and computational geometry. If the disproof is confirmed, researchers will need to reconsider many arguments about the minimum difficulty of solving problems that depend on assuming the hypothesis is true.
Physics review
For physics, OpenAI said it would not yet publish the original materials produced by its AI models. Instead, an outside group will examine a claimed proof that certain interacting quantum field theories exist in four dimensions. These include quantum chromodynamics, or QCD, and a unified version of the Standard Model that is complete.
David Gross will lead the group. Its members include Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. OpenAI said the work also includes a proof that pure Yang-Mills theory exists. This is part of the Clay Mathematics Institute's Millennium Prize Problem on quantum Yang-Mills theory.
OpenAI said its models first produced a proof of the existence of Yang-Mills theory in ordinary language, followed later by a proof for QCD. The company delayed publishing the work because the material was large and complex, and it wanted the formalisation work to be completed first. Unlike the mathematics and computer science projects, the physics team chose to keep the AI-produced materials private while preparing its own explanation of the work.
Release model
OpenAI said it had asked outside experts to guide groups that would help people understand the results. The company described these partnerships as open and independent. Members do not speak on behalf of OpenAI, and OpenAI does not speak on their behalf.
The company also said it does not seek academic credit for discoveries made by its internal AI models. Instead, the researchers working with the groups should receive recognition for the understanding they develop and for the papers and other explanatory materials they produce about the results.
OpenAI recognised that this process involves trade-offs. Choosing the first experts to guide the work inevitably affects who joins first and means that some people have more information than others. The company said it wants feedback on how to involve more people and improve how these results are shared with academic communities.
OpenAI also highlighted a separate contribution of USD $5 million to the Simons Foundation. It said the money would support workshops, conferences and special programmes for researchers studying findings produced by AI. The company said: "We do not yet know which of these three approaches will be most useful, and we welcome feedback on what works and what we can improve."