OpenAI releases AI claims in maths, computer science

OpenAI has released new AI-generated research results in mathematics and computer science, and set up an external collaboration to assess a separate physics result. The work includes claims that, if confirmed, would resolve longstanding problems in all three fields.

The approach marks a change in how OpenAI is disclosing scientific outputs from its models. It has adopted different release strategies for each subject area and asked external researchers to organise and explain the findings. Participants will not sign non-disclosure agreements, will receive no payment and will be free to publish their own conclusions.

In mathematics, OpenAI said its models produced a proof of the local smoothing conjecture in every dimension, a result that it said would also settle the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The proof relies on a new auxiliary partial differential equation.

OpenAI has published both a natural-language write-up generated by its models and a Lean formalisation of the proof. It chose to release the mathematics material directly and leave researchers to organise their own efforts to explain the result.

The local smoothing conjecture sits in harmonic analysis and concerns how waves behave as they become focused. Earlier progress included a 2019 proof in two spatial dimensions by Larry Guth, Hong Wang and Ruixiang Zhang. Wang and Joshua Zahl proved the Kakeya conjecture in three dimensions in 2025.

Computer science

In computer science, OpenAI said its system had proved that the Exponential Time Hypothesis, or ETH, is false. The conjecture has long been used across theoretical computer science as a basis for conditional hardness results tied to the difficulty of Boolean satisfiability and related questions.

To examine that claim, an external group 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 will verify and explain the work. OpenAI has also released the natural-language disproof and the Lean formalisation for public scrutiny.

The group asked for all raw data associated with the result to be made public to support independent verification by the wider research community. OpenAI has also agreed to fund a conference on the implications of the work for the field, although it did not provide further detail.

The ETH was originally proposed by Impagliazzo, Paturi and Francis Zane, and has been influential for roughly three decades in complexity theory and adjacent areas including graph theory, databases, computational biology and computational geometry. A disproof, if upheld, would prompt a reassessment of many conditional lower-bound arguments built on the assumption that the conjecture is true.

Physics review

For physics, OpenAI said it would not yet release the underlying AI-produced artefacts. Instead, an outside group will work through a claimed existence proof for certain interacting quantum field theories in four dimensions, including quantum chromodynamics and a unified completion of the Standard Model.

David Gross will lead the group, which includes Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. OpenAI said the work also contains, as a subproblem, a proof of the existence of pure Yang-Mills theory, which forms part of the Clay Mathematics Institute Millennium Prize problem on quantum Yang-Mills theory.

According to OpenAI, the models first produced a natural-language proof for Yang-Mills existence and later one for QCD. It delayed release because of the size and complexity of the material until formalisation work was completed. Unlike the mathematics and computer science releases, the physics collaboration chose to hold back the AI-generated artefacts while preparing its own write-up.

Release model

OpenAI said it had asked outside experts to act as shepherds for groups intended to build understanding around the results. It described the collaborations as transparent and independent, saying members do not speak on behalf of the company, and the company does not speak on theirs.

It also said it does not seek academic credit for discoveries produced by its internal models. Instead, researchers involved in the collaborations should receive recognition for the understanding, papers and other explanatory materials they create around the results.

OpenAI acknowledged trade-offs in the process, saying that selecting initial shepherds inevitably influences who becomes involved first and creates asymmetries of information. It added that it wants feedback on how to broaden participation and improve the way such results are disclosed to academic communities.

OpenAI also pointed to a separate USD $5 million contribution to the Simons Foundation, which it said would support workshops, conferences and special programmes for researchers examining AI-produced findings. It 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."