OpenAI Claims Three More Results in Math, Computer Science and Physics
Dates and claims
OpenAI says its models produced a natural language disproof of the Exponential Time Hypothesis on October 16, 2026, and that the result was formalized in Lean the next day. The hypothesis, proposed by Russell Impagliazzo, Ramamohan Paturi and Francis Zane, is commonly stated as the claim that 3-SAT cannot be solved in subexponential time. OpenAI's October 26 announcement says it has been used in hundreds of papers to derive conditional hardness results in graph theory, computational biology, databases and computational geometry. The company adds that refuting it reopens questions about how much faster these tasks could become, and that finding such algorithms will take significant further research.
The second claim is a proof of the local smoothing conjecture in every dimension. Christopher Sogge proposed it in 1991. Guth, Wang and Zhang proved the two-dimensional case in 2019, and Wang and Zahl proved the Kakeya conjecture in three dimensions in 2025. OpenAI says its proof, which rests on a novel auxiliary partial differential equation, also resolves the Kakeya and Stein restriction conjectures in all dimensions. The AI output is dated October 18 and the Lean formalization October 19.
The third claim comes from physics. OpenAI says its models produced a proof of the existence of Yang-Mills theory on September 9 and of quantum chromodynamics on September 18, building on Balaban's approach to constructive quantum field theory. The work also covers a unified completion of the Standard Model. Pure Yang-Mills existence is part of the Clay Mathematics Institute's Millennium Prize problem on quantum Yang-Mills theory. The announcement reports a Lean formalization of the Yang-Mills proof, finished October 16, and does not mention one for the QCD proof.
The reviewing groups
OpenAI describes the manuscripts as "a form of raw research data" and says it asked outside experts to organize groups to work through them. Those experts recommended three different release approaches.
For the mathematics result, the AI-written paper and the Lean proof went into OpenAI's public GitHub repository, and researchers are free to organize their own efforts to explain it. For the Exponential Time Hypothesis, a group led by Impagliazzo, Paturi and Ryan Williams of MIT will verify and explain the result. Williams has previously refuted strong versions of the hypothesis and used it in hardness results. The group asked that all raw data be made public and that OpenAI fund a conference on what the result means for the field, and OpenAI agreed to both. The natural language proof and Lean formalization are already in the repository.
For the physics result, David Gross leads a group with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. Gross shared the 2004 Nobel Prize in Physics for his 1973 work on asymptotic freedom. The group chose to hold back the AI-produced artifacts and write up the result itself, and it asks that communications go to YANGMILLS4D@gmail.com
Terms of the collaborations
OpenAI lists four principles. Participants sign no nondisclosure agreements and may share intermediate work and publish their conclusions. OpenAI says it does not seek academic credit for discoveries made by its models, and that inviting a researcher to steward a group does not mean that researcher made the discovery. Members are unpaid, participate independently and do not speak for OpenAI. The announcement states that choosing the first shepherds shapes who gets involved first and creates an asymmetry of information, and it asks for feedback on how to broaden participation.
OpenAI also points to a $5 million contribution to the Simons Foundation, which will fund workshops, conferences and programs for researchers working to understand AI-produced results, and says it will ensure funding for researchers to examine and build on these three results. The proofs and Lean files are in the openai/math repository on GitHub, and the full announcement is at openai.com/index/building-scientific-understanding-with-academic-communities. The announcement gives no date or location for the conference on the Exponential Time Hypothesis and no timeline for the physics group's writeup.
Author Bio
David Borish is the author of The Tony Hawk Paradox: When Video Games Predict Reality and publishes at davidborish.com
