OpenAI scientific discoveries

On 26 October 2026 OpenAI announced three results produced by its internal, unreleased models, in harmonic analysis, complexity theory and quantum field theory. The mathematics result is a proof of Sogge's local smoothing conjecture in every dimension. OpenAI states this also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions, using a novel auxiliary partial differential equation. The computer science result is a claimed refutation of the Exponential Time Hypothesis (ETH), a conjecture on the complexity of Boolean satisfiability. OpenAI says this was verified in Lean.\n\nOpenAI treats the manuscripts as raw research data and asked external experts to act as shepherds who organise groups to understand them. For the math result, the AI output is released and researchers organise their own efforts. For the ETH result, a group led by Russell Impagliazzo and others (UC San Diego and collaborators) is explaining it. The natural language proof and Lean formalization were published on OpenAI's GitHub repository. For the physics result on quantum chromodynamics, the group chose to hold back the AI artifacts and write it up themselves. Third-party video coverage describes this as a Yang-Mills existence result, not the mass gap.\n\nThe collaborations follow four stated principles: transparency with no NDAs, no academic credit claimed by OpenAI, recognition for the working groups, and independence of unpaid volunteer participants. These are claims by OpenAI and still need independent expert verification. The underlying model is not available to the public. The materials are for researchers and anyone who wants to examine the proofs.