OpenAI and Anthropic say their models independently refuted the Exponential Time Hypothesis, a 27-year-old pillar of complexity theory. This guide explains what ETH claims, what a subexponential 3-SAT algorithm does and does not change, who is checking the proofs, and what the verdict means for algorithms, cryptography and AI-generated science.
OpenAI has published 722 manuscripts in 372 result families from an unreleased internal model, claiming progress on problems from the quasi-Riemann hypothesis to matrix multiplication. We count how much is checked in Lean, explain the 372-versus-377 confusion, score the release against the AGMAI guidelines and set out what it means for businesses relying on AI output.
OpenAI announced on 21 September 2026 that an internal model has resolved more than 100 long-standing open mathematical problems, and that an independent advisory group hosted at the Institute for Advanced Study will now advise on how such results are assessed and released. Ten days earlier, Fields Medallists published a declaration calling the goals of AI companies and mathematicians “severely misaligned.” This article checks both name lists, sets out the compute figures OpenAI published for the Navier-Stokes proof, and identifies the one thing the advisory group is explicitly forbidden from advising on.
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