On Oct 26, 2026, OpenAI said its internal models produced three major results—in harmonic analysis, complexity theory, and quantum field theory—and described a new release model built around external academic "shepherds." In "Working with academic communities to build scientific understanding", OpenAI calls the manuscripts "a form of raw research data." The claim drawing immediate attention in computer science is that the system disproved the Exponential Time Hypothesis (ETH), with Lean verification the next day. Outside experts are still checking the work; below is what OpenAI has stated publicly.
What OpenAI announced
In computer science, OpenAI says its system proved ETH is false: a natural-language disproof on Oct 16, 2026, formalized in Lean on Oct 17. According to the Lean scope note, the formal result is a deterministic algorithm that exactly counts satisfying assignments of k-CNF formulas on n variables in time 2O(n(log log n)²/√log n) using polynomial space—subexponential, which would refute ETH. In mathematics, OpenAI says its models proved local smoothing in every dimension (output Oct 18, Lean on Oct 19), with public writeups and proofs mirroring OpenAI's Oct 6 math release. In physics, OpenAI says the models produced a rigorous existence proof for certain interacting 4D quantum field theories with gauge fields and fermions, including QCD and a unified completion of the Standard Model; Yang-Mills output is dated Sept 9, QCD Sept 18, and Lean formalization of Yang-Mills existence finished Oct 16.
OpenAI lists four collaboration principles: transparency (no NDAs), no academic credit sought by OpenAI, recognition for shepherd groups, and independence (voluntary, unpaid). That complements a recently announced $5 million contribution to the Simons Foundation for workshops on AI-produced results.
Why the ETH result matters
ETH is a conjecture about the worst-case complexity of Boolean formula satisfiability (SAT). Roughly, it asserts 3-SAT on n variables cannot be solved in 2o(n) time—ruling out dramatically faster algorithms for an enormous family of hard instances. ETH is widely believed and sits near the P vs NP debate; hundreds of papers use it to derive conditional hardness in graph theory, computational biology, databases, computational geometry, and more.
OpenAI says its system refuted ETH. If that stands, many conditional lower bounds would need re-evaluation, and researchers would ask how much faster those problems could become in principle. OpenAI says finding such algorithms, and turning theoretical advances into practical improvements, will require significant further research. A refuted ETH would not by itself imply P = NP.
Shepherds for the complexity result are Russell Impagliazzo and Ramamohan Paturi (UC San Diego) and Ryan Williams (MIT); Impagliazzo and Paturi, with Francis Zane, originally proposed ETH. At the group's request, OpenAI says all raw data is public, it will fund a conference on implications, and the natural-language writeup and Lean proof are on OpenAI's public GitHub.
The math and physics results
Local smoothing. Christopher Sogge proposed the conjecture in 1991 (extreme wave focusing must be short-lived). Guth, Wang, and Zhang proved two-dimensional local smoothing in 2019; Wang and Zahl proved the Kakeya conjecture in three dimensions in 2025. OpenAI says its models proved local smoothing in all dimensions, also resolving Kakeya and Stein's restriction conjecture everywhere, via a novel auxiliary PDE.
Yang-Mills and QCD. OpenAI describes rigorous existence for interacting 4D theories with gauge fields and fermions, building on Balaban's approach, including pure Yang-Mills existence—part of the Clay Millennium Prize problem; OpenAI does not claim the mass gap that the Clay problem also requires. David Gross (2004 Nobel) leads shepherding with Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov; they chose to hold off releasing AI artifacts and write it up themselves.
How the results are being checked
For ETH and local smoothing, OpenAI published natural-language writeups and Lean on GitHub—inviting scrutiny of both the math and the formalization. For physics, the Gross group withheld AI artifacts for now. The shepherds are unpaid, and Ryan Williams calls it "a claimed refutation of ETH" that his group will put through "an open and independent examination." A Lean check confirms only the formal statement as written, so experts must still confirm it matches ETH.
What happens next
A confirmed ETH refutation would ripple through complexity theory; OpenAI's conference and raw data aim to speed that process. Dimension-uniform local smoothing would reshape harmonic analysis if verified. Physics watchers await the shepherd group's writeup; the Yang-Mills and QCD artifacts have not been released. The release follows OpenAI's earlier 722-manuscript drop but ties a few flagship claims to named experts—whether they endure will depend on verification, not headlines alone.