OpenAI Claims Three Major Scientific Discoveries in Math, Computer Science, and Physics
OpenAI says a deterministic, polynomial-space algorithm for exactly counting fixed-width CNF solutions refutes the Exponential Time Hypothesis in the 3-SAT case. Its wave-equation proof targets Sogge’s conjecture, with outside academic “shepherds” reviewing the work.
OpenAI announced in October 2026 three new “major” discoveries spanning mathematics, computer science, and physics — arriving less than a month after the company released hundreds of manuscripts it said contained solutions to long-standing mathematics problems.
The first result addresses local smoothing for the Euclidean wave equation. According to OpenAI, the proof uses an auxiliary partial differential equation to establish Sogge’s local smoothing conjecture for waves across every spatial dimension of at least two. The company says it also yields results on the Kakeya maximal and dimension conjectures and Stein’s spherical restriction estimates.
The second result carries the title “The Exponential Time Hypothesis is False.” The paper describes a deterministic algorithm capable of exactly counting satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The specific case of 3-SAT, the company states, refutes the Exponential Time Hypothesis — a significant claim in theoretical computer science.
A third discovery in physics was also referenced, though detailed findings were not included in the released materials.
A notable change from OpenAI’s earlier October release is the introduction of external academic oversight. OpenAI is using outside experts it describes as “shepherds” to guide the results through scrutiny. For the computer science result, an independent working group led by researchers Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams will examine and explain the proof. At that group’s request, OpenAI made the materials publicly available immediately so the broader research community can review them.
The results were added to GitHub on October 26, 2026. The math and physics outputs were released directly as model output, consistent with OpenAI’s approach in its earlier October 6 release, while the computer science result is subject to the independent review process.