On 2026-10-26, OpenAI announced three new discoveries in mathematics, computer science and physics, concerning harmonic analysis, complexity theory and quantum field theory (OpenAI). The company states that its models proved the local smoothing conjecture in every dimension and that its system proved the Exponential Time Hypothesis (ETH) false (OpenAI). It reached out to external experts and asked them to act as shepherds, organizing groups to understand the new results (OpenAI).
Key Facts
| Item | Detail | Source |
|---|---|---|
| Math result | Local smoothing conjecture proof in every dimension, with Kakeya and Stein implications | OpenAI |
| Computer science result | Refutation of the Exponential Time Hypothesis, verified in Lean | OpenAI |
| Physics result | Existence proof of certain interacting quantum field theories in four dimensions | The Verge |
| ETH group | Led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams | OpenAI |
| Physics group | Led by David Gross | The Verge |
Timeline
- 2026-10-06: OpenAI made an earlier release of math output, the strategy it followed again for the local smoothing result (OpenAI).
- 2026-10-18: OpenAI obtained the AI output for the math result, which was formalized in Lean the following day (OpenAI).
- 2026-10-26: OpenAI announced the three discoveries and added the results to GitHub (The Verge).
Details (as Reported)
OpenAI describes the manuscripts as a form of raw research data and states that the shepherds advised three different release strategies (OpenAI). For the math result, the AI output was released and researchers are free to organize their own efforts to explain it (OpenAI). On the computer science result, an external group explains the work while the AI output stays public (OpenAI). In physics, an external group defers to its own judgment on releasing materials (OpenAI).
The Verge reported that the ETH paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, and that the 3-SAT case refutes the hypothesis (The Verge). OpenAI notes that ETH has been used in hundreds of papers to derive conditional hardness results, and that finding better algorithms will require significant further research (OpenAI). Impagliazzo and Paturi are original proposers of the hypothesis, and Williams has refuted strong versions of it (OpenAI). The group asked that all raw data be made public, and OpenAI agreed to fund a conference on the implications (OpenAI).
The collaborations follow four principles: transparency, no academic credit for OpenAI, recognition for the groups, and independence (OpenAI). Participants sign no nondisclosure agreements, and participation is voluntary and unpaid (OpenAI).
Engadget reported that the announcement follows a release of manuscripts with over 700 pages covering 372 major math problems, and that the physics group provided an email address for questions about its efforts (Engadget).
What Is Not Yet Confirmed
- OpenAI states that it does not yet know which of the three release approaches will be most useful (OpenAI).
- The ETH work is still to be verified and explained by the Impagliazzo, Paturi and Williams group (OpenAI).
- The physics information has not been released in full (The Verge).
- The AGMAI panel of math advisers recommended that AI companies not adopt the practice of designating certain people to receive output first, citing unequal access, borrowed reputation and biased selection (The Verge).