OpenAI claims research advances in mathematics, computing and physics

OpenAI announced on October 26, 2026, that its AI models had solved or made substantial progress on long-standing scientific problems. The company described results spanning harmonic analysis, computational complexity and quantum field theory, alongside a framework for academic experts to explain and evaluate the findings.

In mathematics, OpenAI claims a proof of the local smoothing conjecture in every dimension that also resolves the Kakeya and Stein’s restriction conjectures. In computer science, it claims to have refuted the Exponential Time Hypothesis using a subexponential algorithm, without establishing P=NP. The physics work concerns rigorous existence proofs for interacting quantum field theories, including Quantum Chromodynamics and pure Yang-Mills theory.

Validation and disclosure will differ by field. The mathematics output will be released for public examination. External complexity theorists, including Russell Impagliazzo, Ramamohan Paturi and Ryan Williams, will help explain the computing result while its output remains publicly available. A physics group led by David Gross will control the timing of its materials and prepare its own writeups. OpenAI says participation is voluntary and unpaid, requires no nondisclosure agreements and leaves collaborators free to reach independent conclusions.

OpenAI has committed $5 million to the Simons Foundation for activities helping researchers understand and extend AI-generated results, plus funding for a complexity theory conference. Reactions include enthusiasm for faster discovery and concerns about unequal access to findings and the difficulty of understanding complex proofs.