What changed
On October 26, 2026, OpenAI announced three new scientific discoveries in mathematics, computer science, and physics. These results include a proof of the local smoothing conjecture in harmonic analysis, a refutation of the Exponential Time Hypothesis (ETH) in computational complexity theory, and progress on quantum field theory. The release strategies for each result differ, with some materials made publicly available and others being worked on by external collaborators.
What this means in practice
The mathematics result concerns the local smoothing conjecture, which was previously proven in two spatial dimensions and the Kakeya conjecture in three dimensions. OpenAI's models produced a proof valid in all dimensions, resolving both conjectures. The AI-generated proof is available in a public GitHub repository as a natural language writeup and a formalized Lean proof.
The computer science result challenges the ETH, a long-standing conjecture about computational complexity. OpenAI's models refuted the ETH, a finding verified in Lean. The result is being shepherded by a group of experts led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams.
The group has requested that all raw data be made public and that OpenAI fund a conference to explore the implications of this work.
Limitations and availability
The physics result is being handled by an external group of collaborators, who have decided to hold off on releasing AI-produced artifacts and instead focus on writing up the findings. The release strategies for each result reflect a balance between transparency and the need for expert interpretation. OpenAI has committed to making all materials available to the collaborations, but the exact timeline for public release is not specified. The AI-generated outputs for the mathematics and computer science results are available in OpenAI's public GitHub repository.
