OpenAI says its internal models proved three major results in math, computer science and physics, including a claimed refutation of the Exponential Time Hypothesis
Announcing three major scientific discoveries, one each in mathematics (harmonic analysis), computer science (complexity theory), and physics (quantum field theory). AI starting to help us improve our understanding of the universe!
Context
If the claims survive expert review, an AI system will have settled long open questions in harmonic analysis, complexity theory and quantum field theory, which would change how fundamental research gets done. These are OpenAI's own claims, and the outside expert groups it recruited have not finished checking them.
OpenAI published the announcement on its site on October 26, and its president Greg Brockman and researcher Dan Roberts shared it on X that evening. OpenAI says each result was produced by its internal models and formalized in the Lean proof assistant. MIT complexity theorist Ryan Williams, one of the outside experts asked to examine the computer science result, posted that the refutation of the Exponential Time Hypothesis is still a claim under independent examination.
Deep dive
OpenAI announced on October 26 that its internal models produced three new results, one each in mathematics, computer science and physics. Greg Brockman, OpenAI's president, shared the news on X, where his post passed 1.8 million views.
In mathematics, OpenAI says its models proved the local smoothing conjecture, proposed by Christopher Sogge in 1991, in every dimension. According to OpenAI, this also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The company says it obtained the output on October 18, formalized it in Lean the next day, and released both the writeup and the Lean proof on GitHub.
In computer science, OpenAI says its system proved that the Exponential Time Hypothesis, a widely assumed limit on how fast the 3SAT problem can be solved, is false. Ryan Williams posted that the preprint claims 3SAT on n variables can be solved in roughly exp(n/(log n)^(1/2)) time. Williams, Russell Impagliazzo and Ramamohan Paturi, two of the original proposers of the hypothesis, will lead an open examination. Williams wrote that the group has not fully vetted the result yet, and that OpenAI told him existing cryptosystems appear unaffected.
In physics, OpenAI says its models produced a rigorous existence proof for quantum chromodynamics and a unified completion of the Standard Model, which includes the existence of pure Yang Mills theory, part of a Clay Millennium Prize problem. A group led by Nobel laureate David Gross will shepherd that work and has chosen not to release the AI artifacts yet.
OpenAI says it seeks no academic credit, will fund a conference on the complexity result, and points to its earlier 5 million dollar contribution to the Simons Foundation.
What to expect next
The key question is verification. The complexity group led by Williams, Impagliazzo and Paturi has invited the community to examine the public proof and Lean formalization, and a flaw or a confirmation could come quickly given the attention. The physics group around David Gross controls its own release timing, so outside review of the Yang Mills and QCD claims will take longer. Watch for responses from the Clay Mathematics Institute, for any attempt to turn the 3SAT algorithm into practical solvers, which Williams said may or may not happen within a year, and for rival labs publishing similar claims.