OpenAI claims advances in mathematical proofs and quantum field theory

OpenAI says its AI models have produced major results in mathematics, computer science and physics, including proofs addressing longstanding conjectures. The company reports that the mathematics and computer science proofs have been formally verified using Lean and published on GitHub. The findings still require independent confirmation from the academic community.

In harmonic analysis, OpenAI claims a proof of the local smoothing conjecture in all dimensions, which would also establish the Kakeya and Stein restriction conjectures in all dimensions. The proof relies on a newly constructed auxiliary partial differential equation. Both natural-language and formally verified versions are publicly available.

In computational complexity, OpenAI says its systems disproved the exponential time hypothesis, a widely used assumption underpinning conclusions about computational difficulty. Researchers would need to reassess those conclusions and investigate opportunities for faster algorithms, although practical applications would require substantial further work. Russell Impagliazzo, Ramamohan Paturi and Ryan Williams are leading external scrutiny, with public research materials and an academic conference planned.

In physics, OpenAI claims a rigorous existence proof for quantum chromodynamics and a unified theory containing the Standard Model’s gauge fields and fermions. The work also addresses the existence of pure Yang-Mills theory, a component of a Millennium Prize Problem, rather than claiming to resolve the entire problem. David Gross is leading an expert review alongside mathematical physics researchers.