OpenAI Group PBC has released 722 mathematical papers produced by an unreleased artificial intelligence model. These documents, published on GitHub, cover approximately 20 mathematical subfields and address long-standing hypotheses, disprove existing theories, and refine solutions to complex problems.
A key achievement involves the quasi-Riemann hypothesis, a component of the 150-year-old Riemann hypothesis concerning prime numbers. Additionally, the model generated over 80 papers focused on theoretical computer science, including new definitions for limits in matrix multiplication and a novel algorithm for integer multiplication.
The research also impacts physics, with over a dozen proofs related to partial differential equations. The model addressed De Giorgi’s conjecture regarding metal alloys and provided insights into the Navier–Stokes equations, which are used to analyze fluid dynamics.
Many of the published papers include Lean files, which allow for automated verification of the proofs. OpenAI intends to provide Lean proofs for additional papers in the future and plans to fund programs and events dedicated to reviewing these AI-generated mathematical discoveries.
