AxiomMath says it has formally verified the Stacks Project, a major open mathematics reference built by contributors since 2005. The library spans topics from algebra to geometry and number theory, and is widely used as a detailed mathematical resource.
The company's AI agents translated its approximately 7,654 pages into around 16 million lines of code in Lean, a programming language used to formalize proofs. A proof assistant checks the code step by step, helping confirm that each result follows logically from its definitions and supporting theorems.
A foundation for future proofs
Because the results in the Stacks Project build on one another, the work involved preserving a large network of links among definitions and proofs. AxiomMath says its agents divided tasks and worked in parallel, while the company also trained its own models for mathematical reasoning.
The completed formalization gives researchers a substantial base for checking new work, particularly in algebraic geometry, an area with comparatively little existing Lean material. Verified results can serve as reusable building blocks, allowing future proofs to build on checked foundations rather than start from scratch.
The approach may also inform software development, where formal verification can help establish that systems behave as intended. As AI agents take on more complex tasks, a growing library of dependable, reusable knowledge could help them produce work that is easier to verify and extend.
