Axiom Math announced in November 2026 that its AI agents have formally verified the Stacks Project, one of the largest mathematical libraries ever assembled, translating roughly 7,654 pages into approximately 16 million lines of computer-checked code written in the programming language Lean.
The Stacks Project was started in 2005 by Columbia mathematician Johan de Jong as an open-source reference covering topics from college-level algebra through advanced algebraic geometry, algebra, and number theory. Columbia mathematician Peter Woit has described it as having “nothing else really comparable,” likening it to the Bourbaki books, a 20th-century series that rebuilt mathematics from its foundations.
Formal verification works by rewriting mathematical proofs as code, which a proof assistant then checks line by line for logical soundness. Axiom’s challenge with the Stacks Project was preserving the interconnected structure of its theorems and definitions — each result builds on those before it — across all 16 million lines of code.
“Things that are big and things that are delicate in life just don’t go together,” said Axiom CEO Carina Hong. To manage the scale, the company’s agents were given a loose hierarchy and allowed to work in parallel, identifying tasks independently. Axiom also trained its own models specifically for mathematics, which Hong said most other verification startups have not done.
Hong, 25, dropped out of a Stanford mathematics Ph.D. program and founded Axiom in March 2025. The company, valued at $1.6 billion, raised a $200 million Series A led by Menlo Ventures in March 2025.
The verification fills what Axiom’s Ashvin Swaminathan called a significant gap: algebraic geometry had little existing formalized foundation for researchers to build on in Lean. Axiom argues that verified mathematical results can serve as reusable building blocks for AI agents writing software, potentially reducing errors as AI-generated code becomes more prevalent.
“If you slop drop in a way that’s bad engineering choices in the beginning, then it’s very hard for them to grow that boundary,” Hong said.
Source: TechCrunch