Axiom Math Verifies Stacks Project in 16 Million Lines of Lean Code
Axiom Math converted the 7,654-page Stacks Project into 16 million lines of verified Lean code, creating a foundation for AI proofs and secure software.
Summary
On November 4, 2026, $1.6 billion startup Axiom Math announced the formal verification of the Stacks Project, one of mathematics’ largest human-written collections. Johan de Jong began the open source reference in 2005, covering college algebra through advanced algebra, geometry and number theory. Columbia mathematician Peter Woit has compared its significance with the foundational Bourbaki books. Axiom’s AI agents translated roughly 7,654 pages into about 16 million lines of Lean code while preserving the library’s interdependent definitions and theorems.
Lean proof assistants check code line by line for logical soundness. Axiom trained proprietary math models, initially guided by an in-house Lean expert, then used agents that selected tasks and worked in parallel under a loose hierarchy. The result gives researchers reusable foundations for formalizing algebraic geometry, previously a major gap, and could support verified software and eventually science. Engineers already apply formal verification to chips, while French researchers have used it to find bugs in family-benefit software. CEO Carina Hong, 25, founded Axiom in March 2025 after leaving Stanford’s math PhD program; the company raised a $200 million Series A led by Menlo Ventures in March 2026. With OpenAI releasing 719 claimed solution manuscripts in October 2026 and computer checks still fallible, Axiom argues that AI-written proofs and code need verified libraries, and Hong challenged coding companies to formalize work at comparable scale.
Positives
- Axiom converted roughly 7,654 Stacks Project pages into about 16 million lines of computer-checked Lean code.
- The verified library supplies reusable foundations for algebraic geometry, an area that previously offered Lean researchers little established groundwork.
- Axiom’s agents preserved interconnected definitions and theorems while selecting tasks and working concurrently under a loose hierarchy.
- The $200 million Series A led by Menlo Ventures gives Axiom funding to pursue verified foundations for software and science.
- Formal verification already supports chip validation and has identified bugs in French family-benefit software.
Risks & concerns
- OpenAI released 719 manuscripts claiming difficult mathematical solutions in October 2026, intensifying concerns about low-quality AI-generated research.
- Computer-based checks can still miss problems, making reliable foundations essential even when mathematical work is automated.
- AI agents writing more software could amplify existing bugs and security vulnerabilities.
- Axiom initially doubted whether loosely directed AI agents could preserve the Stacks Project’s delicate network of dependencies.
- Formalized mathematics previously had a major gap across algebraic geometry, leaving researchers with little verified material to reuse.