Key points
- Axiom Math used AI agents to translate the Stacks Project into approximately 16 million lines of Lean code.
- The verification ensures logical soundness by checking each line of code against formal mathematical definitions and theorems.
- The company intends to build a verified foundation that AI agents can rely on for software development and scientific research.
Axiom Math announced on Wednesday that its AI agents had formally verified the Stacks Project, one of the largest human-written bodies of mathematics.
The evidence
TechCrunch reported that the startup’s fleet of AI agents completed this translation, addressing concerns about the reliability of AI-generated mathematical content.reported The Stacks Project, initiated by Johan de Jong in 2005, serves as an open-source reference covering results from college-level algebra to advanced ideas in geometry and number theory.reported Columbia mathematician Peter Woit has described the project as comparable to the Bourbaki books, noting there is nothing else really comparable in the field.
The decision
Axiom Math is betting on verification rather than speed to ensure mathematical integrity. The company aims to build a verified foundation that AI agents can rely on to write software and eventually conduct science. By converting the Stacks Project into Lean code, the startup provides a structure where a proof assistant checks each line, ensuring that the underlying mathematical structure is sound before any AI agent uses it.
What to make of it
The interconnected nature of the Stacks Project presented significant technical challenges. Engineers had to maintain every connection between theorems and definitions across the 16 million lines of code, tracing results back through a family tree of mathematical dependencies. Axiom CEO Carina Hong told TechCrunch that big and delicate things rarely go together, highlighting the difficulty of verifying such a foundational collection of mathematical results without breaking its intricate links.
In practice
Access to the verified Stacks Project allows developers to benchmark their systems against a known-correct library, reducing the risk of relying on hallucinated or flawed proofs. However, availability is currently limited to this specific library, and the material does not confirm whether broader mathematical domains are yet verified or accessible for general use.
Why it matters
- Founders can use the verified Stacks Project as a ground-truth dataset to validate the logical consistency of their AI agents’ outputs.
- The shift from unchecked claims to formal verification addresses the reliability gap in AI-generated mathematical proofs, which is critical for software and science applications.
- Understanding the complexity of verifying interconnected theorems helps founders anticipate the engineering challenges of scaling formal verification to other domains.
- The project demonstrates that AI agents can handle delicate, large-scale tasks, providing a case study in managing complex dependencies in automated reasoning.
Topics: AI agents, formal verification, Lean, mathematics, Axiom Math
Updated
Then / now / next
Mathematicians relied on human-checked proofs and open-source references like the Stacks Project for foundational mathematics.
Axiom Math has formally verified the Stacks Project using AI agents, translating it into 16 million lines of Lean code.
The company plans to expand this verified foundation to support AI agents in writing software and conducting scientific research.
Story timeline
- Then Mathematicians relied on human-checked proofs and open-source references like the Stacks Project for foundational mathematics.
- 05 Nov 2026 Axiom Math wants to keep AI slop out of mathematics
- Now Axiom Math has formally verified the Stacks Project using AI agents, translating it into 16 million lines of Lean code.
- Next The company plans to expand this verified foundation to support AI agents in writing software and conducting scientific research.
The strongest doubt
Counterpoint from the sources
The interconnectedness of the Stacks Project made Axiom unsure if the verification would succeed, as maintaining every connection across millions of lines of code is technically difficult.
For readers
Developers
- The verified Stacks Project provides a large dataset of correct Lean code for testing AI agents.
- Developers can use the 16 million lines of code to benchmark their systems’ ability to handle complex dependencies.
Researchers
- The project demonstrates the feasibility of using AI agents to verify large, interconnected mathematical libraries.
- Researchers can study the challenges of maintaining theorem connections during the formalization process.
Investors
- Axiom Math has secured $1.6B in funding to build a verified foundation for AI applications.
- The company’s focus on verification addresses a key reliability concern in AI-generated content.
Ask the article
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Your choice stays on this device. No public tally.Questions readers ask
How many lines of code did the AI agents generate?
The AI agents generated approximately 16 million lines of Lean code.
What is the Stacks Project?
It is an open-source reference library of mathematics started in 2005, covering algebra, geometry, and number theory.
Is this verification available for other mathematical libraries?
The source material only confirms the verification of the Stacks Project; it does not state whether other libraries are verified.
Connected stories
Reading receipt
- Axiom Math used AI agents to translate the Stacks Project into approximately 16 million lines of Lean code.
- The verification ensures logical soundness by checking each line of code against formal mathematical definitions and theorems.
- The company intends to build a verified foundation that AI agents can rely on for software development and scientific research.