Key points
- Axiom Math announced the formal verification of the Stacks Project, a major mathematical library.
- The process generated approximately 16 million lines of Lean code from the original text.
- The company aims to build a verified foundation for AI agents to write software and conduct science.
Axiom Math announced on Wednesday that its AI agents had formally verified the Stacks Project, one of the largest bodies of mathematics written by humans. According to TechCrunch, the startup converted the library’s roughly 7,654 pages into about 16 million lines of computer-checked code.reportedThe startup used AI to check the accuracy of a huge math library, turning pages into computer code.Axiom Math’s agents translated the Stacks Project’s 7,654 pages into 16 million lines of verified Lean code. This achievement addresses concerns about unchecked AI-generated proofs flooding the field, as OpenAI recently released hundreds of manuscripts claiming solutions to difficult problems.
The figures
TechCrunch reported that OpenAI released 719 manuscripts last month claiming solutions to hard mathematical problems.reported Axiom Math is valued at $1.6 billion.reported The Stacks Project contains roughly 7,654 pages of content.reported The verification process produced about 16 million lines of Lean code.reported Johan de Jong started the Stacks Project in 2005.reported
Behind the figures
Formal verification requires rewriting mathematical proofs as code in a programming language called Lean. A proof assistant then checks the code line by line. If the proof passes, the structure is considered logically sound. Axiom Math’s fleet of AI agents performed this translation for the Stacks Project. The team had to maintain every interconnected link across the 16 million lines of code, ensuring that results tracing back to earlier definitions remained intact.
What changes, what does not
The verification confirms the logical soundness of the Stacks Project’s theorems and definitions. Mathematicians often hold the project in high regard, with Columbia mathematician Peter Woit comparing it to the famous Bourbaki books. However, the challenge of maintaining delicate connections in large projects initially made Axiom unsure if the effort would succeed. The company states it wants to build a verified foundation for AI agents, not to slow down progress but to stand on firmer ground.
What builders can do with it
Developers can use this verified foundation to ensure AI agents write reliable software. The same formal verification techniques are used by engineers to confirm chip designs work and by researchers in France to catch bugs in software calculating family benefits. Builders can rely on the Stacks Project’s interconnected theorems, which span from college-level algebra to advanced ideas in geometry and number theory. This allows for the construction of systems that depend on logically sound mathematical structures rather than unchecked AI outputs.
Why it matters
- Policy readers can observe a shift from unchecked AI generation to verified outputs in high-stakes fields like mathematics.
- The use of formal verification mirrors techniques in chip design and social benefit software, suggesting broader applicability.
- The scale of the Stacks Project verification demonstrates the capability of AI agents to handle complex, interconnected data structures.
- The startup’s valuation and focus highlight market interest in preventing "AI slop" from compromising scientific and mathematical integrity.
Topics: AI agents, formal verification, mathematics, Lean, Axiom Math
Updated
Then / now / next
Mathematicians contributed to the Stacks Project as an open-source reference since 2005.
Axiom Math’s AI agents have formally verified the library into 16 million lines of code.
The company plans to use this verified foundation for AI agents to write software and do science.
Story timeline
- Then Mathematicians contributed to the Stacks Project as an open-source reference since 2005.
- 05 Nov 2026 Axiom Math wants to keep AI slop out of mathematics
- Now Axiom Math’s AI agents have formally verified the library into 16 million lines of code.
- Next The company plans to use this verified foundation for AI agents to write software and do science.
The strongest doubt
Counterpoint from the sources
Axiom CEO Carina Hong noted that big and delicate things do not go together, and the team was initially unsure if maintaining all connections across 16 million lines would work.
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Your choice stays on this device. No public tally.Terms in this story
Formal verification
Rewriting proofs as code in Lean and checking them line by line with a proof assistant.
Stacks Project
An open-source mathematical library started in 2005, covering algebra, geometry, and number theory.
Lean
A programming language used for rewriting mathematical proofs as code for verification.
Proof assistant
A program that checks code line by line to ensure mathematical proofs are logically sound.
Questions readers ask
What is the Stacks Project?
It is an open-source reference library of mathematics started in 2005 by Johan de Jong, containing results from algebra to number theory.
How does formal verification work?
Mathematicians rewrite proofs as code in Lean, and a proof assistant checks the code line by line to ensure logical soundness.
Why is Axiom Math doing this?
The company aims to build a verified foundation for AI agents to write software and conduct science, avoiding unchecked proofs.
Connected stories
Reading receipt
- Axiom Math announced the formal verification of the Stacks Project, a major mathematical library.
- The process generated approximately 16 million lines of Lean code from the original text.
- The company aims to build a verified foundation for AI agents to write software and conduct science.
Still open: How will other mathematical libraries be verified using this approach?
Still open: What specific software or scientific tasks will AI agents perform using this foundation?