Axiom formalizes entire Stacks Project in Lean with 16 million lines of code
Axiom announced it has formalized the entire Stacks Project, a roughly 7,500-page open-source reference on algebraic geometry foundations, into about 16 million lines of Lean code checked by proof assistants. The company deployed coordinated swarms of AI agents working in parallel under human direction to translate, prove and integrate thousands of theorems while preserving the library's permanent tags and dependency structure. Axiom describes the result as the largest integrated reusable library of formalized mathematics, intended for reuse by researchers and AI agents.
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Axiom Releases Lean Formalization of the Entire Stacks Project
Axiom announced the release of a Lean formalization of the Stacks Project, the roughly 7,500-page open-source reference on algebraic geometry foundations, spanning about 16 million lines of code and described as the largest integrated reusable library of formalized mathematics. The library preserves the Stacks Project's permanent tags, linking each Lean declaration to the canonical text, and is intended for reuse by researchers and AI agents. Axiom says the work relied on the Lean and Mathlib communities and used coordinated swarms of AI agents to translate, prove, and integrate thousands of theorems in parallel. The company frames formal verification as increasingly essential as AI systems generate mathematical arguments faster than humans can inspect, and positions the release as a new starting point for algebraic geometry and neighboring fields.
Read sourceAxiom Math formally verifies Stacks Project to curb AI slop in math
Axiom Math, a $1.6B startup founded in March 2025 by Stanford dropout Carina Hong, announced it has formally verified the Stacks Project, one of the largest bodies of human-written mathematics, translating roughly 7,654 pages into about 16 million lines of Lean code checked by proof assistants. The company deployed a fleet of AI agents working in parallel with a loose hierarchy to preserve the library's interconnected theorems and definitions. Hong said the team was initially unsure whether 'vibe coding' could preserve the beauty of Stacks, and Axiom trained its own math-specialized models rather than relying on outside verification tools. The company argues verified results become reusable building blocks for future proofs and, eventually, for AI-written software, with technical staff member Ashvin Swaminathan calling the Lean formalization a substrate agents can build upon. Hong challenged coding companies to pursue formalization at this scale.
Read sourceAxiom Says It Formalized Entire Stacks Project in Lean With 16 Million Lines of Code
Axiom announced that it has formalized the entire Stacks Project in Lean, producing 16 million lines of code. The result is described as a reusable library of machine-checkable mathematics. According to the post, such a library gives AI agents a much stronger foundation for building new proofs. The announcement frames the formalization as infrastructure that could support automated and AI-assisted mathematical proof development.
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Axiom Translates Stacks Project into Lean, Making AI-Written Proofs Machine-Checkable
A post argues that AI-generated code is often unreadable, but formal proof languages like Lean solve this because a wrong line cannot compile. Mathematicians have used Lean for years, with a checker verifying every step. The Stacks Project, a standard algebraic geometry reference started by Johan de Jong in 2005, contains thousands of pages of lemmas and proofs with permanent tags and dependency chains down to axioms. Axiom has now translated the Stacks Project into Lean while preserving its structure, so a result depending on three earlier lemmas still depends on the same three in code. The post compares this to I.M. Pei's Louvre pyramid glass, which lets viewers see the structure behind it. In normal software, each extra AI-written line is a potential unread bug; in Lean, compiled proofs are machine-checked and the kernel rejects anything that does not follow, allowing agents to import verified lemmas and build on them.
Read sourceAxiom formalizes Stacks Project in Lean using human-led swarm of AI agents
Axiom announced it has formalized the Stacks Project, described as a large and deeply interconnected foundation of algebraic geometry, in the Lean proof assistant, turning it into mathematics a computer can check. The post argues the notable achievement is not only scale but structure: Axiom compares it to the Louvre's glass pyramid, where individual pieces work only because they fit into something larger, and every definition and proof must connect so results proved in one chapter can be used in another. According to the post, this makes the work more than a translation: a human-led swarm of AI agents built a reusable, machine-checkable foundation that AI agents can now use to do mathematics. The post credits the Axiom team and frames the release as a counterexample to the view that AI-generated code at scale is sloppy.
Axiom Math Formalizes Stacks Project in Lean Using Agent Swarm
Axiom Math has formalized the Stacks Project, a major reference work in algebraic geometry, into Lean code so that a computer can verify the logic line by line. The company ran its agent swarm like an engineering organization, with humans assigning some agents to architecture, others to core definitions, and others to individual proofs. Lean checks every completed proof, and each tagged result links to its original text and dependencies. Nothing entered the library unless the logic held. The result is a free, open-source library where a substantial portion of modern algebraic geometry exists as computer-checked code rather than only as text. Mathematicians or AI models seeking to prove something new in the field can reuse the already-verified definitions and theorems instead of rebuilding them, and a computer will flag any step that does not follow.