The effort translates the roughly 7,500-page reference work initiated in 2005 by Columbia University mathematician Johan de Jong into the largest integrated library of formalized mathematics ever built. Axiom's implementation builds directly on open-source foundations established by the Lean and Mathlib communities to cover complex topics like cohomology, schemes, and algebraic stacks. Every Lean declaration includes permanent tags linking directly back to the original source text. This framework ensures both human researchers and automated agents can reliably verify modern algebraic geometry arguments.
Key points
Researchers and automated AI agents can directly import verified definitions and theorems…: Researchers and automated AI agents can directly import verified definitions and theorems into new mathematical proofs using permanent source tags.
The massive codebase establishes stable abstractions across commutative algebra, schemes,…: The massive codebase establishes stable abstractions across commutative algebra, schemes, sheaves, cohomology, and algebraic stacks.
This automated verification library helps bridge the gap when evaluating complex mathemat…: This automated verification library helps bridge the gap when evaluating complex mathematical arguments that exceed manual human review capacities.
Sources checked by our analysis pipeline: 1
Today, Axiom is releasing our Lean formalization of the entire Stacks Project, the roughly 7,500-page open-source reference that lays the foundations of modern algebraic geometry. Spanning some 16 million lines of code, it is the largest integrated, reusable library of formalized mathematics ever built.
With this release, the full mathematical development of the Stacks Project is available as a single, machine-checked library. Researchers and AI agents alike can import its definitions and theorems directly into new formal proofs, while permanent Stacks tags link every Lean declaration back to the canonical text mathematicians already know.
This milestone begins with the Stacks Project itself. Initiated by Columbia University mathematician Johan de Jong in 2005, it has grown through the tireless work of hundreds of mathematicians who have contributed proofs, examples, and refinements over two decades. Our formalization rests equally on the foundations of the Lean and Mathlib communities. Formalizing a corpus of this magnitude was only possible because those communities spent years building a rich mathematical library, along with the abstractions needed to organize it, long before our work began.
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