Axiom said on 4 November that it is releasing a Lean formalization of “the entire Stacks Project”, the open-source reference on algebraic geometry that it describes as “the roughly 7,500-page open-source reference that lays the foundations of modern algebraic geometry”. In its announcement, Axiom calls it “the largest integrated, reusable library of formalized mathematics ever built”.
The project’s website lists 15,751,904 lines of Lean in 62,975 files and 663,090 declarations. That is about 2,100 lines of Lean for each of the roughly 7,500 pages, by our arithmetic.
Business Pill · Verification Cost
An evergreen Business Engineer explainer on verification cost. It teaches the general idea only and does not discuss Axiom or the Stacks Project.
The key insight: Axiom’s site puts its Lean version of the roughly 7,500-page Stacks Project at 15,751,904 lines, about 2,100 lines of Lean per page by our arithmetic, and its two releases in eight days come to about 58.9 million lines.
Axiom’s blog says the library spans “some 16 million lines of code” and that “permanent Stacks tags link every Lean declaration back to the canonical text mathematicians already know”. The site says each tagged result is formalized as Lean definitions and proofs built on Mathlib, and that “Lean’s kernel checks every completed proof”.
Axiom says it “deployed coordinated swarms of AI agents capable of translating, proving, and integrating thousands of theorems in parallel”. It describes “a hierarchical system of AI agents with specialized responsibilities and strict coordination protocols”.
Lines of Lean in Axiom’s two releases: about 43.1 million for the Classification of Finite Simple Groups (27 October 2026, Axiom) and 15.75 million for the Stacks Project (4 November 2026, stacks.axiommath.ai). The 58.9 million total and the 2,100 lines per page are our arithmetic.
What Was Posted on X
Vibe coding at scale has a reputation for slop, so Axiom Math formalized the Stacks Project to show otherwise.
Mathematicians usually trust a proof because experts read it; Axiom Math turned an entire fieldโs reference book into Lean code, so a computer can now confirm the logic line by line.
Axiom ran its agent swarm like an engineering org, with humans assigning some agents the architecture, others core definitions and others individual proofs.
Lean checks every completed proof, and each tagged result links to its original text and dependencies, so the pieces fit together like panes of the Louvreโs pyramid.
And nothing entered the library unless the logic held.
All these means that now we have a free, open-source library where a big chunk of modern algebraic geometry exists as computer-checked code instead of only as text in a book.
In practice, anyone (a mathematician or an AI model) who wants to prove something new in this field can now reuse these already-verified definitions and theorems instead of rebuilding them, and a computer will flag any step that doesnโt follow.
Rohan Paul summarised the release on X at 17:53Z, describing how Axiom says it organised its agents and how the Lean library can be reused by mathematicians and AI models.
Two Tiers of Code
The library has two parts, the site says. “StacksCore is code that a person has checked against the Stacks Project and brought up to Mathlib standards”, while “StacksFrontier is code written by AI agents that has not had that review yet”. It adds: “Lean checks every proof in both”.
The site says every pull request, to either tier, is reviewed by four maintainers: Kenny Lau, Brian Nugent, Ashvin A. Swaminathan and Yunzhou Xie. The site does not say how many of the 15.75 million lines sit in each tier.
What the Agents Found
Axiom says its system “surfaced dozens of statements in the Stacks Project that required local refinement, including missing hypotheses, edge cases in positive characteristic, and claims that did not hold in the full generality stated”. It says the agents “constructed explicit counterexamples to prove where the original statements broke down”.
Axiom notes that in a 21 October announcement, Stacks Project founder Johan de Jong “requested that AI-generated comments and pull requests not be submitted directly to the upstream Stacks Project repository for the time being”. Axiom says it keeps its formalization, counterexamples and refinements in its own repository.
Second Release in Eight Days
On 27 October, Axiom released a formalization of the Classification of Finite Simple Groups, which it said produced “approximately 43.1 million lines of code” from a proof that “extends across roughly 15,000 pages”. We covered that release at the time.
By our arithmetic, the two releases come to about 58.9 million lines of Lean in eight days. The classification works out to about 2,900 lines per page of the original proof, against about 2,100 for the Stacks Project.
As we read the release, the product is reuse rather than a single proof: Axiom stresses importable definitions and theorems with stable tags, which is what lets later proofs, by people or agents, build on checked foundations.
As we read the two-tier design, Lean’s kernel answers whether a proof is valid, while human review in StacksCore answers whether a statement says what the textbook means; Axiom itself calls statement faithfulness even more important than verifying the proof.
Axiom, 4 November 2026
“Ensuring that each formal statement faithfully captures the mathematical meaning of the original text is even more important than verifying its proof.”
Three Implications
FOR MATHEMATICIANS Axiom says researchers and AI agents can import the library’s definitions and theorems directly into new formal proofs.
FOR AI-GENERATED MATHS Axiom says its agents surfaced dozens of Stacks Project statements that needed local refinement and built counterexamples where statements broke down.
FOR OPEN-SOURCE MAINTAINERS Axiom keeps its work in its own repository, noting de Jong’s request that AI-generated pull requests not go directly to the upstream project for now.
The framework names “The Verifier Moat”, built on domain-specific reward signals for reasoning-heavy verticals.
As we read it, a large library of machine-checked definitions and theorems is the kind of domain-specific checking asset that framework describes, in mathematics. The framework predates this release and does not discuss Axiom.
The line, file and declaration counts are Axiom’s own, from its site; we have not built the library. Axiom does not say how much of the code has had human review in StacksCore, and the claim that the formalization covers the entire Stacks Project and is the largest such library is Axiom’s. Pages-per-line ratios depend on Axiom’s rounded page counts.
This Week In The AI Supercycle
Anthropic’s Reality Check, The Capital Squeeze, & The New World Order
This week’s issue: for two years the AI build-out was priced as a growthstory. This week it started being priced as a credit story.
Axiom has released a Lean formalization of the roughly 7,500-page Stacks Project that its site puts at 15,751,904 lines, about 2,100 lines per page by our arithmetic, with Lean’s kernel checking every completed proof. Part of the code, the StacksFrontier tier, was written by AI agents and has not yet had human review, the site says.
A note on sourcing. The release, quotations and the 21 October de Jong request are from Axiom’s 4 November 2026 blog post; line, file and declaration counts and the StacksCore and StacksFrontier tiers are from Axiom’s project site, stacks.axiommath.ai, read on 4 November; the classification figures are from Axiom’s 27 October post. Lines-per-page ratios and totals are our arithmetic.
Gennaro Cuofano is a CRO and tech executive who has worked in AI since late 2015, starting with bringing NLP, natural-language generation, voice and chatbot products to the marketing industry. His background is in law and finance: he holds a Master's degree in Law and an International MBA with an emphasis on corporate finance (LUISS Business School and the University of San Diego, 2012), and worked as a financial analyst at a real-estate investment firm in San Diego and as an assistant controller. His work focuses on business model strategy, business engineering and, more broadly, structural analysis: how companies make money, read from their own filings. He created FourWeekMBA and leads research there and at The Business Engineer, his newsletter on AI and business strategy, with over 95,000 subscribers and more than 1,000 published analyses. His writing has also appeared on Entrepreneur (for example, How to Digitize a Family Business in Europe) and HackerNoon. Find him on LinkedIn and Substack. See how we source.
