It feels as if artificial intelligence is solving a new mathematical problem almost every week. Last month alone, OpenAI published 719 manuscripts claiming to have solved some of the field’s most difficult problems. Even computer verification can make mistakes. After years of AI-generated junk content, it’s natural to wonder whether mathematics will be the next field affected.
AxiomMath can avoid this fate not by slowing down, but by building a stronger foundation. This $1.6 billion startup aims to create a verified foundational layer upon which AI agents can rely to write software and ultimately conduct scientific research.
On Wednesday, the company announced that it has formally verified the Stacks Project, one of the largest mathematical achievements ever written by humans. Mathematicians typically hold the Stacks Project in very high regard. Peter Woit, a mathematician at Columbia University, once said that “little else can compare to it” and likened the project to the famous Bourbaki series—a collection of works from the 20th century that rebuilt mathematics from its foundations.
Johan de Jong, a colleague of Woit in Colombia, launched the Stacks Project in 2005 as an open-source reference. Since then, mathematicians have contributed to it, expanding its content from undergraduate-level algebra to the most advanced ideas in algebra, geometry, and number theory.
The company's AI agent swarm translated this 7,654-page database into approximately 16 million lines of machine-checkable code.
The purpose of formalized mathematics is to ensure the reliability of its underlying structure. Mathematicians rewrite proofs as code using a programming language called Lean, and then a program called a proof assistant checks the code line by line. If the proof passes, mathematicians can be confident that it is logically valid.
Engineers also use the same approach—formal verification—to confirm whether chip designs are feasible; French researchers used it to discover a software vulnerability in the calculation of family benefits.
For a project like the Stacks Project, checking theorems one by one is just part of the work. Theorems and definitions in the Stacks Project are interconnected, with each building upon what came before. Like a family tree, many results in the Stacks Project can be traced back to earlier ones.
This interdependence made Axiom initially uncertain whether the project was feasible. The team had to ensure every connection remained intact within approximately 16 million lines of Lean code.
Axiom CEO Carina Hong told TechCrunch: “Large scale and precision are typically incompatible in practice. [Stacks] is a set of mathematical results that form the mathematical foundation. You want [theorems] to be consistent with each other, not contradictory like paradoxes. You also want these definitions not to conflict with one another.”
The 25-year-old CEO dropped out of Stanford’s PhD program in mathematics and founded the company in March 2025. In March of this year, Axiom raised $200 million in an A-round led by Menlo Ventures.
Hong said, "We weren't sure if vibe coding could preserve the aesthetic of Stacks."
To complete this project, the team established a flexible structure for the agents and ran them in parallel. “For Stacks, we set up a hierarchy… but not one that strictly defines exactly what each agent should do,” said Ashvin Swaminathan, a member of the Axiom technology team. “The agents find their own tasks and identify what can be processed in parallel.”
Axiom also trained its own models to excel at mathematics. Hong said this approach is not taken by most other verification-focused startups. Initially, the team relied on an internal Lean expert to teach the agents to form human-like judgment criteria. Over time, Hong said, the agents have learned this judgment ability on their own.
This achievement fills one of the largest gaps in formalized mathematics. “When you look at the mathematics that has already been formalized, you see a massive black hole—and that black hole encompasses algebraic geometry,” said Swaminathan.
Swaminathan said that until now, researchers wanting to use Lean to verify new work in algebraic geometry had very little existing foundation to rely on. “Now they do.”
Axiom believes that each verified result becomes a building block, allowing future proofs to be built upon already-checked mathematics without starting from scratch. UCLA mathematician and Fields Medalist Terence Tao summarized this more concisely: “The more formal proofs you have, the more formal proofs you can make.”
The target audience for Axiom is not just mathematicians. Developers have long worked to ensure their code is free of bugs and security vulnerabilities. As AI agents write more and more software, this issue will only grow larger.
Axiom betting: future software needs to be built on proven foundations, just like Stacks today.
Swaminathan said, “We believe that mathematics is the domain where you begin building these things, and it’s a transferable skill. Agents can read our code, understand it, and build new infrastructure on top of it. The formalizations we’ve made in Lean now serve as the foundational base upon which agents can build.”
The way Axiom’s agents build Stacks—working in parallel and selecting their own tasks—is exactly how Hong expects many AI jobs will operate in the future. She believes AI agents need a well-structured, reusable knowledge base to avoid generating low-quality content.
Hong said: "You want [agents] to have a reusable repository where they can build upon it and continuously push the frontier. If you start by stuffing it with poor engineering choices, it becomes much harder for them to expand that boundary."
Hong is very confident in this approach and has even issued a public challenge. She said, "I publicly challenge all programming companies to undertake formal verification at this scale."