It feels like the AI is solving a new math problem every week. Last month, OpenAI alone published 719 manuscripts claiming solutions to some of the field’s toughest problems. Even computer checks may fail. After years of underperformance in AI, it’s natural to wonder if math is next.
AxiomMath is betting that mathematics can avoid that fate, not by slowing down, but by standing on a stronger footing. The $1.6 billion startup wants to build a trusted, verified foundation for AI agents to create software and eventually do science.
The company announced Wednesday that it has officially verified the Stax Project, one of the largest mathematical systems ever written by humans. Mathematicians often don’t put much emphasis on the stack. Colombian mathematician Peter Woyt compared the project to the “famous Bourbaki books” (a series that rebuilt mathematics from the ground up in the 20th century) and argued that “there really is nothing else that can match it.”
Woit’s colleague at Columbia University, Johan de Jong, started the Stacks project in 2005 as an open source reference. Since then, mathematicians have contributed to this research, building on results ranging from university-level algebra to cutting-edge ideas in the field, spanning algebra, geometry, and number theory.
The company’s fleet of AI agents translates approximately 7,654 pages in the library into approximately 16 million lines of computer-checked code.
Formalizing mathematics is a way to ensure that the underlying structure is sound. Mathematicians rewrite the proof as code in a programming language called Lean, and a program called a proof assistant checks the code line by line. If the proof passes, the mathematician can trust that it is logically correct.
Engineers use the same idea, called formal verification, to check how chip designs work, while researchers in France are using it to find bugs in the software that calculates family allowances.
For libraries like the Stacks project, checking each theorem is only part of the job. Theorems and definitions in the stack are interconnected, each building on the previous one. Similar to a family tree, many results in a stack date back to what came before it.
Because of their interconnectedness, Axiom was initially unsure whether the project would work. The team needed to keep all connections intact across approximately 16 million lines of lean code.
“In life, big things and delicate things don’t go together,” Axiom CEO Carina Hon told TechCrunch. “[The stack]is a collection of mathematical results that are the basis of mathematics.[Theorems]want to be consistent and non-paradoxical. We want the definitions to not conflict with each other.”
The 25-year-old CEO dropped out of his PhD in mathematics from Stanford University. In March, Axiom raised $200 million in Series A led by Menlo Ventures.
“We weren’t sure if we could maintain the beauty of the stack with vibe coding,” Hong said.
To make the project a success, the team gave the agents a loose structure and allowed them to run in parallel. “At Stax, we imposed a hierarchy…[but]it wasn’t a complete hierarchy that dictated what every agent was doing,” said Ashvin Swaminathan, a member of Axiom’s technical staff. “Agents were finding tasks on their own and identifying things they could work on in parallel.”
Axiom has also trained its own models to excel at math. According to Hong, this approach is something that few other verification startups have taken. Initially, the team relied on one of its in-house Lean experts to teach agents about human taste. Over time, Hong said, agents have developed their own preferences.
This result fills one of the biggest gaps in formalized mathematics. “If you look at what is formulated in mathematics, there is a huge black hole, and that black hole covers algebraic geometry,” Swaminathan said.
Until now, Swaminathan said, researchers who wanted to see new results in algebraic geometry in Lean had little to build from. “Well, that’s what I do now.”
Axiom claims that each verified result becomes a building block, so future proofs can rely on checked mathematics rather than starting from scratch. UCLA mathematician and Fields Medal winner Terence Tao explained the general case more simply. “The more formal proofs you have, the more formal proofs you can create.”
Axiom’s target audience is not just mathematicians. Developers have long struggled to ensure that their code is free of bugs and security holes. This problem will grow as AI agents increasingly write the world’s code.
Axiom believes that future software must be built on a proven foundation, just like Stacks is doing today.
“We believe that mathematics is the domain and transferable skill where you start building these things,” Swaminathan said. “Agents can read and understand our code and build new infrastructure on top of it. Our lean formalization is the foundation on which agents can build.”
The way Axiom’s agents build stacks, work in parallel, and choose their own tasks is how Hong expects much of the future work in AI to happen. She argues that AI agents will need a well-constructed, reusable body of knowledge to avoid producing anything shoddy.
“(Agents) need reusable libraries to build on and continue to push the front lines,” Hong said. “If you initially make engineering choices that slop down in the wrong direction, it becomes very difficult to extend that limit.”
Hong is confident enough in that approach to take on the challenge. “I publicly call on all coding companies to commit to formalization on this scale.”
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