It seems AI is solving a new math problem every week. Last month alone, OpenAI released 719 manuscripts claiming solutions to complex field problems, even computer checks can fail. After years of AI-generated content, it is reasonable to question if mathematics is the next to suffer from low-quality output.
Axiom Math is betting that mathematics can avoid this outcome by strengthening its foundation rather than slowing down. This $1.6 billion startup aims to construct a verified base that AI agents can trust for software development and scientific research.
On Wednesday, the company announced that it had formally verified the Stacks Project, one of the largest collections of human-written mathematics. Mathematicians hold this project in high regard; Columbia professor Peter Woit described it as having “nothing else really comparable,” likening it to the influential Bourbaki books that rebuilt mathematics in the 20th century.
Johan de Jong, a Columbia colleague of Woit, initiated the Stacks Project in 2005 as an open-source reference. Mathematicians have continuously contributed to the repository, expanding results from college-level algebra up to the most advanced concepts in algebra, geometry, and number theory.
Axiom’s fleet of AI agents translated the library’s approximately 7,654 pages into about 16 million lines of computer-checked code. Formalizing math involves rewriting proofs as code in a language called Lean, with a proof assistant verifying the logic line by line to ensure soundness.
Engineers employ this technique, known as formal verification, to confirm chip designs function correctly, while researchers in France have utilized it to detect bugs in software calculating social benefits.
For a library like the Stacks Project, validating each theorem is only part of the task. Since the theorems are interconnected and build upon one another, Axiom initially doubted the project would succeed, requiring the preservation of every link across 16 million lines of Lean code.
“Things that are big and delicate in life just don’t go together,” Axiom CEO Carina Hong explained. “Stacks is a collection of mathematical results that is the foundation of mathematics. You want theorems to be consistent and not paradoxical, and definitions that do not contradict each other.”
The 25-year-old CEO dropped out of a Stanford math Ph.D. program to found the company in March 2025. During that month, Axiom secured $200 million in Series A funding led by Menlo Ventures. “We were not sure if vibe coding would be able to preserve the beauty of Stacks,” Hong noted.
To accomplish this, the team provided its agents with a loose structure and allowed them to operate in parallel. “The agents were finding tasks for themselves and identified things that they could work on in parallel,” reported Ashvin Swaminathan, a member of Axiom’s technical staff.
Axiom trained its own models to excel in mathematics, a strategy Hong believes distinguishes them from other verification startups. Initially, an in-house Lean expert guided the agents, but over time, Hong stated, the agents developed a human-like sense of quality on their own.
This achievement fills a significant void in formalized mathematics. “When you look at what has been formalized in mathematics, there’s this huge black hole. And that black hole covers algebraic geometry,” Swaminathan observed. “Well, now they do.”
Axiom argues that each verified result serves as a building block, allowing future proofs to rely on established math rather than starting from scratch. Terence Tao, the Fields Medal winner, succinctly summarized this benefit: “The more formalized proofs you have, the more formalized proofs you can make.”
Mathematicians are not the only target audience. Developers have long struggled to ensure code is bug-free, a challenge exacerbated as AI agents write more of the world's software.
Axiom anticipates that future software must rest on verified foundations, similar to how Stacks currently operates. “Agents can read our code, understand it, and build new infrastructure on top of it. Our Lean formalization is now the substrate that agents can build upon,” Swaminathan said.
The method Axiom’s agents used to build Stacks—working in parallel and self-identifying tasks—aligns with how Hong expects much of AI's future work to proceed. Proponents believe AI agents require a reusable body of knowledge to avoid generating flawed work.
Hong is confident enough in this approach to issue a challenge: “I openly challenge all the coding companies to work on formalization at this scale.”
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