Axiom Math Verifies Stacks Project, Aims to Clean Up AI in Mathematics

As [artificial intelligence](/topic/artificial-intelligence) continues to revolutionize various fields, the realm of mathematics is not immune to its influence. Axiom Math, a startup valued at $1.6 billion, is taking a stand against what it terms 'AI slop' — the unchecked proliferation of erroneous mathematical proofs generated by AI systems. On November 5, 2026, the company announced a significant milestone: the formal verification of the Stacks Project, one of the largest and most respected bodies of mathematical work ever created.

Founded by Carina Hong, who dropped out of a Stanford Ph.D. program, [Axiom Math aims](/axiom-math-aims-to-safeguard-mathematics-from-ai-inaccuracies) to establish a verified foundation for AI agents to rely on when generating software and conducting scientific research. The Stacks Project, initiated in 2005 by Johan de Jong at Columbia University, has been a collaborative effort among mathematicians to build a comprehensive reference that spans from basic algebra to advanced concepts in algebraic geometry and number theory.

The Stacks Project is often compared to the Bourbaki books, which redefined mathematics in the 20th century. It consists of approximately 7,654 pages and has been continuously developed by mathematicians over the years. The project is not just a collection of theorems; it is an intricate web of interconnected results, where each theorem builds upon the previous ones, akin to a family tree.

Axiom Math's verification process involved translating the entire library into about 16 million lines of code using a programming language called Lean. This formalization process ensures that the foundational structure of the mathematics is sound and logically consistent. Mathematicians rewrite proofs in Lean, and a proof assistant meticulously checks the code line by line to confirm its validity.

The verification of the Stacks Project was no small feat. The interconnectedness of the theorems posed significant challenges for Axiom Math. Each theorem's validity depended on the correctness of the ones that preceded it, creating a complex web of dependencies that the team had to maintain throughout the verification process.

"Things that are big and things that are delicate in life just don’t go together," said Axiom CEO Carina Hong in an interview with DotMR. "[Stacks] is a collection of mathematical results that is the foundation of mathematics. You want [theorems] to be consistent and not, like, paradoxical. You want the definitions to not fight with each other."

Despite initial doubts about whether their approach, which they referred to as 'vibe coding,' could preserve the beauty and integrity of the Stacks Project, the Axiom team proceeded with a flexible structure. They allowed their AI agents to operate in parallel, identifying tasks independently while adhering to a loose hierarchy. Ashvin Swaminathan, a member of Axiom’s technical staff, explained, "With Stacks, we imposed a hierarchy… [but] it was not, like, a complete hierarchy of dictating what every single agent was doing."

The successful verification of the Stacks Project has broader implications beyond just the realm of mathematics. Formal verification is a concept borrowed from engineering, where it is used to ensure that chip designs function correctly. In the context of software, it has been employed to identify bugs in complex calculations, such as those used for family benefits in France.

Axiom Math's approach could pave the way for a new standard in mathematical proofs, particularly as AI continues to generate solutions at an unprecedented pace. Last month alone, [OpenAI](/topic/openai) released 719 manuscripts claiming solutions to some of the hardest problems in mathematics. However, the accuracy of these AI-generated proofs has been called into question, leading to a growing concern about the reliability of AI in mathematical contexts.

As Axiom Math moves forward, the company plans to expand its verification efforts to other significant mathematical libraries and projects. The success of the Stacks Project verification could serve as a model for future endeavors, ensuring that AI-generated mathematics is not only innovative but also trustworthy.

In a landscape where AI's influence is rapidly expanding, Axiom Math's commitment to verification may play a crucial role in maintaining the integrity of mathematical research. As the company continues to refine its methods and expand its capabilities, it stands at the forefront of a movement aimed at cleaning up the mathematical landscape, ensuring that AI serves as a tool for progress rather than a source of confusion.