Axiom Math agents verify Stacks Project into 16 million lines of Lean code

Axiom Math announced on Wednesday that its AI agents had formally verified the Stacks Project, a major library of mathematical results. This verification translates human-written mathematics into computer-checked code to ensure logical soundness.This means AI can now check millions of lines of complex math to ensure they are correct.The verification of the Stacks Project into Lean code provides a machine-checkable basis for further formalization efforts.

The evidence

TechCrunch reported that the startup converted roughly 7,654 pages of the Stacks Project into about 16 million lines of code.reported The Stacks Project began in 2005 as an open-source reference by Johan de Jong.reported Mathematicians have contributed to it continuously since then.

Columbia mathematician Peter Woit described the Stacks Project as having nothing comparable in the field. He compared it to the famous Bourbaki books, which rebuilt mathematics from its foundations in the 20th century.reported This context highlights the scale and importance of the verified library.

The decision

Axiom Math aims to build a verified foundation that AI agents can rely on for writing software. The company plans to eventually use this foundation for scientific work. This approach seeks to avoid the spread of unchecked proofs, often called AI slop.

The startup invested $1.6 billion to pursue this verification strategy.reported It bets that mathematics can avoid being flooded with incorrect results by standing on firmer ground. This involves using formal verification to check every step of a proof.

The takeaway

Formalizing math requires rewriting proofs as code in a programming language called Lean. A proof assistant then checks the code line by line for logical errors. If the proof passes, mathematicians can trust that it is logically sound.

Engineers use similar formal verification methods to confirm that chip designs work correctly. Researchers in France have also used this technique to catch bugs in software. That software calculates family benefits, showing the practical application of these methods.

Building on this

Developers can use this verified library as a trusted base for building complex software systems. The 16 million lines of Lean code provide a foundation that AI agents can rely on.reported This reduces the risk of errors propagating from unchecked mathematical assumptions.

The interconnected nature of the Stacks Project means that each theorem builds on previous ones. Maintaining these connections across millions of lines of code was a significant challenge. Developers must ensure that any new code respects these existing dependencies.

Axiom Math’s approach suggests that AI agents can be used to formalize large bodies of knowledge. This could accelerate the verification of other mathematical libraries or scientific theories. However, the process is resource-intensive and requires careful management of complex dependencies.