Lean4 Formalization of the Classification of Finite Simple Groups Reaches Near‑24‑Hour Build Milestone

Overview

The AxiomMath repository on GitHub hosts a Lean4 formalization of the Classification of Finite Simple Groups (CFSG). The project provides a proof that the complete list of finite simple groups is correct, built on the Mathlib library and the TauCeti infrastructure.

Technical Details

• Lean4 version: v4.35.0-rc3, using Classical.choice, propext, and Quot.sound axioms (no native_decide).
• The proof follows the first‑generation CFSG approach.
• Build process: `lake build` compiles the entire project.
• Recent optimizations, including changes to Lake and other tweaks, aim to reduce total compilation time to under 24 hours.
• The statement of CFSG used is the one defined in the TauCeti project.

Practical Implications

If the build time is achieved, the formalization becomes a practical tool for mathematicians who want to verify group‑theoretic results in a machine‑checked environment. It also demonstrates that large, highly complex mathematical libraries can be compiled within a day on standard hardware, encouraging further formalization efforts.

How to Verify the Announcement

1. Visit the GitHub repository (https://github.com/AxiomMath/CFSG/)
2. Check the README for the exact Lean version and build commands.
3. Look at the CI logs or the `lake build` output to confirm the reported build duration.
4. Compare the formalized statement with the CFSG statement from TauCeti to ensure they match.

Open Questions

• It is not yet clear whether the proof has been fully peer‑reviewed by the broader mathematical community.
• The long‑term maintenance of the Lean code and its compatibility with future Lean releases remain uncertain.

Keywords

["Lean4", "Classification of Finite Simple Groups", "formal verification", "Mathlib", "TauCeti", "build time", "GitHub repository"]