GoKawiilLean Formalization Completes Classification of Finite Simple Groups
A research team has produced a complete machine-checked formalization in the Lean proof assistant of the classification of finite simple groups, following the original first-generation proof. The formalization comprises over 43 million lines of Lean code and 2.05 million declarations, drawing on 715 papers and books. The team also reports finding an issue in a previously published argument for the Unbalanced Group Theorem and describes the alternative proof route they used instead.
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The classification theorem, originally assembled from thousands of journal pages by roughly a hundred mathematicians, has long been difficult to verify in full due to its scale and distributed authorship. A kernel-checked formal version could give mathematicians much higher confidence in the result's correctness, including the corrected handling of the Unbalanced Group Theorem issue. This effort also demonstrates how proof assistants like Lean may be applied to some of the largest and most complex proofs in modern mathematics.
- A complete Lean formalization of the classification of finite simple groups has been achieved, with every step verified by Lean's kernel.
- The project uncovered and fixed an issue in a published proof of the Unbalanced Group Theorem, documented in an accompanying paper.
- The formalization totals 43.1 million lines of code, 2.05 million declarations, and references 715 papers and books.
Source: cfsg.axiommath.ai, 2026-10-27
Published there as: “Classification of Finite Simple Groups Formalized in Lean”
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