Palomar: A registry of Lean verified mathematics
Palomar is a new registry designed to verify mathematics proofs formalized in the Lean proof assistant language. The initiative aims to provide a reliable, preprint-style server for Lean code to ensure that AI-generated or human-written proofs are mathematically sound and free of errors.
Why it matters
As AI increasingly generates mathematical proofs, tools like Palomar are essential for maintaining academic rigor and verification in formal mathematics.
In recent months there has been a proliferation of AI-generated proofs of various old and new results, some of which have been formalized in the proof assistant language Lean. However, checking that a given Lean repository actually proves the claimed statement is somewhat non-trivial, especially for an audience which is not expert in the use of Lean: one has to first check that the claimed formal Lean statements have proofs that typecheck, that the proofs do not contain any “cheats” such as adding additional axioms, and that the formal statements also match (in a semantic sense) the informal description of the claimed results.
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