Proof Kernels Don't Guarantee Meaning

Formal proof checkers like Lean mechanically verify that a finite symbolic derivation follows from a chosen set of axioms and definitions, but they do not by themselves establish that those formal definitions capture the intended real‑world or mathematical concepts (for example, that Mathlib's `ℝ` is 'the' continuum). As AI accelerates automated formalization and produces large unread corpora, the only 'reader' of many machine‑generated definitions may be the proof kernel—raising the risk that formal derivability drifts from mathematicians' intended meanings. — If AI‑verified proofs become the public standard for correctness, the uncoupling of syntactic certification from semantic intent could mislead research, pedagogy, and any policy or legal uses that rely on mathematical claims.