Formalization is the process of translating an informal idea, claim, or procedure into precise language that a computer can interpret and check. In mathematics, this means expressing a theorem and its assumptions in a formal system, then representing its proof in a form a proof assistant can verify.
Formalization matters because it exposes ambiguity and enables repeatable checks, but a verified formal proof only confirms the statement that was encoded. It does not prove that the encoding faithfully captures the original human claim. In practice, researchers review the formal statement, proof, and supporting records; in cybersecurity, similar care helps validate AI-generated code, analysis, or alerts. Keeping versions and review records makes it easier to trace what was formalized and how it was checked.