Formal verification means writing a proof in a language like Lean or Coq that a computer checks line by line against the rules of logic. If the checker accepts it, the logical structure is guaranteed to be airtight — something human peer review, however careful, has never been able to promise.

This matters enormously for AI-generated math. When an AI produces a long, complex argument — OpenAI's Navier-Stokes proof ran to 165 pages — there is no realistic way for humans to audit every step quickly. Formal verification offloads that job to a machine that cannot be fooled or fatigued.

It doesn't tell you the proof is interesting or that it answers the right question, which is partly why controversy can persist even after a checker signs off. But on the narrow question of logical consistency, a verified proof is as certain as mathematics gets.