" no ideal mathematician would say that a proof is simply "an argument that convinces someone who knows the subject." This entire student-mathematician exchange

" no ideal mathematician would say that a proof is simply "an argument that convinces someone who knows the subject." This entire student-mathematician exchange is facetious at best." From your point of view, what would be a possible definition of proof from an ideal mathematician, and what would be a more-correct form of the article's definition?