Some of that's pretty silly. An unquestionably rigorous proof is indeed "I know it when I see it", give or take a few differences. (E.g., my adviser Andy Gleas

Some of that's pretty silly. An unquestionably rigorous proof is indeed "I know it when I see it", give or take a few differences. (E.g., my adviser Andy Gleason told me to take a theorem that had been proved by Tarski-Principle hand-waving and see if I could find a constructive proof for it. I did, by invoking a theorem from Vol. II of van der Waerden. He was pleased.) A published proof is a claim that if one tries to flesh it out to an unquestionably rigorous one, one will succeed. (Errors are however distressingly common.) The accusation of Platonism in the article is mainly hogwash.