The document discusses the concept of mathematical proof and debates around its nature. It argues that viewing proof as a Wittgensteinian family resemblance concept or cluster concept is insufficient, as mathematics is not just a collection of discrete language games. Rather, we have a single rich incoherent concept of proof. This presents difficulties for those who want to make ideological use of the concept or teach it. The document also examines statements from the "standard view" that proofs should be formal, and resistances to this position, for example that informal proofs provide understanding in a way formal proofs do not.