 Perhaps the most important constant in Wittgenstein’s Philosophy of Mathematics, middle and late, is that he consistently maintains that mathematics is our, human invention, and that, indeed, everything in mathematics is invented. Just as the middle Wittgenstein says that “[w]e make mathematics”, the later Wittgenstein says that we ‘invent’ mathematics (RFM I, §168; II, §38; V, §§5, 9 and 11; PG 469–70) and that “the mathematician is not a discoverer: he is an inventor” (RFM, Appendix II, §2; (LFM 22, 82). Nothing exists mathematically unless and until we have invented it.