 The core of Wittgenstein’s conception of mathematics is very much set by the Tractatus Logico-Philosophicus (1922; hereafter Tractatus), where his main aim is to work out the language-reality connection by determining what is required for language, or language usage, to be about the world. Wittgenstein answers this question, in part, by asserting that the only genuine propositions that we can use to make assertions about reality are contingent (‘empirical’) propositions, which are true if they agree with reality and false otherwise (4.022, 4.25, 4.062, 2.222). From this it follows that all other apparent propositions are pseudo-propositions of various types and that all other uses of ‘true’ and ‘truth’ deviate markedly from the truth-by-correspondence (or agreement) that contingent propositions have in relation to reality. Thus, from the Tractatus to at least 1944, Wittgenstein maintains that “mathematical propositions” are not real propositions and that “mathematical truth” is essentially non-referential and purely syntactical in nature. On Wittgenstein’s view, we invent mathematical calculi and we expand mathematics by calculation and proof, and though we learn from a proof that a theorem can be derived from axioms by means of certain rules in a particular way, it is not the case that this proof-path pre-exists our construction of it.