 In arguing against mathematical discovery, Wittgenstein is not just rejecting Platonism, he is also rejecting a rather standard philosophical view according to which human beings invent mathematical calculi, but once a calculus has been invented, we thereafter discover finitely many of its infinitely many provable and true theorems. As Wittgenstein himself asks (RFM IV, §48), “might it not be said that the rules lead this way, even if no one went it?” If “someone produced a proof [of ‘Goldbach’s theorem’]”, “[c]ouldn’t one say”, Wittgenstein asks (LFM 144), “that the possibility of this proof was a fact in the realms of mathematical reality”—that “[i]n order [to] find it, it must in some sense be there”—“[i]t must be a possible structure”?