 The first and most important thing to note about Wittgenstein’s later Philosophy of Mathematics is that RFM, first published in 1956, consists of selections taken from a number of manuscripts (1937–1944), most of one large typescript (1938), and three short typescripts (1938), each of which constitutes an Appendix to (RFM I). For this reason and because some manuscripts containing much material on mathematics (e.g., MS 123) were not used at all for RFM, philosophers have not been able to read Wittgenstein’s later remarks on mathematics as they were written in the manscripts used for RFM and they have not had access (until the 2000–2001 release of the Nachlass on CD-ROM) to much of Wittgenstein’s later work on mathematics. It must be emphasized, therefore, that this Encyclopedia article is being written during a transitional period. Until philosophers have used the Nachlass to build a comprehensive picture of Wittgenstein’s complete and evolving Philosophy of Mathematics, we will not be able to say definitively which views the later Wittgenstein retained, which he changed, and which he dropped. In the interim, this article will outline Wittgenstein’s later Philosophy of Mathematics, drawing primarily on RFM, to a much lesser extent LFM (1939 Cambridge lectures), and, where possible, previously unpublished material in Wittgenstein’s Nachlass.