Wittgenstein's contributions to the philosophy of mathematics, in contrast to his work in so many other areas of philosophy, have often been dismissed as of little value. Georg Kreisel, for example, ends his review of the Remarks on the Foundations of Mathematics by saying that "it seems to me to be a surprisingly insignificant product of a sparkling mind".' I hold the opposite opinion, and my aim in this paper is to show that Wittgenstein's philosophy of mathematics has only been held in such low regard because it has been misunderstood, and that in fact it is no less original and important than the rest of his work.2