whither10.tex We describe three successive crises faced by mathematicians during the twentieth century, and their implications for the nature of mathematics. 1

David Corfield starts his interesting book with a radical rejection of much that has been written about the philosophy of mathematics. He has no interest in ontology, epistemology, logicism, Platonism, Kantianism, nominalism, fictionalism etc., and does not mention most of them. Taking his cue from Nietzsche, Lakatos and a few others, he likens the traditional approach to the examination of a dead body, [pp. 3-5]. He criticizes the attitude that has led many philosophers of mathematics to imagine that everything of interest to their subject occurred between 1880 and 1930, contrasting this with a very different attitude among the philosophers of physics. We shall see that events since the publication of his book make it even more relevant now than it might have seemed in 2003. One of Corfield’s strongest arguments for turning away from the philosophy of dead mathematics is that it focuses on logical correctness, and is powerless to explain why some topics are regarded as crucial to the subject while others are considered irrelevant, no more than technical games. He argues that if one