Results

**1 - 3**of**3**### Reviewed by E Brian Davies,

"... 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 ..."

Abstract
- Add to MetaCart

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 Corfieldâ€™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

### WHITHER MATHEMATICS?

, 2004

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

Abstract
- Add to MetaCart

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

### The Annual Boole Lecture was established and is sponsored by the Boole Centre for Research in

"... seminal work on logic in the mid-1800s is central to modern digital computing. To mark this great contribution, leaders in the field of computing and mathematics are invited to talk to the general public on directions in science, on past achievements and on visions for the future. Mathematics is fac ..."

Abstract
- Add to MetaCart

seminal work on logic in the mid-1800s is central to modern digital computing. To mark this great contribution, leaders in the field of computing and mathematics are invited to talk to the general public on directions in science, on past achievements and on visions for the future. Mathematics is facing a dilemma at its heart: the nature of mathematical proof. We have known since Church and Turing independently showed that mathematical provability was undecidable that there are theorems whose shortest proofs are enormous. Within the last half-century we have discovered practical examples of such theorems: the classification of all finite simple groups, the Four Colour Theorem and Keplerâ€™s Conjecture. These theorems were only proved with the aid of a computer. But computer proof is very controversial, with many mathematicians refusing to accept a proof that has not been thoroughly checked and understood by a human. The choice seems to be between either abandoning the investigation of theorems whose only proofs are enormous or changing traditional mathematical practice to include computer-aided proofs. Or is there a way to make large computer proofs more accessible to human mathematicians?