Revolutions in Mathematics [Paperback]

Social revolutions--critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. The publication of Kuhn'sThe Structure of Scientific Revolutionsin 1962 led to an exciting discussion of revolutions in the natural sciences; an off-shoot of this was a debate in the United States in the mid-1970's as to whether the concept of revolution could be applied to mathematics as well as science. This book is the first comprehensive examination of the question. It reprints the original papers of leading supporters and opponents, together with additional chapters giving their current views. To this are added new contributions from nine other experts in the history of mathematics, who each discuss an important episode and consider whether it was a revolution. The whole question of mathematical revolutions is thus examined comprehensively and from a variety of perspectives, and will interest mathematicians, philosophers, and historians alike.

1. Ten Laws Concerning Patterns of Change in the History of Mathematics 1975,M. Crowe
2. T.S. Kuhn's Theories and Mathematics: A Discussion Paper on the New Historiography of Mathematics 1976,H. Mehrtens
3. Appendix 1992: Revolutions Considered,H. Mehrtens
4. Conceptual Revolutions and the History of Mathematics: Two Studies in the Growth of Knowledge 1984,J. Dauben
5. Appendix 1992: Revolutions Revisited,J. Dauben
6. Descartes's Geometrie and Revolutions in Mathematics,P. Mancosu
7. Was Leibniz a Mathematical Revolutionary?,E. Grosholz
8. The Fine Structure of Mathematical Revolutions: Metaphysics, Legitimacy, and Rigor: The Case of the Calculus from Newton to Berkeley and MacLaurin,G. Giorello
9. Non-Euclidean Geometry and Revolutions in Mathematics,Y. Zheng
10. The Revolution in the Geometrical Vision of Space in the Nineteenth Century and the Hermeneutical Epistemology of MathlóÚ