Synopses & Reviews
Social revolutions--critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. The publication of Kuhn's The Structure of Scientific Revolutions in 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.
Review
"Some of the major historical developments in mathematics are considered at length, enriching the overall quality of the presentation. . . . a good reference for those who are interested in the history of mathematics." --Science Books and Films
"The insightful contributions found in this book prove that the tools of Kuhnian analysis, in particular the idea of a revolution, may be applied usefully to produce history of the sort that goes beyond description in the logical presentation of ideas, to reveal what is at the heart of the process of discovery." --Science
Synopsis
The essays in this book provide the first comprehensive treatment of the concept of revolution in mathematics. In 1962 an exciting discussion of revolutions in the natural sciences was prompted by the publication of Kuhn's The structure of scientific revolutions.
Synopsis
Social revolutions--critical periods of decisive, qualitative change--are a commonly acknowledged historical fact. The publication of Kuhn's The Structure of Scientific Revolutions in 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.
Table of Contents
1. Ten "Laws" Concerning Patterns of Change in the History of Mathematics 1975,
M. Crowe2. 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 Mathematics, L. Boi
11. Meta-Level Revolutions in Mathematics, C. Dunmore
12. The Nineteenth-Century Revolution in Mathematical Ontology, J. Gray
13. A Restoration that Failed: Paul Finsler's Theory of Sets, H. Breger
14. The Fregean Revolution in Logic, D. Gillies
15. Afterword 1992: A Revolution in the Historiography of Mathematics?, D. Gillies