Revolutions in Mathematics

Erscheinungsjahr 1995
ISBN: 978-0-19-851486-2
Verlag: OUP Oxford

Buch, Englisch, 364 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 559 g

The publication of Kuhn's The Structure of Scientific Revolutions in 1962 led to an exciting discussion of revolutions in the natural sciences. A fascinating, but little known, off-shoot of this was a debate which began 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. Michael Crowe declared that revolutions never occur in mathematics, while Joseph Dauben argued that there have been mathematical revolutions and gave some examples. This book is the first comprehensive examination of the question. It reprints the original papers of Crowe, Dauben, and Mehrtens, together with additional chapters giving their current views. To this are added new contributions from nine further 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.

Autoren/Hrsg.

Gillies, Donald

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Kultur- und Ideengeschichte
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Geisteswissenschaften Geschichtswissenschaft Geschichtliche Themen Wissenschafts- und Universitätsgeschichte
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Human- und Sozialwissenschaften

Inhaltsverzeichnis

- Preface

- Introduction

- 1: Michael Crowe: Ten 'laws' concerning patterns of change in the history of mathematics 1975

- 2: Herbert Mehrtens: T.S. Kuhn's theories and mathematics: a discussion paper on the new historiography of mathematics 1976

- 3: Herbert Mehrtens: Appendix 1992 revolutions reconsidered

- 4: Joseph Dauben: Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge 1984

- 5: Joseph Dauben: Appendix 1992: revolutions revisited

- 6: Paolo Mancosu: Descartes's geometrie and revolutions in mathematics

- 7: Emily Grosholz: Was Leibniz a mathematical revolutionary?

- 8: Giulio Giorello: The 'fine structure' of mathematical revolutions: metaphysics, legitimacy, and rigour. The case of calculus from Newton to Berkeley and MacLaurin

- 9: Yuxin Zheng: Non-Euclidean geometry and revolutions in mathematics

- 10: Luciano Boi: The 'revolution' in the geometrical vision of space in the nineteenth century, and the hermeneutical epistemology of mathematics

- 11: Caroline Dunmore: Meta-level revolutions in mathematics

- 12: Jeremy Gray: The nineteenth-century revolution in mathematical ontology

- 13: Herbert Breger: A restoration that failed: Paul Finsler's theory of sets

- 14: Donald Gillies: The Fregean revolution in logic

- 15: Michael Crowe: Afterword 1992: A revolution in the historiography of mathematics?

- About the contributors

- Bibliography

- Index