Revolutions in Mathematics: Revolution In Mathmatics

Paperback | April 30, 1999

EditorDonald Gillies

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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. A fascinating but little knownoffshoot of this debate was begun in the USA in the mid-1970s: can the concept of revolutions 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 someexamples.The original papers of Crowe, Dauben, and Mehrtens are reprinted in this book, 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 arevolution.This book is an excellent reference work and an ideal course text for both graduate and undergraduate courses in the history and philosophy of science and mathematics.

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From Our Editors

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.

From the Publisher

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. A fascinating but little knownoffshoot of this debate was begun in the US...

From the Jacket

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.

Donald Gillies is at King's College London.

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Format:PaperbackDimensions:364 pages, 9.21 × 6.14 × 0.79 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198514867

ISBN - 13:9780198514862

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Table of Contents

PrefaceIntroduction1. Michael Crowe: Ten 'laws' concerning patterns of change in the history of mathematics 19752. Herbert Mehrtens: T.S. Kuhn's theories and mathematics: a discussion paper on the new historiography of mathematics 19763. Herbert Mehrtens: Appendix 1992 revolutions reconsidered4. Joseph Dauben: Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge 19845. Joseph Dauben: Appendix 1992: revolutions revisited6. Paolo Mancosu: Descartes's geometrie and revolutions in mathematics7. 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 MacLaurin9. Yuxin Zheng: Non-Euclidean geometry and revolutions in mathematics10. Luciano Boi: The 'revolution' in the geometrical vision of space in the nineteenth century, and the hermeneutical epistemology of mathematics11. Caroline Dunmore: Meta-level revolutions in mathematics12. Jeremy Gray: The nineteenth-century revolution in mathematical ontology13. Herbert Breger: A restoration that failed: Paul Finsler's theory of sets14. Donald Gillies: The Fregean revolution in logic15. Michael Crowe: Afterword 1992: A revolution in the historiography of mathematics?About the contributorsBibliographyIndex

From Our Editors

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.

Editorial Reviews

'are graced with excellent collective bibliographies, and Gillies's has a good index'Annals of Science, 51 (1994)