Revolutions in Mathematics

Häftad, Engelska, 1995

1 869 kr

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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.

Produktinformation

Utgivningsdatum1995-11-02
Mått153 x 231 x 20 mm
Vikt550 g
FormatHäftad
SpråkEngelska
Antal sidor364
FörlagClarendon Press
ISBN9780198514862

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Preface ; Introduction ; 1. Ten 'laws' concerning patterns of change in the history of mathematics 1975 ; 2. T.S. Kuhn's theories and mathematics: a discussion paper on the new historiography of mathematics 1976 ; 3. Appendix 1992 revolutions reconsidered ; 4. Conceptual revolutions and the history of mathematics: two studies in the growth of knowledge 1984 ; 5. Appendix 1992: revolutions revisited ; 6. Descartes's geometrie and revolutions in mathematics ; 7. Was Leibniz a mathematical revolutionary? ; 8. The 'fine structure' of mathematical revolutions: metaphysics, legitimacy, and rigour. The case of calculus from Newton to Berkeley and MacLaurin ; 9. Non-Euclidean geometry and revolutions in mathematics ; 10. The 'revolution' in the geometrical vision of space in the nineteenth century, and the hermeneutical epistemology of mathematics ; 11. Meta-level revolutions in mathematics ; 12. The nineteenth-century revolution in mathematical ontology ; 13. A restoration that failed: Paul Finsler's theory of sets ; 14. The Fregean revolution in logic ; 15. Afterword 1992: A revolution in the historiography of mathematics? ; About the contributors ; Bibliography ; Index

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