The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development / Edition 1

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A compact survey, at the elementary level, of some of the most importa nt concepts of mathematics. Attention is paid to their technical featu res, historical development and broader philosophical significance. Ea ch of the various branches of mathematics is discussed separately, but their interdependence is emphasised throughout. Certain topics { such as Greek mathematics, abstract algebra, set theory, geometry and the philosophy of mathematics { are discussed in detail. Appendices outlin e from scratch the proofs of two of the most celebrated limitative res ults of mathematics: the insolubility of the problem of doubling the c ube and trisecting an arbitrary angle, and the Gwdel incompleteness th eorems. Additional appendices contain brief accounts of smooth infinit esimal analysis { a new approach to the use of infinitesimals in the c alculus { and of the philosophical thought of the great 20th century m athematician Hermann Weyl.

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Editorial Reviews

From the Publisher
'... impressively broad and far-ranging... written in an accessible and engaging style... The appendix on Gödel's clear and easy to follow... a clear and straightforward survey of the conceptual development of mathematics. It is a wonderful addition to the literature...provides an accessible introduction to the subject matter. I recommend it to anyone who has an interest in mathematics and its development.'
Philosophia Mathematica, 8:3 (2000)
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Product Details

  • ISBN-13: 9781402000072
  • Publisher: Springer Netherlands
  • Publication date: 8/31/2001
  • Series: Western Ontario Series in Philosophy of Science, #63
  • Edition description: Softcover reprint of the original 1st ed. 1999
  • Edition number: 1
  • Pages: 262
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.55 (d)

Table of Contents

Foreword. Acknowledgements. 1. Numerals and Notation. 2. The Mathematics of Ancient Greece. 3. The Development of the Number Concept. 4. The Evolution of Algebra, I. 5. The Evolution of Algebra, II. 6. The Evolution of Algebra, III. 7. The Development of Geometry, I. 8. The Development of Geometry, II. 9. The Calculus and Mathematical Analysis. 10. The Continuous and the Discrete. 11. The Mathematics of the Infinite. 12. The Philosophy of Mathematics. Appendices. Bibliography. Index of Names. Index of terms.
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