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18 Unconventional Essays on the Nature of Mathematics

  • Book
  • © 2006

Overview

Editors:
  1. Reuben Hersh

    1. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, USA

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  • Collection of the most interesting recent writings on the philosophy of mathematics written by highly respected researchers from philosophy, mathematics, physics, and chemistry

  • Interdisciplinary book that will be useful in several fields—with a cross-disciplinary subject area, and contributions from researchers of various disciplines

  • Includes supplementary material: sn.pub/extras

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xxi
    Download chapter PDF

  2. A Socratic Dialogue on Mathematics

    • Alfréd Rényi
    Pages 1-16

  3. “Introduction” to Filosofia e matematica

    • Carlo Cellucci
    Pages 17-36

  4. On Proof and Progress in Mathematics

    • William P. Thurston
    Pages 37-55

  5. The Informal Logic of Mathematical Proof

    • Andrew Aberdein
    Pages 56-70

  6. Philosophical Problems of Mathematics in the Light of Evolutionary Epistemology

    • Yehuda Rav
    Pages 71-96

  7. Towards a Semiotics of Mathematics

    • Brian Rotman
    Pages 97-127

  8. Computers and the Sociology of Mathematical Proof

    • Donald MacKenzie
    Pages 128-146

  9. From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management

    • Terry Stanway
    Pages 147-159

  10. Do Real Numbers Really Move? Language, Thought, and Gesture: The Embodied Cognitive Foundations of Mathematics

    • Rafael Núñez
    Pages 160-181

  11. Does Mathematics Need a Philosophy?

    • William Timothy Gowers
    Pages 182-200

  12. How and Why Mathematics Is Unique as a Social Practice

    • Jody Azzouni
    Pages 201-219

  13. The Pernicious Influence of Mathematics upon Philosophy

    • Gian-Carlo Rota
    Pages 220-230

  14. The Pernicious Influence of Mathematics on Science

    • Jack Schwartz
    Pages 231-235

  15. What Is Philosophy of Mathematics Looking for?

    • Alfonso C. del Ávila Palacio
    Pages 236-249

  16. Concepts and the Mangle of Practice Constructing Quaternions

    • Andrew Pickering
    Pages 250-288

  17. Mathematics as Objective Knowledge and as Human Practice

    • Eduard Glas
    Pages 289-303

  18. The Locus of Mathematical Reality: An Anthropological Footnote

    • Leslie A. White
    Pages 304-319

  19. Inner Vision, Outer Truth

    • Reuben Hersh
    Pages 320-326
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Keywords

About this book

This book comes from the Internet. Browsing the Web, I stumbled on philosophers, cognitive scientists, sociologists, computer scientists, even mathematicians!—saying original, provocative things about mathematics. And many of these people had probably never heard of each other! So I have collected them here. This way, they can read each other’s work. I also bring back a few provocative oldies that deserve publicity. The authors are philosophers, mathematicians, a cognitive scientist, an anthropologist, a computer scientist, and a couple of sociologists. (Among the mathematicians are two Fields Prize winners and two Steele Prize w- ners. ) None are historians, I regret to say, but there are two historically o- ented articles. These essays don’t share any common program or ideology. The standard for admission was: Nothing boring! Nothing trite, nothing tr- ial! Every essay is challenging, thought-provoking, and original. Back in the 1970s when I started writing about mathematics (instead of just doing mathematics), I had to complain about the literature. Philosophy of science was already well into its modern revival (largely stimulated by the book of Thomas Kuhn). But philosophy of mathematics still seemed to be mostly foundationist ping-pong, in the ancient style of Rudolf Carnap or Willard Van Ormond Quine. The great exception was Proofs and Refutations by Imre Lakatos. But that exciting book was still virtually unknown and unread, by either mathematicians or philosophers. (I wrote an article en- tled “Introducing Imre Lakatos” in the Mathematical Intelligencer in 1978.

Reviews

From the reviews:

"This is not a book about foundations or formal logic. It is … about the philosophy of mathematics, but perhaps more about the human practice of mathematics. … This is a terrific collection of essays. … all of the essays give us new insight into that curious thing we do when we do mathematics." (William J. Satzer, MathDL, January, 2006)

"The current book is destined to become a classic as well for numerous reasons which will soon become transparent. … Reuben Hersh is to be commended for orchestrating this masterful collection of essays from distinguished individuals … . I predict that this book will become a classic for the coming generations of mathematics philosophers as well as for mathematics educators interested in changing dominant conceptions of what is mathematics, finally!" (Bharath Sriraman, Zentralblatt für Didaktik der Mathematik, Vol. 38 (4), 2006)

"Editor Reuben Hersh has orchestrated a highly provocative book, particularly for mathematicians, but also for anyone interested in the philosophy and practice of mathematics. … This is a very appealing collection of essays. … I highly recommend this book to those wondering how math is carried out, both mathematicians and laymen. I also recommend it to educators interested in changing the dominant view of math and how to do math." (Hector Zenil, Computing Reviews, January, 2008)

Editors and Affiliations

  • Department of Mathematics and Statistics, University of New Mexico, Albuquerque, USA

    Reuben Hersh

About the editor

REUBEN HERSH is professor emeritus at the University of New Mexico, Albuquerque. He is the recipient (with Martin Davis) of the Chauvenet Prize and (with Edgar Lorch) the Ford Prize. Hersh is the author (with Philip J. Davis) of The Mathematical Experience and Descartes' Dream, which won the National Book Award in l983, and What is Mathematics, Really?

Bibliographic Information

  • Book Title: 18 Unconventional Essays on the Nature of Mathematics

  • Editors: Reuben Hersh

  • DOI: https://doi.org/10.1007/0-387-29831-2

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag New York 2006

  • Softcover ISBN: 978-0-387-25717-4Published: 16 September 2005

  • eBook ISBN: 978-0-387-29831-3Published: 16 January 2006

  • Edition Number: 1

  • Number of Pages: XXII, 326

  • Number of Illustrations: 10 b/w illustrations

  • Topics: Mathematics, general, Mathematical Logic and Foundations

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