18 Unconventional Essays on the Nature of Mathematics / Edition 1

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This book collects some of the most interesting recent writings that are tackling, from various points of view, the problem of giving an accounting of the nature, purpose, and justification of real mathematical practice—mathematics as actually done by real live mathematicians. What is the nature of the objects being studied? What determines the directions and styles in which mathematics progresses (or, perhaps, degenerates)? What certifies its claim to certainty, or to a priori status, to independence of experience? Why is mathematics the same for all times and places, or is it really the same, or in what senses is it the same and in what senses different? Many of these writings were read at conferences in Europe and America under the heading of "history" or "cultural studies" as well as "philosophy." It is the editor's hope to help foster healthy interdisciplinary mutual aid in this young and fertile area. 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?

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Editorial Reviews

From the Publisher
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)

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Product Details

  • ISBN-13: 9780387257174
  • Publisher: Springer New York
  • Publication date: 9/16/2005
  • Edition description: 2006
  • Edition number: 1
  • Pages: 326
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.73 (d)

Meet the Author

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?

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Table of Contents

Introduction by Reuben Hersh.- A. Renyi: Socratic Dialogue.- C. Cellucci: Filosofia e Matematica, introduction.- W. Thurston: On Proof and Progress in Mathematics.- A. Aberdein: The Informal Logic of Mathematical Proof.- Y. Rav: Philosophical Problems of Mathematics in Light of Evolutionary Epistemology.- B. Rotman: Towards a Semiotics of Mathematics.- D. Mackenzie: Computers and the Sociology of Mathematical Proof.- T. Stanway: From G.H.H. and Littlewood to XML and Maple: Changing Needs and Expectations in Mathematical Knowledge Management.- R. Nunez: Do Numbers Really Move?.- T. Gowers: Does Mathematics Need a Philosophy?.- J. Azzouni: How and Why Mathematics is a Social Practice.- G.C. Rota: The Pernicious Influence of Mathematics Upon Philosophy.- J. Schwartz: The Pernicious Influence of Mathematics on Science.- Alfonso Avila del Palacio: What is Philosophy of Mathematics Looking For?.- A. Pickering: Concepts and the Mangle of Practice: Constructing Quaternions.- E. Glas: Mathematics as Objective Knowledge and as Human Practice.- L. White: The Locus of Mathematical Reality: An Anthropological Footnote.- R. Hersh: Inner Vision, Outer Truth.

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