What Is Mathematics, Really?

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $4.99
Usually ships in 1-2 business days
(Save 80%)
Other sellers (Paperback)
  • All (13) from $4.99   
  • New (6) from $21.53   
  • Used (7) from $4.99   

More About This Textbook

Overview

Virtually all philosophers treat mathematics as isolated, timeless, ahistorical, inhuman. In What Is Mathematics, Really? renowned mathematician Reuben Hersh argues the contrary. In a subversive attack on traditional philosophies of mathematics, most notably Platonism and formalism, he shows that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. The humanist standpoint helps him to resolve ancient controversies about proof, certainty, and invention versus discovery. The second half of the book provides a fascinating history of the "mainstream" of philosophy - ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, Hilbert, Carnap, and Quine. Then come the mavericks who saw mathematics as a human artifact - Aristotle, Locke, Hume, Mill, Peirce, Dewey, Wittgenstein. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. Platonism and elitism fit together naturally. Humanism, on the other hand, links mathematics with people, with society, and with history. It fits with liberal anti-elitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge and culture. Thus Hersh's argument has educational and political consequences.
Read More Show Less

Editorial Reviews

Larry Feldman
This book represents an outstanding resource for helping the mathematics-education community understand the roots of mathematical thought....The book is filled with fascinating mathematical problems and uses very little obscure symbolism.
— The Mathematics Teacher
From the Publisher

"Ruben Hersh puts the people into the philosophy and the philosophy into the mathematics: he will take your mind to places it has never dreamed of."--Ian Stewart, The Mathematical Institute, University of Coventry

"Reuben Hersh's insider's view of the big questions about the nature of mathematics is witty, provocative, insightful, and always accessible. It should revitalize discussions among mathematicians, philosophers, and historians--and all those people who have wondered what mathematics is all about."--Philip Kitcher

"Reuben Hersh's What Is Mathematics, Really? is the most thorough, comprehensive survey of all that has been written on the philosophy of mathematics. It will remain the standard reference in the philosophy of mathematics, indispensable to both mathematicians and philosophers. The author combines the experience of a research mathematician with a keen sense of philosophical relevance to give brief, incisive sketches that strikingly summarize every philosopher's contribution (of the lack of it). Reuben Hersh's volume should be required reading of all undergraduate mathematics majors, as well as of any cultivated person with or without a mathematical background."--Gian-Carlo Rota, Department of Mathematics, MIT

Read More Show Less

Product Details

  • ISBN-13: 9780195130874
  • Publisher: Oxford University Press, USA
  • Publication date: 7/28/1999
  • Edition description: New Edition
  • Pages: 368
  • Lexile: 1090L (what's this?)
  • Product dimensions: 9.00 (w) x 6.10 (h) x 1.10 (d)

Meet the Author

About the Author:
Reuben Hersh taught at several distinguished colleges and universities around the country. Now retired, he resides in Santa Fe, New Mexico.

Read More Show Less

Table of Contents

Preface: Aims and Goals
Acknowledgments
Dialogue with Laura
1 Survey and Proposals 3
2 Criteria for a Philosophy of Mathematics 24
3 Myths/Mistakes/Misunderstandings 35
4 Intuition/Proof/Certainty 48
5 Five Classical Puzzles 72
6 Mainstream Before the Crisis 91
7 Mainstream Philosophy at Its Peak 119
8 Mainstream Since the Crisis 137
9 Foundationism Dies/Mainstream Lives 165
10 Humanists and Mavericks of Old 182
11 Modern Humanists and Mavericks 198
12 Contemporary Humanists and Mavericks 220
13 Mathematics Is a Form of Life 235
Mathematical Notes/Comments 249
Bibliography 317
Index 335
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Review Guidelines
Add Recommendations
Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously
    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)