Most mathematicians, when asked about the nature and meaning of mathematics, vacillate between the two unrealistic poles of Platonism and formalism. By looking carefully at what mathematicians really do when they are doing mathematics, Reuben Hersh offers an escape from this trap. This book of selected articles and essays provides an honest, coherent, and clearly understandable account of mathematicians' proof as it really is, and of the existence and reality of mathematical entities. It follows in the footsteps of Poincare, Hadamard, and Polya. The pragmatism of John Dewey is a better fit for mathematical practice than the dominant ""analytic philosophy''. Dialogue, satire, and fantasy enliven the philosophical and methodological analysis.

Reuben Hersh has written extensively on mathematics, often from the point of view of a philosopher of science. His book with Philip Davis, The Mathematical Experience, won the National Book Award in science.

About the Author
Reuben Hersh is emeritus professor of mathematics at the University of New Mexico, USA.

Reviews
I view Hersh as a hero: not a perfect idol, but more a real-life hero who through stubborn hard work and prolific writing has made a difference in the types of conversations we are having now about ourselves and the ways we relate to the world. ... [A]s I dove into the book, I found myself fascinated by its riches, and surprised that [it] worked so well. ... I think most readers would agree that the sequencing of the articles actually worked ... many will enjoy getting a complete overview of Hersh's argument. ... I remain enthralled by Hersh's ideas and impressed by his persistent defense of his controversial but significant perspective. I believe the American Mathematical Society has done a service to the mathematical community by putting together this collection. ... Reuben Hersh's collection is full of provocative ideas, offering perspectives on our profession that may help us understand better ourselves and our craft and even to teach our students better. This volume will remain on my easy-to-reach shelf for a long time to come." - MAA Reviews

"... I found the author's arguments powerful and compelling, and conveyed with great clarity and concision. ... It is refreshing to occasionally step back and talk about mathematics rather than doing it, and this book provides solid rhetorical ammunition." - LMS Newsletter



Book Information
ISBN 9780821894200
Author Reuben Hersh
Format Paperback
Page Count 291
Imprint American Mathematical Society
Publisher American Mathematical Society
Weight(grams) 542g