Experiencing Mathematics
What Do We Do, When We Do Mathematics?
Will be published approx. on 30. January 2014
Book
Paperback/Softback
291 pages
978-0-8218-9420-0 (ISBN)
Description
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.
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.
Reviews / Votes
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
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Professional and scholarly
Weight
542 gr
ISBN-13
978-0-8218-9420-0 (9780821894200)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Person
Reuben Hersh is emeritus professor of mathematics at the University of New Mexico, USA.
Content
Preface
Permissions and acknowledgments
Acknowledgments
Overture
The ideal mathematician (with Philip J. Davis)
Manifesto
Self-introduction
Chronology
Mathematics has a front and a back
Part I. Mostly for the right hand
Introduction to part
True facts about imaginary objects
Mathematical intuition (Poincare, Polya, Dewey)
To establish new mathematics, we use our mental models and build on established mathematics
How mathematicians convince each other or "The kingdom of math is within you"
On the interdisciplinary study of mathematical practice, with a real live case study
Wings, not foundations!
Inner vision, outer truth
Mathematical practice as a scientific problem
Proving is convincing and explaining
Fresh breezes in the philosophy of mathematics
Definition of mathematics
Introduction to "18 unconventional essays on the nature of mathematics"
Part II. Mostly for the left hand
Introduction to part 2
Rhetoric and mathematics (with Philip J. Davis)
Math lingo vs. plain English: Double entendre
Independent thinking
The "origin" of geometry
The wedding
Mathematics and ethics
Ethics for mathematicians
Under-represented, then over-represented: A memoir of Jews in American mathematics
Paul Cohen and forcing in 1963
Part III. Selected book reviews
Introduction to part 3
Review of Not exactly ... in praise of vagueness by Kees van Deemter
Review of How mathematicians think by William Byers
Review of The mathematician's brain by David Ruelle
Review of Perfect rigor by Masha Gessen
Review of Letters to a young mathematician by Ian Stewart
Review of Number and numbers by Alain Badiou
Part IV. About the author
An amusing elementary example
Annotated research bibliography
Curriculum vitae
List of articles
Index
Permissions and acknowledgments
Acknowledgments
Overture
The ideal mathematician (with Philip J. Davis)
Manifesto
Self-introduction
Chronology
Mathematics has a front and a back
Part I. Mostly for the right hand
Introduction to part
True facts about imaginary objects
Mathematical intuition (Poincare, Polya, Dewey)
To establish new mathematics, we use our mental models and build on established mathematics
How mathematicians convince each other or "The kingdom of math is within you"
On the interdisciplinary study of mathematical practice, with a real live case study
Wings, not foundations!
Inner vision, outer truth
Mathematical practice as a scientific problem
Proving is convincing and explaining
Fresh breezes in the philosophy of mathematics
Definition of mathematics
Introduction to "18 unconventional essays on the nature of mathematics"
Part II. Mostly for the left hand
Introduction to part 2
Rhetoric and mathematics (with Philip J. Davis)
Math lingo vs. plain English: Double entendre
Independent thinking
The "origin" of geometry
The wedding
Mathematics and ethics
Ethics for mathematicians
Under-represented, then over-represented: A memoir of Jews in American mathematics
Paul Cohen and forcing in 1963
Part III. Selected book reviews
Introduction to part 3
Review of Not exactly ... in praise of vagueness by Kees van Deemter
Review of How mathematicians think by William Byers
Review of The mathematician's brain by David Ruelle
Review of Perfect rigor by Masha Gessen
Review of Letters to a young mathematician by Ian Stewart
Review of Number and numbers by Alain Badiou
Part IV. About the author
An amusing elementary example
Annotated research bibliography
Curriculum vitae
List of articles
Index