Description
Book SynopsisTrade ReviewI 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 NewsletterTable of Contents
- 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 (Poincaré, 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
