PrefacePermissions and acknowledgmentsAcknowledgmentsOvertureThe ideal mathematician (with Philip J. Davis)ManifestoSelf-introductionChronologyMathematics has a front and a backPart I. Mostly for the right handIntroduction to partTrue facts about imaginary objectsMathematical intuition (Poincaré, Polya, Dewey)To establish new mathematics, we use our mental models and build on established mathematicsHow mathematicians convince each other or “The kingdom of math is within you”On the interdisciplinary study of mathematical practice, with a real live case studyWings, not foundations!Inner vision, outer truthMathematical practice as a scientific problemProving is convincing and explainingFresh breezes in the philosophy of mathematicsDefinition of mathematicsIntroduction to "18 unconventional essays on the nature of mathematics"Part II. Mostly for the left handIntroduction to part 2Rhetoric and mathematics (with Philip J. Davis)Math lingo vs. plain English: Double entendreIndependent thinkingThe “origin” of geometryThe weddingMathematics and ethicsEthics for mathematiciansUnder-represented, then over-represented: A memoir of Jews in American mathematicsPaul Cohen and forcing in 1963Part III. Selected book reviewsIntroduction to part 3Review of Not exactly ... in praise of vagueness by Kees van DeemterReview of How mathematicians think by William ByersReview of The mathematician’s brain by David RuelleReview of Perfect rigor by Masha GessenReview of Letters to a young mathematician by Ian StewartReview of Number and numbers by Alain BadiouPart IV. About the authorAn amusing elementary exampleAnnotated research bibliographyCurriculum vitaeList of articlesIndex

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