New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
 2014; approx. 282 pp; softcover ISBN-10: 0-8218-9420-X ISBN-13: 978-0-8218-9420-0 List Price: US$39 Member Price: US$31.20 Order Code: MBK/83 Not yet published.Expected publication date is February 7, 2014. See also: A Mathematical Medley: Fifty Easy Pieces on Mathematics - George G Szpiro Mathematics under the Microscope: Notes on Cognitive Aspects of Mathematical Practice - Alexandre V Borovik Triangle of Thoughts - Alain Connes, Andre Lichnerowicz and Marcel Paul Schutzenberger The question "What am I doing?" haunts many creative people, researchers, and teachers. Mathematics, poetry, and philosophy can look from the outside sometimes as ballet en pointe, and at other times as the flight of the bumblebee. Reuben Hersh looks at mathematics from the inside; he collects his papers written over several decades, their edited versions, and new chapters in his book Experiencing Mathematics, which is practical, philosophical, and in some places as intensely personal as Swann's madeleine. --Yuri Manin, Max Planck Institute, Bonn, Germany 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 Poincaré, 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. Hersh is emeritus professor of mathematics at the University of New Mexico. Readership The book is of interest to everyone who wonders what math really is, whether they are students, teachers, mathematicians, philosophers, or otherwise. Table of Contents Overture The ideal mathematician (with Philip J. Davis) Manifesto Self-introduction Mathematics has a front and a back Chronology References Mostly for the right hand Introduction to part 1 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" 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 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 An amusing elementary example Annotated research bibliography Curriculum vitae List of articles