Experiencing Mathematics: What Do We Do, When We Do Mathematics?

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 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 Content: "Mostly for the right hand". Introduction 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 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 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 -- About the author. An amusing elementary example Annotated research bibliography Curriculum Vitae List of articles.