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Experiencing Mathematics: What Do We Do, When We Do Mathematics? Paperback – February 7, 2014

ISBN-13: 978-0821894200 ISBN-10: 082189420X

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Editorial Reviews


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

What happens when mid-career a mathematician unexpectedly becomes philosophical? These lively and eloquent essays address the questions that arise from a crisis of reflectiveness: What is a mathematical proof and why does it come after, not before, mathematical revelation? Can mathematics be both real and a human artifact? Do mathematicians produce eternal truths, or are the judgments of the mathematical community quasi-empirical and historically framed? How can we be sure that an infinite series that seems to converge really does converge? This collection of essays by Reuben Hersh makes an important contribution. His lively and eloquent essays bring the reality of mathematical research to the page. He argues that the search for foundations is misleading, and that philosophers should shift from focusing narrowly on the deductive structure of proof, to tracing the broader forms of quasi-empirical reasoning that star the history of mathematics, as well as examining the nature of mathematical communities and how and why their collective judgments evolve from one generation to the next. If these questions keep you up at night, then you should read this book. And if they don't, then you should read this book anyway, because afterwards, they will! --Emily Grosholz, Department of Philosophy, Penn State, Pennsylvania, USA

... 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

About the Author

Reuben Hersh is emeritus professor of mathematics at the University of New Mexico, USA.

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