What is Mathematics, Really by Reuben Hersh (1997) [5 Formats] {VTS}

Title: What Is Mathematics, Really?
Author: Reuben Hersh
Category: Academic/Mathematics/Philosophy
Publisher: OUP Australia and New Zealand (1997)
Language: English
ISBN-10: 0195113683
ISBN-13: 978-0195113686



Publisher's info - "Virtually all philosophers treat mathematics as isolated, timeless, ahistorical, inhuman. In What Is Mathematics, Really? renowned mathematician Reuben Hersh argues the contrary. In a subversive attack on traditional philosophies of mathematics, most notably Platonism and formalism, he shows that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Mathematical objects are created by humans, not arbitrarily, but from activity with existing mathematical objects, and from the needs of science and daily life. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. The humanist standpoint helps him to resolve ancient controversies about proof, certainty, and invention versus discovery. The second half of the book provides a fascinating history of the "mainstream" of philosophy - ranging from Pythagoras, Plato, Descartes, Spinoza, and Kant, to Bertrand Russell, Hilbert, Carnap, and Quine. Then come the mavericks who saw mathematics as a human artifact - Aristotle, Locke, Hume, Mill, Peirce, Dewey, Wittgenstein. In his epilogue, Hersh reveals that this is no mere armchair debate, of little consequence to the outside world. Platonism and elitism fit together naturally. Humanism, on the other hand, links mathematics with people, with society, and with history. It fits with liberal anti-elitism and its historical striving for universal literacy, universal higher education, and universal access to knowledge andculture. Thus Hersh's argument has educational and political consequences."

Review:
"In What Is Mathematics, Really?, author Reuben Hersh proposes a philosophy of mathematics that he calls "humanism" and uses this philosophy to analyze age- old questions of proof, certainty and invention versus discovery. He also surveys the history of the philosophy of mathematics. Readers of all levels of mathematical experience will be stimulated by the fascinating and perspicacious discussions Hersh has to offer." -Amazon Reviews

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