What Is Mathematics, Really? - ISBN:0195130871

What Is Mathematics, Really?

Date: 08 May 2011, 00:30

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Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, 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. 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. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos. What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.
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 math. Readers of all levels of mathematical experience will be stimulated by the fascinating and perspicacious discussions Hersh has to offer.
From Library Journal
Hersh, mathematician and coauthor of The Mathematical Experience (1983), attempts to answer here the philosophical question, "What is mathematics?" Many practitioners think of themselves as "platonists," discovering truths about ideal, eternally existing, abstract objects. The principal alternative to this concept is the "formalist" notion that mathematics is a game in which theorems are developed logically, starting from a set of axioms chosen almost arbitrarily. Hersh's humanistic position is, in essence, that mathematics is what mathematicians do. This is hard to disagree with but does not really explain how the subject evolves. Many feel that all mathematics begins with real-world applications, from which we try to extract the common properties and thence create a universe of abstract objects that can reveal unexpected beauty. In this somewhat disjointed book, Hersh reviews the history of the philosophy of mathematics, discusses the major players, and convincingly sets forth his thesis while undermining those of the competitors. For academic collections.?Harold D. Shane, Baruch Coll., CUNY

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