What is Mathematics, Really?

reuben Hersh

Oxford University Press, 1997 - Medical - 343 pages

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.

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Review: What Is Mathematics, Really?

User Review  - Lyle - Goodreads

In the later chapters, it turned more or less into a survey of what different philosophers have to say about math. Which is nice, because you can't just turn up that stuff with a Google search; it's a ...

Contents

• Survey and Proposals: 3
• Criteria for a Philosophy of Mathematics: 24
• MythsMistakesMisunderstandings: 35
• IutuitionProofCertniuty: 48
• Five Classical Puzzles: 72
• Mainstream Before the Crisis: 91
• Mainstream Philosophy at Its Peak119: 119
• Mainstream Since the Crisis: 137
• Foundationism DicsMainstream Lives: 165
• Humanists and Mavericks of Old: 182
• Modern Humanists and Mavericks: 198
• Coutemporary Humanists and Mavericks: 220
• mathematics: 235
• Mathematical NotesCommeuts: 251
• Mathematical issues from chapters 113 A simple account of square: 314
• Index: 335

About the author

Reuben Hersh taught at several distinguished colleges and universities around the country. Now retired, he resides in Santa Fe, New Mexico.

Bibliographic information

• Title: What is Mathematics, Really?
• Author: reuben Hersh
• Edition: illustrated, reprint
• Publisher: Oxford University Press, 1997
• ISBN: 0195130871, 9780195130874
• Length: 343 pages
• Subjects: Mathematics / History & Philosophy; Mathematics / Study & Teaching; Medical / Endocrinology & Metabolism; Science / Philosophy & Social Aspects