What Is Mathematics, Really?

Paperback | June 4, 1999

byReuben Hersh

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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. Hershpulls 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 themainstream 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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From Our Editors

An entertaining and energetically written work, this book urges to look at mathematics in a social context in order to fully appreciate it. Author Reuben Hersh certainly stirs up a hot debate for anyone with interests in math or the philosophy of science. Reading this book will make you wish the author had written your math textbooks!

From the Publisher

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. Hershpulls the screen back to reveal mathematics a...

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

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Format:PaperbackDimensions:368 pages, 6.1 × 9.02 × 1.1 inPublished:June 4, 1999Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0195130871

ISBN - 13:9780195130874

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From Our Editors

An entertaining and energetically written work, this book urges to look at mathematics in a social context in order to fully appreciate it. Author Reuben Hersh certainly stirs up a hot debate for anyone with interests in math or the philosophy of science. Reading this book will make you wish the author had written your math textbooks!

Editorial Reviews

"Hersh terms his philosophy of mathematics humanism, and his approach as social-historical. His basic theses are expounded early on: 1) Mathematics is part of human culture, 2) Mathematical knowledge isn't infallible, 3) There are different versions of proof or rigor, and 4) Mathematicalobjects are a special part of culture. The book contains two main sections. The first is programmatic. It includes discussions of the traditional philosophies of mathematics (constructivism, formalism, and Platonism), proof, intuition, "gossip," fallibility, applications, and teaching. The secondpart is historical. More than 40 thinkers are discussed in detail, from Pythagoras, Aristotle, and Plato up to current figures. Hersh grapples with the question of the reality of mathematical objects. Hersh brings into question the central role of (traditional) proof in mathematics. His main pointis that one should recognize different levels of existence." - Joseph Auslander, University of Maryland