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Philosophia Mathematica Advance Access originally published online on September 15, 2008
Philosophia Mathematica 2009 17(1):113-115; doi:10.1093/philmat/nkn023
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© The Author [2008]. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

Book Review

WILLIAM BYERS. How mathematicians think: Using ambiguity, contradiction, and paradox to create mathematics

Robert Thomas*

St John's College and Department of Mathematics, University of Manitoba, Winnipeg R3T 2N2 Canada. thomas@cc.umanitoba.ca

WILLIAM BYERS. How mathematicians think: Using ambiguity, contradiction, and paradox to create mathematics. Princeton: Princeton University Press, 2007. Pp. viii + 415. ISBN 978-0-691-12738-5.

The first 10% of the full text of this article appears below.

Without wishing to suggest that professional philosophers would regard the book as philosophy, I can report that this book is definitely philosophical. Most of the book pertains to mathematical invention, but not just the psychology thereof, with many examples of the way in which mathematical advances move from two different and incompatible ways of viewing something to a higher viewpoint on it that makes better sense and better mathematics. A simple example of this is the invention of zero, where the two incompatible viewpoints are that numbers are for counting and that there is nothing to count. The number one exemplified almost the same degree of blockage for the ancient Greeks, for whom the least . . . [Full Text of this Article]


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