How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Byers, William
ISBN 10: 0691127387 ISBN 13: 9780691127385
Published by Princeton University Press, 2007
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Synopsis:
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results.
Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure.
The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory?
Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.
About the Author: William Byers is professor of mathematics at Concordia University in Montreal. He has published widely in mathematics journals.
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Bibliographic Details
Title: How Mathematicians Think: Using Ambiguity, ...
Publisher: Princeton University Press
Publication Date: 2007
Binding: Hardcover
Condition: Very Good
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
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ISBN 10: 0691127387
ISBN 13: 9780691127385
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
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ISBN 10: 0691127387
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How Mathematicians Think : Using Ambiguity, Contradiction, and Paradox to Create Mathematics
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How Mathematicians Think : Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Published by
Princeton University Press, 2007
ISBN 10: 0691127387
ISBN 13: 9780691127385
Used
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First Edition
Seller: Better World Books, Mishawaka, IN, U.S.A.
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Condition: Good. 1st Edition. Former library copy. Pages intact with minimal writing/highlighting. The binding may be loose and creased. Dust jackets/supplements are not included. Includes library markings. Stock photo provided. Product includes identifying sticker. Better World Books: Buy Books. Do Good. Seller Inventory # 5780777-6
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
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ISBN 10: 0691127387
ISBN 13: 9780691127385
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Hardcover. Condition: Very Good. 1. With dust jacket. It's a well-cared-for item that has seen limited use. The item may show minor signs of wear. All the text is legible, with all pages included. It may have slight markings and/or highlighting. Seller Inventory # 0691127387-8-6-29
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Published by
Princeton University Press, 2007
ISBN 10: 0691127387
ISBN 13: 9780691127385
Used
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Hardcover. Condition: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less. Seller Inventory # G0691127387I3N00
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Published by
Princeton University Press, 2007
ISBN 10: 0691127387
ISBN 13: 9780691127385
Used
Hardcover
Seller: ThriftBooks-Atlanta, AUSTELL, GA, U.S.A.
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Hardcover. Condition: Good. No Jacket. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less. Seller Inventory # G0691127387I3N00
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Published by
Princeton University Press, 2007
ISBN 10: 0691127387
ISBN 13: 9780691127385
Used
Hardcover
Seller: ThriftBooks-Dallas, Dallas, TX, U.S.A.
Seller rating 5 out of 5 stars
Hardcover. Condition: Very Good. No Jacket. May have limited writing in cover pages. Pages are unmarked. ~ ThriftBooks: Read More, Spend Less. Seller Inventory # G0691127387I4N00
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Published by
Princeton University Press, U.S.A., 2007
ISBN 10: 0691127387
ISBN 13: 9780691127385
Used
Hardcover
First Edition
Seller: 20th Century Lost & Found, La Grande, OR, U.S.A.
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Hardcover. Condition: Fine. Dust Jacket Condition: Fine. 1st Edition. This is an important book, one that should cause an epoch-making change in the way we think about mathematics. While mathematics is often presented as an immutable, absolute science in which theorems can be proved for all time in a platonic sense, here we see the creative, human aspect of mathematics and its paradoxes and conflicts. This has all the hallmarks of a must-read book."--David Tall, coauthor of Algebraic Number Theory and Fermat's Last Theorem. Seller Inventory # 020185