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Princeton University Press

How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

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Title: How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Author: Byers, William
ISBN: 9780691145990
Publisher: Princeton University Press
Published: 2010
Binding: Quality
Language: English
Condition: Used: Near Fine
Excellent, unmarked copy with little wear and tight binding. We ship in recyclable American-made mailers. 100% money-back guarantee on all orders.

D 1247570

Publisher Description:

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.