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

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
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ebook, 424 pages

Published
April 12th 2010
by Princeton University Press
(first published January 1st 2007)

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## Community Reviews

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Jan 09, 2012
Jonathan Peto
rated it
5 of 5 stars
·
review of another edition

Shelves:
math,
nonfiction

This book is hard for me to rate. It is not perfect, but I'm going to go ahead and give it five stars, because I think Byers is onto something. His ultimate argument is that mathematics, at its heart, is a creative activity. I don't think that should be a radical thesis, but apparently it is.

What does Byers do? He undercuts the notion that math is purely logical, completely rational. He mines the history of mathematics for its great ideas and uses them as examples of how ambiguity, contradiction ...more

What does Byers do? He undercuts the notion that math is purely logical, completely rational. He mines the history of mathematics for its great ideas and uses them as examples of how ambiguity, contradiction ...more

Aug 27, 2012
Greg Linster
rated it
5 of 5 stars
·
review of another edition

Shelves:
all-time-favorites

Perhaps, like me, you've wondered about what mathematicians really do. Describing what mathematicians do, and also how they think about what they do, is precisely the subject of William Byers excellent book

I have always had a love/hate relationship with mathematics. Throughout my formal education, I found math to be intimidating, especially in my undergraduate and graduate studies. After rea ...more

*How Mathematicians Think*. In short, this book helped me wrap my mind around what mathematics really is.I have always had a love/hate relationship with mathematics. Throughout my formal education, I found math to be intimidating, especially in my undergraduate and graduate studies. After rea ...more

Dec 27, 2013
Julian
rated it
4 of 5 stars
·
review of another edition

Shelves:
mathematics,
philosophy

I expected, from the title, a book about the working habits of mathematicians with biographical sketches, but I was surprised to discover a solid work on the philosophy of mathematics instead. The math described is quite accessible so this would be a good book for the layman interested in questions about the limits of artificial intelligence, the relationship between mathematics and objective truth, et cetera.

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