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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

3.6 of 5 stars 3.60  ·  rating details  ·  52 ratings  ·  10 reviews
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 ...more
ebook, 424 pages
Published April 12th 2010 by Princeton University Press (first published January 1st 2007)
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Jonathan Peto
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
J Scott Shipman
I read this title originally in 2007, and at the time enjoyed Byers unique treatment of ambiguity. From his work, I concluded that there was good ambiguity (where you "know" there is a problem and have a hunch at a solution) and bad ambiguity (where cluelessness prevails). Byers treatment of contradiction, paradox, and patterns went largely over my head. At the time it was an ok forward to this year. Last month I finished Howard Margolis' Patterns, Thinking, and Cognition A Theory o ...more
Greg Linster
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 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
I gave up on this book after about 200 pages. It was too philosophical for me. The only thing I got out of the first 200 pages was the quote: "To grapple with infinity is one of the bravest and extraordinary endeavors that human beings have ever undertaken". I can't convince myself that's grammatically correct, but it's cool anyway, and who am I to judge?
Kung Ying xiang
Since this is one of the first few books I have read on mathematics in a long time, I think it does provide exposure into the philosophy of Mathematics, and how mathematical ideas are created. However, it does tend to get draggy or repetitive at some points
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.
Uses more words than necessary to explain his ideas. I kind of understand what he's trying to say but not really. I'm sure there is a more eloquent way to convey his ideas.
Sue Wilson
I am really enjoying how this book is making me think about mathematics and the teaching of math. It would be a great addition to a math education course.
Chris Brownell
Great read! I highly recommend it to all my friends.
Kris Langman
Great book on the creative side of mathematics.
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