How Mathematicians Think

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. This book reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results.

An amazing tour de force. Utterly new, utterly truthful. -- Reuben Hersh, author of "What Is Mathematics, Really?" Byers gives a compelling presentation of mathematical thinking where ambiguity, contradiction, and paradox, rather than being eliminated, play a central creative role. -- David Ruelle, author of "Chance and Chaos" 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" I strongly recommend this book. The discussions of mathematical ambiguity, contradiction, and paradox are excellent. In addition to mathematics, the book draws on other sciences, as well as philosophy, literature, and history. The historical discussions are particularly interesting and are woven into the mathematics. -- Joseph Auslander, Professor Emeritus, University of Maryland

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