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

HOW MATHEMATICIANS THINK: Using Ambiguity, Contradiction, and Paradox to Create Mathematics

WILLIAM BYERS 

Many people assume that mathematicians' thinking processes are strictly methodical and algorithmic. Integrating his experience as a mathematician and a Buddhist, Byers examines the validity of this assumption. Much of mathematical thought is based on intuition and is in fact outside the realm of black-and-white logic, he asserts. Byers introduces and defines terms such as mathematical ambiguity, contradiction, and paradox and demonstrates how creative ideas emerge out of them. He gives as examples some of the seminal ideas that arose in this manner, such as the resolution of the most famous mathematical problem of all time, the Fermat conjecture. Next, he takes a philosophical look at mathematics, pondering the ambiguity that he believes lies at its heart. Finally, he asks whether the computer accurately models how math is performed. The author provides a concept-laden look at the human face of mathematics. Princeton, 2007, 415 p., hardcover, $35.00.

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