Negative Math: How Mathematical Rules Can Be Positively Bent - Hardcover

Martínez, Alberto A.

Hardcover

ISBN 10: 0691123098 ISBN 13: 9780691123097

Publisher: Princeton University Press, 2005

Synopsis

A student in class asks the math teacher: "Shouldn't minus times minus make minus?" Teachers soon convince most students that it does not. Yet the innocent question brings with it a germ of mathematical creativity. What happens if we encourage that thought, odd and ungrounded though it may seem?

Few books in the field of mathematics encourage such creative thinking. Fewer still are engagingly written and fun to read. This book succeeds on both counts. Alberto Martinez shows us how many of the mathematical concepts that we take for granted were once considered contrived, imaginary, absurd, or just plain wrong. Even today, he writes, not all parts of math correspond to things, relations, or operations that we can actually observe or carry out in everyday life.

Negative Math ponders such issues by exploring controversies in the history of numbers, especially the so-called negative and "impossible" numbers. It uses history, puzzles, and lively debates to demonstrate how it is still possible to devise new artificial systems of mathematical rules. In fact, the book contends, departures from traditional rules can even be the basis for new applications. For example, by using an algebra in which minus times minus makes minus, mathematicians can describe curves or trajectories that are not represented by traditional coordinate geometry.

Clear and accessible, Negative Math expects from its readers only a passing acquaintance with basic high school algebra. It will prove pleasurable reading not only for those who enjoy popular math, but also for historians, philosophers, and educators.

Key Features:

• Uses history, puzzles, and lively debates to devise new mathematical systems


• Shows how departures from rules can underlie new practical applications


• Clear and accessible


• Requires a background only in basic high school algebra

About this title

About the Author

Alberto A. Martinez teaches history of science and mathematics at the University of Texas, Austin. He studies history to better understand scientific creativity and to clarify ambiguities in the elements of physics and algebra.

From the Back Cover

"An excellent book, truly readable and accurate. I repeatedly found myself intrigued and informed by Martínez's examples and approaches, which succeed in transforming competent historical analysis into an informative and thought-provoking meditation on mathematical meaning."--Joan L. Richards, Brown University

"Beautifully written. Accurate and reliable. The author's point, that mathematics is constructed according to our judgment of what will serve us, is very important and little understood."--Reuben Hersh, University of New Mexico

"Martinez writes with an accessible and conversational style. His discussion of the relationship of mathematics to physics and its role in the concrete features of the world makes this book attractive to general readers and academics alike."--Ronald Anderson, Boston College

From the Inside Flap

"An excellent book, truly readable and accurate. I repeatedly found myself intrigued and informed by Martínez's examples and approaches, which succeed in transforming competent historical analysis into an informative and thought-provoking meditation on mathematical meaning."--Joan L. Richards, Brown University

"Beautifully written. Accurate and reliable. The author's point, that mathematics is constructed according to our judgment of what will serve us, is very important and little understood."--Reuben Hersh, University of New Mexico

"Martinez writes with an accessible and conversational style. His discussion of the relationship of mathematics to physics and its role in the concrete features of the world makes this book attractive to general readers and academics alike."--Ronald Anderson, Boston College

Reviews

It's a rare person who describes negative numbers (or any numbers) as "unassuming but fun," and he is likely the same person who would notice that negative numbers "stand as just about the only kind of numbers about which a book has not been written." That man is Martinez, and in this book, he touches on mathematics history and great mathematical squabbles about the "evident meaning" of negative numbers, all with the goal of sexing up negative numbers and proposing a "meaningful math" that could rekindle the "connection between mathematical truth and physical experience." No small feat, and the outcome is a qualified success: he writes with clarity and provides context (French novelist Henri Beyle resented the notion that two negatives make a positive) that helps layreaders to deal with abstruse subject matter, but many of his canny re-interpretations of mathematical laws depend on questionable means, such as rejiggering "the definition that we choose to give to the = sign." English majors who never understood why they were required to take math classes may enjoy Martinez's blend of humanism and philosophy, and number-people will certainly want to give this a look.
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Edition details

• Publisher: Princeton University Press
• Publication date: 2005
• ISBN 10: 0691123098
• ISBN 13: 9780691123097
• Binding: Hardcover
• Language: English
• Number of pages: 288