Negative Math: How Mathematical Rules Can be Positively Bent

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Princeton University Press, 2006 - Mathematics - 267 pages
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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


  

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Negative math: how mathematical rules can be positively bent

User Review  - Not Available - Book Verdict

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 ... Read full review

Contents

Introduction
1
The Problem
10
History Much Ado about Less than Nothing
18
The Search for Evident Meaning
36
History Meaningful and Meaningless Expressions
43
Impossible Numbers?
66
History Making Radically New Mathematics
80
From Hindsight to Creativity
104
Can Minus Times Minus Be Minus?
131
Unity in Mathematics
166
Making a Meaningful Math
174
Finding Meaning
175
Designing Numbers and Operations
186
Physical Mathematics?
220
notes
235
further reading
249

Math Is Rather Flexible
110
Sometimes 1 Is Greater than Zero
112
Traditional Complications
115
acknowledgments
259
index
261
Copyright

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About the author (2006)

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.

Bibliographic information