What Is a Number?: Mathematical Concepts and Their Origins

What Is a Number?: Mathematical Concepts and Their Origins

by Robert Tubbs

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Overview

Mathematics often seems incomprehensible, a melee of strange symbols thrown down on a page. But while formulae, theorems, and proofs can involve highly complex concepts, the math becomes transparent when viewed as part of a bigger picture. What Is a Number? provides that picture.

Robert Tubbs examines how mathematical concepts like number, geometric truth, infinity, and proof have been employed by artists, theologians, philosophers, writers, and cosmologists from ancient times to the modern era. Looking at a broad range of topics—from Pythagoras’s exploration of the connection between harmonious sounds and mathematical ratios to the understanding of time in both Western and pre-Columbian thought—Tubbs ties together seemingly disparate ideas to demonstrate the relationship between the sometimes elusive thought of artists and philosophers and the concrete logic of mathematicians. He complements his textual arguments with diagrams and illustrations.

This historic and thematic study refutes the received wisdom that mathematical concepts are esoteric and divorced from other intellectual pursuits—revealing them instead as dynamic and intrinsic to almost every human endeavor.

Product Details

ISBN-13: 9780801890185
Publisher: Johns Hopkins University Press
Publication date: 01/29/2009
Pages: 320
Product dimensions: 5.90(w) x 8.90(h) x 0.90(d)
Age Range: 18 Years

About the Author

Robert Tubbs is an associate professor of mathematics at the University of Colorado, Boulder, and the coauthor of Making Transcendence Transparent: An Intuitive Approach to Classical Transcendental Number Theory.

Table of Contents

Preface
1. Mysticism, Number, and Geometry: An Introduction to Pythagoreanism
2. The Elgin Marbles and Plato's Geometric Chemistry
3. An Introduction to Infinity
4. The Flat Earth and the Spherical Sky
5. Theology, Logic, and Questions about Angels
6. Time, Infinity, and Incommensurability
7. Medieval Theories of Vision and the Discovery of Space
8. The Shape of Space and the Fourth Dimension
9. What Is a Number?
10. The Dual Nature of Points and Lines
11. Modern Mathematical Infinity
12. Elegance and Truth
Notes
Bibliography
Index

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