Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice

Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice

by Amir R. Alexander
Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice

Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice

by Amir R. Alexander

Hardcover(1)

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Overview

This challenging book argues that a new way of speaking of mathematics and describing it emerged at the end of the sixteenth century. Leading mathematicians like Hariot, Stevin, Galileo, and Cavalieri began referring to their field in terms drawn from the exploration accounts of Columbus and Magellan. As enterprising explorers in search of treasures of knowledge, these mathematicians described themselves as sailing the treacherous seas of mathematics, facing shipwreck on the shoals of paradox, and seeking shelter and refuge on the shores of geometrical demonstrations. Mathematics, formerly praised for its logic, clarity, and inescapable truths, was for them a hazardous voyage in inhospitable geometrical lands.

Significantly, many of the same practitioners who promoted the vision of mathematics as heroic exploration also played central roles in developing the most important mathematical innovation of the period—the infinitesimal methods. This was no coincidence: the heroic tales of exploration and discovery helped shape a new form of mathematical practice, complete with new questions, new acceptable answers, and new standards of evidence. It was this new vision of mathematics as a grand adventure that allowed for the development of the new techniques that led to the Newtonian calculus.

In demonstrating this, the book moves from real voyages to imaginary ones, from the coasts of the Canadian Arctic to the tropical forests of Guyana, and from the inner structure of matter to the intricacies of the mathematical continuum. Throughout, a common rhetoric and imagery of exploration and discovery run like a thread through these diverse elements and bind them together.


Product Details

ISBN-13: 9780804732604
Publisher: Stanford University Press
Publication date: 07/29/2002
Series: Writing Science
Edition description: 1
Pages: 312
Sales rank: 918,775
Product dimensions: 6.00(w) x 9.00(h) x 0.90(d)

About the Author

Amir Alexander has taught history, philosophy, and the history of Science at Stanford Universityand the University of California, Los Angeles.

Table of Contents

List of Illustrationsxi
Acknowledgmentsxiii
Introduction1
1.Prologue: The Origins of the Exploration Narrative6
2.Breaking Alien Coastlines16
3.Mathematical Empires69
4.Seeing the Truth: Hariot and the Structure of Matter98
5."The Club of Hercules": Hariot's Mathematical Atomism130
6.Navigating Mathematical Oceans171
Conclusion198
Appendix AThe Mathematical Narrative205
Appendix BHariot's Method of Calculating Meridional Parts214
Notes217
Bibliography269
Index283
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