The Best of All Possible Worlds: Mathematics and Destiny

by Ivar Ekeland

University of Chicago Press, 2006 Cloth: 978-0-226-19994-8 | Paper: 978-0-226-19995-5 Library of Congress Classification Q172.E36 2006 Dewey Decimal Classification 509

ABOUT THIS BOOK | AUTHOR BIOGRAPHY | REVIEWS | TOC | REQUEST ACCESSIBLE FILE

ABOUT THIS BOOK

Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer.

This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today.

Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.

AUTHOR BIOGRAPHY

Ivar Ekeland is professor of mathematics and economics at the University of British Columbia and director of the Pacific Institute for Mathematical Sciences. He is the author of several books, including Mathematics and the Unexpected and The Broken Dice, both published by the University of Chicago Press.

REVIEWS

"A run through the history of the last four hundred years, seen through the eyes of a French mathematician. Mathematics appears as a unifying principle for history. Ekeland moves easily from mathematics to physics, biology, ethics, and philosophy."

— Freeman Dyson, New York Review of Books

"[Readers] will not regret a minute spent reading this book. This intelligent, eloquent, very accessible work will make new connections for virtually every reader. Ekeland is clearly a master teacher. Essential."

— Choice

"A book that provides much information about the ideas of optimization and critical points and is full of details about a large cast of characters. . . .The book can be savored in bits and pieces. . . . But the reader who just chooses to start on page one and keep going will almost certainly find it impossible to put the book down, because it is densely packed with delightful items of information and is as entertaining as a fast-moving thriller."

— Hector Sussmann, Notice of the AMS

TABLE OF CONTENTS

Introduction
1. Keeping the Beat
2. The Birth of Modern Science
3. The Least Action Principle
4. From Computations to Geometry
5. Poincaré and Beyond
6. Pandora's Box
7. May the Best One Win
8. The End of Nature
9. The Common Good
10. A Personal Conclusion
Appendix 1. Finding the Second Diameter of a Convex Table
Appendix 2. The Stationary Action Principle for General Systems
Bibliographical Notes
Index

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The Best of All Possible Worlds: Mathematics and Destiny

by Ivar Ekeland

University of Chicago Press, 2006 Cloth: 978-0-226-19994-8 Paper: 978-0-226-19995-5

Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer.

This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today.

Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.

AUTHOR BIOGRAPHY

Ivar Ekeland is professor of mathematics and economics at the University of British Columbia and director of the Pacific Institute for Mathematical Sciences. He is the author of several books, including Mathematics and the Unexpected and The Broken Dice, both published by the University of Chicago Press.

REVIEWS

"A run through the history of the last four hundred years, seen through the eyes of a French mathematician. Mathematics appears as a unifying principle for history. Ekeland moves easily from mathematics to physics, biology, ethics, and philosophy."

— Freeman Dyson, New York Review of Books

"[Readers] will not regret a minute spent reading this book. This intelligent, eloquent, very accessible work will make new connections for virtually every reader. Ekeland is clearly a master teacher. Essential."

— Choice

"A book that provides much information about the ideas of optimization and critical points and is full of details about a large cast of characters. . . .The book can be savored in bits and pieces. . . . But the reader who just chooses to start on page one and keep going will almost certainly find it impossible to put the book down, because it is densely packed with delightful items of information and is as entertaining as a fast-moving thriller."

— Hector Sussmann, Notice of the AMS

TABLE OF CONTENTS

Introduction
1. Keeping the Beat
2. The Birth of Modern Science
3. The Least Action Principle
4. From Computations to Geometry
5. Poincaré and Beyond
6. Pandora's Box
7. May the Best One Win
8. The End of Nature
9. The Common Good
10. A Personal Conclusion
Appendix 1. Finding the Second Diameter of a Convex Table
Appendix 2. The Stationary Action Principle for General Systems
Bibliographical Notes
Index

REQUEST ACCESSIBLE FILE

If you are a student who has a disability that prevents you
from using this book in printed form, BiblioVault may be able to supply you
with an electronic file for alternative access.

Please have the disability coordinator at your school fill out this form.

It can take 2-3 weeks for requests to be filled.

ABOUT THIS BOOK | AUTHOR BIOGRAPHY | REVIEWS | TOC | REQUEST ACCESSIBLE FILE