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.
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.
The deity of Leibniz and Maupertuis can only make action stationary; to us remains the challenge to make the world as good as possible.... We can neither evade such problems nor address them without science. Ekeland's admirable account gives us the tools to consider these important questions in greater depth. - Peter Pesic, Times Literary Supplement "A vivid picture of human history and destiny.... Ekeland moves easily from mathematics to physics, biology, ethics, and philosophy." - Freeman Dyson, New York Review of Books "[Ekeland's] explanations are clear and elegant... and his prose is fluid, exhilarating, and suspenseful. I tried to put this book down after chapter 4 but couldn't. It was as if some compelling force of nature had a purpose, an opposing directive in the best of all possible worlds." - Joseph Mazur, Nature"