In Pursuit of Zeta-3: The World's Most Mysterious Unsolved Math Problem

Product Description
An engrossing look at the history and importance of a centuries-old but still unanswered math problemFor centuries, mathematicians the world over have tried, and failed, to solve the zeta-3 problem. Math genius Leonhard Euler attempted it in the 1700s and came up short. The straightforward puzzle considers if there exists a simple symbolic formula for the following: 1+(1/2)^3+(1/3)^3+(1/4)^3+. . . . But why is this issue―the sum of the reciprocals of the positive integers cubed―so important? With In Pursuit of Zeta-3, popular math writer Paul Nahin investigates the history and significance of this mathematical conundrum.Drawing on detailed examples, historical anecdotes, and even occasionally poetry, Nahin sheds light on the richness of the nature of zeta-3. He shows its intimate connections to the Riemann hypothesis, another mathematical mystery that has stumped mathematicians for nearly two centuries. He looks at its links with Euler’s achievements and explores the modern research area of Euler sums, where zeta-3 occurs frequently. An exact solution to the zeta-3 question wouldn’t simply satisfy pure mathematical interest: it would have critical ramifications for applications in physics and engineering, such as quantum electrodynamics. Challenge problems with detailed solutions and MATLAB code are included at the end of each of the book’s sections.Detailing the trials and tribulations of mathematicians who have approached one of the field’s great unsolved riddles, In Pursuit of Zeta-3 will tantalize curious math enthusiasts everywhere.
Review
“In this investigation of a mysterious unsolved problem in number theory, Paul Nahin expertly interweaves intriguing historical background with the mathematics, providing many well-constructed exercises for readers to puzzle over. Whether one is a calculus student, an engineer, or simply a lover of mathematics, this book will provide many hours of self-guided study and enjoyment.”
―Jennifer Beineke, coeditor of The Mathematics of Various Entertaining Subjects
“Zeta-3 is fundamental to describing the quantum universe but whether or not it is a unique constant is truly one of the greatest unsolved mysteries in mathematics. In this book, Paul Nahin tells a compelling tale of mathematical intrigue.”
―Christopher Tully, Princeton University
About the Author
Paul J. Nahin is the author of many popular math books, including
How to Fall Slower Than Gravity,
Dr. Euler’s Fabulous Formula, and
An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire and received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics. He lives in Exeter, New Hampshire.