In Pursuit of Zeta-3

The World's Most Mysterious Unsolved Math Problem

Paul Nahin

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English

Princeton University Pres
16 May 2023

Mathematics & Sciences; Mathematics; Philosophy of mathematics; History of mathematics; Physics; Engineering: general

For 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 tantalise curious math enthusiasts everywhere.

'Nahin's style is entertaining, directly addressing his readers. . . . Highly recommended.'

Adhemar Bultheel, MAA Reviews

'This book will be both enjoyable and a rich source of useful as well as intriguing information to a wide range of readers.'

Michael Th. Rassias, zbMATH Open

By: Paul Nahin
Imprint: Princeton University Pres
Country of Publication: United States
Dimensions: Height: 203mm, Width: 133mm,
ISBN: 9780691247649
ISBN 10: 0691247641
Pages: 344
Publication Date: 16 May 2023
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

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

Nahin's style is entertaining, directly addressing his readers. . . . Highly recommended. ---Adhemar Bultheel, MAA Reviews This book will be both enjoyable and a rich source of useful as well as intriguing information to a wide range of readers. ---Michael Th. Rassias, zbMATH Open I thoroughly enjoyed this book! ---Jonathan Shock, Mathemafrica.org