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In Pursuit of Zeta-3: The World's Most Mysterious Unsolved Math Problem
An engrossing look at the history and importance of a centuries-old but still unanswered math problem
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 tantalize curious math enthusiasts everywhere.
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 tantalize curious math enthusiasts everywhere.
344 pages, Hardcover
Published October 19, 2021
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About the author
Paul J. Nahin
53 books126 followersPaul J. Nahin is professor emeritus of electrical engineering at the University of New Hampshire and the author of many best-selling popular math books, including The Logician and the Engineer and Will You Be Alive 10 Years from Now? (both Princeton).
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April 30, 2022
I'm a very big fan of Nahin's books - I own most of his popular science books and his "Inside Interesting Integrals" book - his "When least is best" book is very probably one of the best Pop/Sci books I have ever read (likely one of the best book of any category), but I didn't enjoy this one.
What I love about his books is not only that he doesn't stint on the maths, but that he frequently relates back some mathematical nugget to make observations about the underlying physics, and that latter element is what I think is missing here. He certainly doesn't stint on the maths in this book either, in fact there is rather too much of it - page after page of algebraic manipulation just becomes too tiresome and I often find myself skipping to the next piece of text, but frustrating I didn't get the goal of much the discourse, it often felt like doing maths for the sake of it (no bad thing of course, but you can do that yourself).
There is plenty of interest in here of course, with the usual fabulous insights into the mathematical personalities, especially the prolific, and ever popular Euler, in this book, but while I'm happy to add it to my collection, it didn't make the impression that his books normally do.
What I love about his books is not only that he doesn't stint on the maths, but that he frequently relates back some mathematical nugget to make observations about the underlying physics, and that latter element is what I think is missing here. He certainly doesn't stint on the maths in this book either, in fact there is rather too much of it - page after page of algebraic manipulation just becomes too tiresome and I often find myself skipping to the next piece of text, but frustrating I didn't get the goal of much the discourse, it often felt like doing maths for the sake of it (no bad thing of course, but you can do that yourself).
There is plenty of interest in here of course, with the usual fabulous insights into the mathematical personalities, especially the prolific, and ever popular Euler, in this book, but while I'm happy to add it to my collection, it didn't make the impression that his books normally do.
Displaying 1 of 1 review