Books

Books : reviews

Paul J. Nahin.
Time Machines: time travel in physics, metaphysics and science fiction: 2nd edn.
Springer. 1999

Paul J. Nahin.
Dr Euler's Fabulous Formula: cures many mathematical ills.
Princeton University Press. 2006

In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler’s Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of complex number theory.

In some ways a sequel to Nahin’s An Imaginary Tale, this book examines the many applications of complex numbers alongside intriguing stories from the history of mathematics. Dr Euler’s Fabulous Formula is accessible to any reader familiar with calculus and differential equations, and promises to inspire mathematicians for years to come.

Paul J. Nahin.
Number-Crunching: taming unruly computational problems from mathematical physics to science fiction.
Princeton University Press. 2011

How do technicians repair broken communications cables at the bottom of the ocean without actually seeing them? What’s the likelihood of plucking a needle out of a haystack the size of the Earth? And is it possible t use computers to create a universal library of everything ever written or every photo ever taken? These are just some of the intriguing questions that best-selling popular math writer Paul Nahin tackles in Number-Crunching. Through brilliant math ideas and entertaining stories, Nahin demonstrates how odd and unusual math problems can be solved by bringing together basic physics ideas and today’s powerful computers. Some of the outcomes discussed are so counterintuitive they will leave readers astonished.

Nahin looks at how the art of number-crunching has changed since the advent of computers, and how high-speed technology helps to solve fascinating conundrums such as the three-body, Monte Carlo, leapfrog, and gambler’s ruin problems. Along the way, Nahin traverses topics that include algebra, trigonometry, geometry, calculus, number theory, differential equations, Fourier series, electronics, and computers in science fiction. He gives historical background for the problems presented, offers many examples and numerous challenges, supplies MATLAB codes for all the theories discussed, and includes detailed and complete solutions.

Exploring the intimate relationship between mathematics, physics, and the tremendous power of modern computers, Number-Crunching will appeal to anyone interested in understanding how these three important fields join forces to solve today’s thorniest puzzles.

Paul J. Nahin.
In Pursuit of Zeta-3: the world's most mysterious unsolved math problem.
Princeton University Press. 2021

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 whether there is 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 conundrum, an exact solution to which would have critical implications for applications in physics and engineering. Featuring challenge problems with detailed solutions and MATLAB code, In Pursuit of Zeta-3 will tantalize math enthusiasts everywhere.