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.
