Among the myriad of constants that appear in mathematics, p, e, and i are the most familiar. Following closely behind is g, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery.
In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics.
Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + . . . up to 1/n, minus the natural logarithm of n--the numerical value being 0.5772156. . .. But unlike its more celebrated colleagues p and e, the exact nature of gamma remains a mystery--we don't even know if gamma can be expressed as a fraction.
Among the numerous topics that arise during this historical odyssey into fundamental mathematical ideas are the Prime Number Theorem and the most important open problem in mathematics today--the Riemann Hypothesis (though no proof of either is offered!).
Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians.
"[A] wonderful book. . . . Havil's emphasis on historical context and his conversational style make this a pleasure to read. . . . Gamma is a gold mine of irresistible mathematical nuggets. Anyone with a serious interest in maths will find it richly rewarding."--Ben Longstaff, New Scientist
"This book is a joy from start to finish."--Gerry Leversha, Mathematical Gazette
"[Gamma] is not a book about mathematics, but a book of mathematics. . . . [It] is something like a picaresque novel; the hero, Euler's constant g, serves as the unifying motif through a wide range of mathematical adventures."--Dan Segal, Notices of the American Mathematical Society
"The book is enjoyable for many reasons. Here are just two. First, the explanations are not only complete, but they have the right amount of generality. . . . Second, the pleasure Havil has in contemplating this material is infectious."--Jeremy Gray, MAA Online
"It is only fitting that someone should write a book about gamma, or Euler's constant. Havil takes on this task and does an excellent job."--Choice
"This book is accessible to a wide range of readers, and should particularly appeal to those who feel a love for mathematics and are dissuaded by the dryness and formality of text-books, but are also not satisfied by the less rigorous approach of most popular books. Mathematics is presented throughout as something connected to reality. . . . Many readers will find in this book exactly what they have been missing."--Mohammad Akbar, Plus Magazine, Millennium Mathematics Project, University of Cambridge
Table of Contents
This book has been translated into:
Other Princeton books authored or coauthored by Julian Havil: