Gamma: Exploring Euler's Constant

Julian Havil

Jan 2010 · Princeton Science Library Book 53 · Princeton University Press

About this ebook

Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, 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 π 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.

Ratings and reviews

A great book using Euler's gamma number as a hook to draw the reader in and using it as a red thread throughout. I enjoyed a good read, bringing me back to high school days when I was first starting to explore these infinite series and their extensions using imaginary numbers. This book also brings back the joy in mathematics by historically tracing the development of analytical series to the people who developed them first and with whom they interacted. Napier logarithm, Tycho Brahe, Kepler and Euler's contributions are discussed in the first part, not avoiding making the links to the famous Greeks. Harmonic, Gamma and Rieman-dzeta functions are discussed. The second part contains many applications, such as information and number theoretical links and many others, with some higher level analysis developed in Appendices (definitely at College level). I recommend this book to mathematically gifted last year high school students for whom the normal curriculum neither is challenging enough, nor very interesting, and who are searching and are ready for expanding and challenging their brain beyond the standard curriculum. I know I would have devoured this book at that time in my life. (It has an introduction by Freeman Dyson, the physicist).

It's not the easiest read, but if you can handle the math you will be rewarded

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About the author

Julian Havil is a retired former master at Winchester College, England, where he taught mathematics for thirty-three years. He received a Ph.D. in mathematics from Oxford University. Freeman Dyson is professor emeritus of physics at the Institute for Advanced Study in Princeton. He is the author of several books, including Disturbing the Universe and Origins of Life.