# Gamma: Exploring Euler's Constant

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.