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.