*Proofs from THE BOOK*Aigner and Ziegler have attempted not to write that Book itself, which would be hubris on a grand scale, but to select proofs which would be candidates for inclusion in it, restricting themselves to those which use only basic higher mathematics.

A lot of solid mathematics is packed into *Proofs*. Its thirty chapters,
divided into sections on Number Theory, Geometry, Analysis, Combinatorics,
and Graph Theory, cover a broad range of subjects: the infinity of primes,
applications of Euler's formula, five-coloring of plane graphs, Latin
squares, the problem of the thirteen spheres, Borsuk's conjecture,
inequalities, the irrationality of pi, and so on. Each chapter is
largely independent; some include necessary background as an appendix.

The proofs included are all relatively accessible, but readers will
want to have done the better part of an undergraduate degree in pure
mathematics, or an equivalent. The key to the approachability of *Proofs*
lies not so much in the accessibility of its mathematics, however,
as in the rewards it offers: elegant proofs of interesting results,
which don't leave the reader feeling cheated or disappointed.

*Proofs from THE BOOK* would be ideal for anyone who studied pure
mathematics at university, hasn't done much mathematics since, and wants
to recapture some of its pleasures without too much work. Mathematics
students feeling unmotivated by more mundane and unexciting course-work
may also relish its approach, though it may also spoil them. *Proofs from
THE BOOK* is attractively presented, intellectually invigorating, and
a lot of fun.

Note: as of 2010, *Proofs from THE BOOK* was up to a fourth edition.

June 1999

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