Proofs from THE BOOK is a book of mathematical
proofs by Martin Aigner and Günter M. Ziegler.
The book is dedicated to the mathematician
Paul Erdős, who often referred to "The Book"
in which God keeps the most elegant proof
of each mathematical theorem.
During a lecture in 1985, Erdős said, "You
don't have to believe in God, but you should
believe in The Book."
== Content ==
Proofs from THE BOOK contains 32 sections
(44 in the fifth edition), each devoted to
one theorem but often containing multiple
proofs and related results.
It spans a broad range of mathematical fields:
number theory, geometry, analysis, combinatorics
and graph theory.
Erdős himself made many suggestions for the
book, but died before its publication.
The book is illustrated by Karl Heinrich Hofmann.
It has gone through five editions in English,
and has been translated into Persian, French,
German, Hungarian, Italian, Japanese, Chinese,
Polish, Portuguese, Korean, Turkish, Russian
and Spanish.
In November 2017 the American Mathematical
Society announced the 2018 Leroy P. Steele
Prize for Mathematical Exposition to be awarded
to Aigner and Ziegler for this book.
The proofs include:
Proof of Bertrand's postulate
Proof that e is irrational (also showing the
irrationality of certain related numbers)
Six proofs of the infinitude of the primes,
including Euclid's and Furstenberg's
Monsky's theorem (4th edition)
Wetzel's problem on families of analytic functions
with few distinct values
Steve Fisk's proof of the art gallery theorem
