Paul Erdos liked to talk about The Book, in which God maintains the perfect ?
proofs for mathematical theorems, following the dictum of G. H. Hardy that
there is no permanent place for ugly mathematics. Erdos also said that you ?
need not believe in God but, as a mathematician, you should believe in
The Book. A few years ago, we suggested to him to write up a first (and
very modest) approximation to The Book. He was enthusiastic about the
idea and, characteristically, went to work immediately, filling page after
page with his suggestions. Our book was supposed to appear in March
1998 as a present to Erdos’ 85th birthday. With Paul’s unfortunate death ?
in the summer of 1996, he is not listed as a co-author. Instead this book is
dedicated to his memory.
“The Book”
We have no definition or characterization of what constitutes a proof from
The Book: all we offer here is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever
insights and wonderful observations. We also hope that our readers will
enjoy this despite the imperfections of our exposition. The selection is to a
great extent influenced by Paul Erdos himself. A large number of the topics ?
were suggested by him, and many of the proofs trace directly back to him,
or were initiated by his supreme insight in asking the right question or in
making the right conjecture. So to a large extent this book reflects the views
of Paul Erdos as to what should be considered a proof from The Book.