Page 7 -

Introduction and Dedication

This book is dedicated to Paul Erd˝ os, the greatest mathematician I
have ever known, whom it has been my rare privilege to consider
colleague, collaborator, and dear friend.
I like to think that Erd˝ os, whose mathematics embodied the princi-
ples which have impressed themselves upon me as defining the true
character of mathematics, would have appreciated this little book
and heartily endorsed its philosophy. This book proffers the thesis
that mathematics is actually an easy subject and many of the famous
problems, even those in number theory itself, which have famously
difficult solutions, can be resolved in simple and more direct terms.
There is no doubt a certain presumptuousness in this claim. The
great mathematicians of yesteryear, those working in number the-
ory and related fields, did not necessarily strive to effect the simple
solution. They may have felt that the status and importance of mathe-
matics as an intellectual discipline entailed, perhaps indeed required,
a weighty solution. Gauss was certainly a wordy master and Euler
another. They belonged to a tradition that undoubtedly revered math-
ematics, but as a discipline at some considerable remove from the
commonplace. In keeping with a more democratic concept of intelli-
gence itself, contemporary mathematics diverges from this somewhat
elitist view. The simple approach implies a mathematics generally
available even to those who have not been favored with the natural
endowments, nor the careful cultivation of an Euler or Gauss.

vii