\term{Number theory} is the study of the integers.  {\em Why} anyone would
want to study the integers is not immediately obvious.  First of all,
what's to know?  There's 0, there's 1, 2, 3, and so on, along with their
negatives.  Which one don't you understand?
%Number theory is
%right at the core of mathematics; even Ug the Caveman surely had some
%grasp of the integers--- at least the positive ones.  In fact, the
%integers are so elementary that one might ask, ``What's to study?''
%There's 0, there's 1, 2, 3 and so on, and there's the negatives.
%Which one don't you understand?  
%Doesn't math become easy when we
%don't have to worry about nasty numbers like $\sqrt{7}$, $1 / \pi$,
%and $i$?  We can even forget about fractions!
After all, the mathematician G. H. Hardy wrote:
 %
 \begin{quotation}
 \noindent [Number theorists] may be justified in rejoicing that there
 is one science, at any rate, and that their own, whose very remoteness
 from ordinary human activities should keep it gentle and clean.
 \end{quotation}
 %
What most concerned Hardy was that number theory not be used in
warfare; he was a pacifist.  Good for him, but if number theory is
remote from \textit{all} human activity, then why study it?
We'll come back to that question later on, but ironically, we'll see that
poor Hardy must be turning in his grave.

\endinput