We cannot discuss the proof here as it requires some knowledge of zeta functions of curves over finite fields.

Charles Small, Harvard '64:

The moral is that the zeta function exhibits a subtle connection between the "global" (topological, characteristic 0) nature of the curve and its "local" (diophantine, characteristic p for all but finitely many "bad" primes p)  behaviour.  The full extent of this connection only becomes apparent in the context of varieties more general than curves....

"Some friends of mine
 are in this band...."

-- David Auburn, "Proof"

"Women and Mathematics
is a joint program of
the Institute for Advanced Study
and Princeton University."

 -- School of Mathematics,  
1 Einstein Drive,
Princeton, New Jersey