  By considering mirror symmetry applied to conformal field theories
corresponding to strings propagating in quintic hypersurfaces in projective
4-space, Candelas, de la Ossa, Green and Parkes calculated the ``number of
rational curves on the hypersurface'' by comparing three point functions.
Actually, the number of curves may be infinite for special examples; what is
really being calculated is a path integral. The point of this talk is to give
mathematical techniques and examples for computing the finite number that
``should'' correspond to an infinite family of curves (which coincides with
that given by the path integral in every known instance), and to suggest that
these techniques should provide the answer to the not yet solved problem of how
to calculate instanton corrections to the three point function in general.
