  We define a formal Gromov-Witten theory of the quintic 3-fold via
localization on CP4. Our main result is a direct geometric proof of holomorphic
anomaly equations for the formal quintic in precisely the same form as
predicted by B-model physics for the true Gromov-Witten theory of the quintic
3-fold. The results suggest that the formal quintic and the true quintic
theories should be related by transformations which respect the holomorphic
anomaly equations. Such a relationship has been recently found by Q. Chen, S.
Guo, F. Janda, and Y. Ruan via the geometry of new moduli spaces.
