string theory suggests that the universe works in a 10 dimensional construct: 4-dimensional spacetime and a 6-dimensional compact object called a calabi-yau space. physics suggests that it might be possible for two different calabi-yaus to give identical physics. these are called mirror pairs. what is the geometric relation between these two objects? one incredible suggestion is that counting curves in one calabi-yau is tied to the coefficients of an integral on the mirror. up to this point geometers had enough trouble counting degree 2 or 3 curves in a calabi-yau and it usually involved esoteric machinery. now it could be calculated by just an integral on a different space and looking at the coefficients. i will outline some of conjectures and implications then try to do an example on a particular three-fold.