Counting rational curves in the plane

It is well known that through two points in the plane passes exactly one straight line; some people also know that through five points in general position passes exactly one conic. A classical and difficult problem in enumerative geometry was to determine the number N_d of rational plane curves of degree d passing through 3d-1 points in general position. The problem was solved around 1994 by M. Kontsevich, who gave a recursive formula for N_d. I am going to show how the formula is related to intersection theory on a certain moduli space of stable maps.