In this talk, we will discuss the proof of the fact that there are 12 rational curves through 8 general points in P^2. Time permitting, I will say a few words about Kontsevich's formula to calculate the number of degree d rational curves through 3d-1 general points in P^2. The talk will be accessible to anyone who has taken Math 631. Speaker(s): Sridhar Venkatesh (UM)