Abstract: The problem of counting the number of smooth conics in P² through 5 general points can be solved very simply using linear algebra. By the end of this talk I will present a longer and unnecessary second proof, using some more complicated machinery. Along the way this will give me an excuse to provide a very narrow introduction to Gromov–Witten theory. The advantage of this overkill second method is that almost the exact same proof can be used to determine the number of rational plane curves of degree d through 3d-1 points for any d. Until Gromov–Witten theory came along, this is a problem which had only been solved up to d=5.