Erdos conjectured that $N$ points in the plane determine at least $c N (log N)^{-1/2}$ different distances. Recently Nets Katz and I came close to proving the conjecture, showing that the number of distinct distances is at least $c N (log N)^{-1}$.Elekes and Sharir made a connection between the distinct distance problem and incidence geometry - the study of intersection patterns of points and lines. There has been a lot of progress in this area over the last few years starting with Dvir's solution of the Kakeya problem in finite fields using the polynomial method. The new wrinkle in our proof is a way to mix polynomial methods with topological methods.