Distinct Distances in Two Dimensions

The following problem is due to Erdos (1946): Given n distinct points in the plane, what is the minimum number of distinct distances determined by them? Erdos conjectured that this number is n^{1-o(1)}. We show that any set of n points in the plane has an element from which the number of distinct distances to the other points is at least n^{6/7}. (Joint work with Cs.D. Toth)