Mathematical Conversations

Given $N$ distinct points on the plane, what's the minimal number, $g(N)$, of distinct distances between them? Erdős conjectured in 1946 that $g(N)\geq O(N/(log N)^{1/2})$. In 2010, Guth and Katz showed that $g(N)\geq O(N/log N)$ using the polynomial method.