An old and open problem is to bound the gap between consecutive integers which can be represented as a sum of two squares. If N is such an integer, the current state of knowledge is a bound of the form N^(1/4), due to Bambah and Chowla. This, essentially trivial, bound is about 70 years old. In joint work with R.C. Vaughan and R. Zhang, we show that one can get much shorter intervals if "sum of squares" is replaced binary quadratic form of small discriminant.