Let p(x,y,z) be a polynomial. The partition regularity problem asks the following question: for any finite coloring of integers, is there any x,y,z of the same color such that p(x,y,z)=0. In this talk, we will go over the history of the partition regularity problem for quadratic polynomials. We will also talk about a recent joint work with S. Donoso, A. Koutsogiannis and A. Ferre Moragues on the partition regularity problem over imaginary quadratic number fields.