The interpolation problem can be roughly stated as follows. Given a set of points in the plane find a polynomial $f(x, y)$ with these points as roots. More generally, one can also ask for the vector space of all interpolating polynomials with bounded degree and with specified vanishing order at each one of the points.

In this talk we will look at the problem of estimating the dimension of such space and will explain why does it become hard to give a general answer to this question. We will spice the exposition with a couple of examples.