It is well known that polynomials are dense in the continuous functions, so that given a continuous function, a uniformly convergent sequence of polynomials exists. However, in choosing nodes to approximate functions, it often happens that one must choose the nodes before knowing the functions. So is there a sequence of nodes such that, for any function, the interpolating polynomials uniformly converge to the function? Sadly, the answer is no. I will prove this, and also discuss various related results.