Let w(F) be the width needed to refute a CNF F in resolution. It is well known that the space needed to refute F in resolution is lower bounded by w(F), and it has been open whether something similar holds for polynomial calculus (PCR). We show, by a novel 'forcing' argument, that the space needed to refute F in PCR is lower bounded by the square root of w(F). Joint work with Nicola Galesi and Leszek Kolodziejczyk.