Ante rem structuralism is the doctrine that mathematics describes a realm of abstract (structural) universals. According to its proponents, appeal to the existence of these universals provides a source of distinctive insight into the epistemology of mathematics, in particular insight into the so-called ?access problem? of explaining how mathematicians can reliably access truths about an abstract realm to which they cannot travel and from which they receive no signals. Stewart Shapiro offers the most developed version of this view to date. Through an examination of Shapiro's proposed structuralist epistemology for mathematics I argue that ante rem structuralism fails to provide the ingredients for a satisfactory resolution of the access problem for infinite structures (whether small or large).