Set theory has long been taken as the foundations of all of mathematics, or at least a large part of it, happily coexisting with the categorical view, for example. Since 2006 there has been an emergence of a new candidate for foundations of mathematics, the univalent foundations, whose more vocal proponents feel that mathematics of the future will be done exclusively by proof assistants and the associated computer libraries. We discuss the connections and differences between the ZFC set theory and univalent foundations and show that the univalent foundations and set theory address two different sets of questions in mathematics, and in particular we explain that it is provably the case that univalent foundations cannot answer some specific questions in mathematics (as cannot set theory, for a different set of specific questions).