From small steps to great leaps, metaphors of spatial mobility abound to describe discovery processes. Here, we ground these ideas in formal terms by systematically studying mobility patterns in the scientific knowledge landscape. We use low-dimensional embedding techniques to create a knowledge space made up of 1.5 million articles from the fields of physics, computer science, and mathematics. By analyzing the publication histories of individual researchers, we discover patterns of scientific mobility that closely resemble physical mobility. In aggregate, the trajectories form mobility flows that can be described by a gravity model, with jumps more likely to occur in areas of high density and less likely to occur over longer distances. We identify two types of researchers from their individual mobility patterns: interdisciplinary explorers who pioneer new fields, and exploiters who are more likely to stay within their specific areas of expertise. Our results suggest that spatial mobility analysis is a valuable tool for understanding the evolution of science.