Through a critical deployment of the surface/depth metaphor, this article explores the catalytic potential of topological thinking to establish points of articulation between apparently opposed notions and canons of thought. Starting from a genealogy of mathematical developments and philosophical mediations toward the end point of geography, we address the interplay between the formal (axiomatic) and conceptual (problematic) dimensions of topology in suggesting some potentially alternative ways of re-imagining the role of topological thinking for spatial theory and human geography.