 Even when he was writing about physiology, Helmholtz’s vocation as a mathematical physicist was apparent. Helmholtz used mathematical reasoning to support his arguments for the sign theory, rather than exclusively philosophical or empirical evidence. Throughout his career, Helmholtz’s work is marked by two preoccupations: concrete examples and mathematical reasoning. Helmholtz’s early work in physiology of perception gave him concrete examples of how humans perceive spatial relations between objects. These examples would prove useful to illustrate the relationship between metric geometry and the spatial relations between objects of perception. Later, Helmholtz used his experience with the concrete science of human perception to pose a problem for the Riemannian approach to geometry. 