The effectiveness of mathematics in physics makes people take for granted the intimate connection between both disciplines. However, history shows that this is not always the case, because mathematics has played a minor role, not only in Aristotelian physics in ancient Greece, but also in Confucian and neo-Confucian science in ancient China. The objective of this study is to discuss the role of mathematics in physics and propose a structuralistic view as an epistemological stance to interpret this role. This paper opens with a brief historical overview on the relationship between mathematics and physics, followed by a report on Taiwanese college students' work on and responses to an activity simulating Galileo's inclined plane experiment, in order to investigate in what way they analyzed the data and to what extent this activity enriched the affective, knowledge-oriented, and historical aspects of their thinking. Additionally, an investigation of a mathematician's and a physicist's beliefs was conducted to search for an epistemological stance that reveals the relationship between mathematics and physics. The study suggests that a structuralist view may be appropriate for promoting students' learning and their epistemological interpretations of mathematics and physics.