In this thesis, I address the philosophical problem of why mathematics is useful for physics. I discuss the contemporary philosophical debate on the topic, which is focused on the representational role of mathematics. In contrast to this, I then defend a pragmatic view in which representation is only one of the uses of mathematics in physics, and which stresses the use of mathematics in experimental and technological contexts. I argue that physicists can make mathematics useful in concrete situations because they have a language that enables them to coordinate activities in mathematical and concrete contexts. In particular, there are concepts that are meaningful in both contexts of work. I call these “hybrid” concepts, and I analyse them with a view that takes the meaning of a term to be determined by its use. For physicists to successfully combine work in mathematical and concrete contexts, they need to have mastered the accepted uses of hybrid terms in both contexts. In the historical development of science, many concepts underwent changes so that today, they are particularly apt to connect the two contexts of work. I will use two case studies to show how this approach can illuminate the usefulness of mathematics in concrete situations: the development of the concept of “velocity” from its mathematisation in the Middle Ages to its first technological usefulness in the context of gunnery in the eighteenth century, and the development of the term “spin” from its introduction into atomic physics in the 1920s to its use in modern MRI. I claim that if we trace the historical development of hybrid terms with a use-focused view of meaning, it becomes clear why mathematics became more and more useful in experimental and technological contexts.