The relationship between physics and mathematics is hardly ever presented with sufficient clarity to satisfy either physicists or mathematicians. It is a situation that often leads to misunderstandings that may spread quickly from teacher to student, such as the idea that mathematics is a mere instrument for the physicist. In this paper, we examine the historical construction of this relationship, with reference to the French philosopher Michel Paty, and we look briefly at its presence in the construction of thermodynamics. We then present the results of an empirical study on the way these relations are perceived among undergraduate students, in their last year of a university course on physics, in the discipline of Thermodynamics. The study points to significant relations between the students' performance in terms of problem solving and the epistemic view they hold.