| Summary: | The objective of this article, which is part of the research program developed by the authors on the role of representation in science and science education, is to highlight the use of mechanisms and mathematical principles as representational heuristics of physical phenomena. They have been used by Descartes and Fermat in their respective investigations in the field of optics, more specifically in their analysis of the light refraction phenomenon. With examples drawn from the works of the cited authors, we sought to reveal the distinct, but not exclusive commitments and conceptions about the dynamics involved in building and developing scientific theories. From the heuristic point of view, we raise the hypothesis of the complementarity and convergence between both representations, with the argument it's up to the mechanisms to capture the constituting material principle of the phenomenon, while the abstract mathematical principles should take care of its formal organization. By emphasizing aspects related to the dynamics of the construction and development of scientific theories, heuristic elements essential to an understanding of the Nature of Science (NOS) and therefore relevant to the Descartes, Fermat, Epistemology of physics, Heuristics, Physics Education teaching and learning process of physics will emerge.
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