The mathematical representation of nature is so important in the scientific research of the world that some authors have defended the existence of an ontological burden in the mathematical formalism used by scientists. According to this view, the use of a certain formalism would entail an implicit commitment to the type of entities that the populate the material world. This paper will analyze (i) whether mathematics carries an unavoidable ontological burden in its application to physics, and (ii) whether this alleged (...) ontological burden compromises in some way the metaphysical realism on which scientific activity is based. To do this, the applicability of mathematics to the physical world will be taken for granted and, based on the different examples presented throughout the text, it will be found that there are no reasons to hold such assumptions. Therefore, the non-existent ontological implications of mathematical formalism do not pose any threat to realistic metaphysics in any of its modalities, such as structural realism. (shrink)