The aim of this paper is to criticise the view that it is possible to suggest an interpretation of Aristotle’s philosophy of mathematics compatible with his realistic metaphysics while avoiding problems of both fictionalist and realist interpretations, by regarding mathematical objects as a kind of potential beings. In Aristotle’s ontology, not only actual beings but also potential beings are seen as something existent. Thus, if mathematical objects exist as potential beings, the precision problem does not occur. A difficulty with this interpretation is, though, that Aristotle uses the term ‘potentiality’ homonymously, and not every kind of potentiality means a mode of existence. Therefore, only when the matter of mathematical objects, which is regarded as the potentiality of mathematical objects, can be called potentiality in the sense of another mode of existence, there will be a ground to say that mathematical objects are items in Aristotle’s ontological inventory. However, the matter of mathematical objects differs from those potential beings considered as of another mode of existence. First, unlike an incomplete substance such as a boy, the pure extension which is identified as the mathematical matter does not have the internal causal power to actualize itself or something else into its actualities, i.e., geometrical objects. Secondly, according to Aristotle’s actualism, actuality is always prior to its potentiality in existence in the sense that potentiality’s existence depends on actuality’s. Nevertheless, the existence of pure extension is prior to that of any of its possible actualizations. Moreover, the fact that mathematical objects are not actualized in the sensible world makes it doubtful whether mathematical objects exist in any form of actuality at all. This seems to indicate that mathematical objects themselves do not exist at all as well, since, for Aristotle, what is only in potentiality and never actualized, e.g., infinity, is considered not as something existent but rather as a kind of non-being.