According to a common presentation, Platonism in the philosophy of mathematics is the view according to which the entities with which mathematics is concerned, numbers, are abstract objects which exist independently of the mind. The latter feature, in particular, is alleged to secure the “realist” component of mathematical Platonism. Surprisingly enough, however, this characterization of Platonism is not normally paired with a philosophical explanation of the implicated notion of mind-dependent (respectively, mind-independent) existence. Since there seems to be more than one metaphysically relevant sense in which an entity may be said to depend (or not to depend) on the mind, this is not a minor lack; for not every such sense seems to be relevant to the realism issue. This paper is aimed to fill this gap, and to provide the Platonist with a conceptual analysis of the realism-relevant sense in which her claim that numbers exist mind-independently should be understood. Result of this analysis will also be the conclusion that Non-Gödelian Platonism, a view recently proposed by J. Divers and A. Miller, should not be really regarded as a form of Platonism.