Realism within philosophy of mathematics comes in different guises. It concerns both the language of mathematics, so that mathematical propositions have objective truth-values, and the subject-matter of mathematics, so that propositions purport to describe and quantify over objectively existing objects. The two combined have usually been connected to mathematical platonism and the views of Plato, Gottlob Frege, or Kurt Gödel. On the object realist side of mathematical platonism, you find a certain analogy between mathematical reality and physical reality, so that the existence of mathematical objects is likened to the existence of physical objects. The existence of the number 2 is thus allied to the existence of the chair I am sitting on. As the former is abstract and the latter is in space-time, this relatedness appears unlikely.
History and Philosophy of ScienceGeneral Mathematics