Why does mathematical Platonism treat arithmetic as a study of abstract structures?

Mathematical Platonism posits that mathematics is the study of abstract objects—entities that are nonphysical, nonmental, and exist independently of human thought.12

Platonists treat arithmetic as a study of abstract structures because they view mathematical theories as providing true descriptions of these objective, unchanging realities. For example, the sequence of positive integers is considered an object of study analogous to the solar system in astronomy.12

In the specific context of structuralism, a version of Platonism developed by Michael Resnik and Stewart Shapiro, individual numbers are not viewed as objects in the ordinary sense. Instead, they are defined as positions within a pattern or structure. Just as a "shortstop" position in baseball is a role defined by its relation to other positions rather than by the specific person occupying it, numbers are defined by their structural relations to one another, such as the property of being between two other numbers.32