How does mathematical Platonism describe abstract objects?

In the philosophy of mathematics, mathematical Platonism is the doctrine that abstract objects exist and that mathematical theorems provide true descriptions of them.12

Defining Abstract Objects

According to the traditional Platonist view, abstract objects are characterized by the following traits:
* Nonspatiotemporality: They are not located anywhere in the physical universe.12
* Nonphysical and Nonmental: They are not made of matter, nor are they merely ideas in the human mind.12
* Independence: They exist objectively and independently of human thought, similar to how the Moon exists independently of our ideas about it.12
* Unchanging and Noncausal: Because they lack physical extension and location, they are eternal and cannot enter into cause-and-effect relationships.12

Platonists argue that mathematics is the study of these abstract structures, which include numbers, functions, sets, and vectors. While traditional Platonism maintains these strict definitions, some nontraditional versions—such as those proposed by Penelope Maddy, Michael Resnik, and Stewart Shapiro—have explored alternative frameworks, including the idea that sets may have spatiotemporal locations or that mathematical objects are simply positions within patterns.12