Why are mathematical objects considered nonphysical in Platonism?

In the philosophy of mathematics, mathematical objects are considered nonphysical in Platonism because they are defined as abstract objects that exist independently of the physical universe.12

Platonists characterize these objects by several key traits that distinguish them from physical matter:

• Nonspatiotemporality: Abstract objects are not located anywhere in space or time. Unlike physical objects, they are not extended in space and do not occupy a position in the physical world.12
• Noncausality: Because they lack physical matter and spatial extension, mathematical objects cannot enter into cause-and-effect relationships with other objects.12
• Independence: They exist objectively and independently of human minds and thoughts. While humans can have mental ideas of mathematical objects (such as the number 4), the objects themselves are distinct from those ideas, much like the Moon exists independently of our thoughts about it.12
• Unchanging Nature: Platonists view these objects as eternal and unchanging, existing outside the flux of the physical world.12

Consequently, Platonists argue that mathematical theorems provide true descriptions of these nonphysical, abstract structures rather than describing physical piles or mental constructs.13