Some philosophers hold that there are abstract objects (such as numbers, mathematical objects and fictional entities) and universals (properties that can be possessed by multiple objects, such as "redness" or "squareness"), both of which are outside of space and time and/or are causally inert.
Realism, best exemplified by Plato and his Platonic Forms, teaches that universals really exist, independently and somehow prior to the world.
On the other hand, Nominalism holds that there is really no such thing as abstract objects, which really exist only as names, because a single object cannot exist in multiple places simultaneously.
Moderate Realism, as espoused by Aristotle among others, tries to find some middle ground between Nominalism and Realism, and holds that there is no realm as such in which universals exist, but rather they are located in space and time wherever they happen to be manifest. Conceptualism, the doctrine that universals exist only within the mind and have no external or substantial reality, is also an intermediate solution.
Other positions such as Formalism and Fictionalism do not attribute any existence to mathematical entities, and are anti-Realist.
The Philosophy of Mathematics overlaps with metaphysics in this area.