Distinguishing the physical world from mathematical entities is pragmatic, reflects how it relates to you. It’s impossible to fully know what the physical world is, but it’s possible to interact with it (and to care about what happens in it), and these interactions depend on what it is. When reasoning about constructed mathematical entities, you get to know what you are working with, but not in the case of the physical world. So we can similarly consider an agent living in a different mathematical entity, and for that agent that mathematical entity would be their real physical world.
Because we have to deal with the presence of the real world, it might be convenient to develop concepts that don’t presume knowledge of its nature, which should apply to mathematical entities if we forget (in some perspective) what they are. It’s also relevant to recall that the idea of a “mathematical entity” is informal, so strictly speaking it doesn’t make sense to claim that the physical world is “a mathematical entity”, because we can’t carefully say what exactly “a mathematical entity” is in general, there are only more specific examples that we don’t know the physical world to be one of.
Distinguishing the physical world from mathematical entities is pragmatic, reflects how it relates to you. It’s impossible to fully know what the physical world is, but it’s possible to interact with it (and to care about what happens in it), and these interactions depend on what it is. When reasoning about constructed mathematical entities, you get to know what you are working with, but not in the case of the physical world. So we can similarly consider an agent living in a different mathematical entity, and for that agent that mathematical entity would be their real physical world.
Because we have to deal with the presence of the real world, it might be convenient to develop concepts that don’t presume knowledge of its nature, which should apply to mathematical entities if we forget (in some perspective) what they are. It’s also relevant to recall that the idea of a “mathematical entity” is informal, so strictly speaking it doesn’t make sense to claim that the physical world is “a mathematical entity”, because we can’t carefully say what exactly “a mathematical entity” is in general, there are only more specific examples that we don’t know the physical world to be one of.