π is not an invention, it's the relation between a circle's lenght and its radius.
Not hard to understand.
> According to intuitionism, mathematical objects are products of our mind, like characters in a novel. I agree, as far as it goes...
> Fictionalism holds that the mathematical universe is a collective fiction, like Star Trek or Game of Thrones.
You're right, it feels like quite a loose analogy, and only holds when discussing a "canonical" fictional universe. Still, I'm sympathetic to the idea that when we're talking about a circle we're talking about a shared abstract understanding rather than something which objectively exists.
Now go with your atomic imperfections and external influences and take a nap, because it must be exhausting to be so repellent.
The way I see it, the circle is an abstract idea which resides within the language that we use to share our understanding about the patterns we observe in the external world. Those patterns may conform to the abstraction to varying degrees but they are fundamentally not the same thing. Mathematics is a very precise and formal way to communicate this type of knowledge, but that doesn't mean the ideas therein exist objectively. This contrasts with the views of someone like Max Tegmark, who has the impression that the universe is inherently mathematical.