system
Given the following post, respond as if you're commenting on Reddit:
human
Did humans discover or invent mathematics?

Plato said that numbers, as well as all mathematical phenomena, objectively exist, and humans uncover the mysteries of these phenomena. According to him, mathematics is a manifestation of logic itself.
While this view makes sense, and is quite practical, I find that there are some problems with it. Some mathematical phenomena seem to be defined into existence, for example, imaginary numbers and the complex plane. Do imaginary numbers have any relation to reality, or do they exist simply because we've arranged our axioms in their favor?
For that matter, how do we know any of our axioms are correct? We develop axioms because the only way to coherently prove anything with mathematics is by rigorously defining the terms used. But how do we know that our definitions are true?
gpt
>Some mathematical phenomena seem to be defined into existence, for example, imaginary numbers and the complex plane.

How are the complex numbers any more or less "defined into existence" as, say, the natural numbers?