Math is a human construct to describe inherent parts of the universe (among other things).
The universe is compatible with math not because the math is part of it, but because the universe is what math was invented to describe. Most fundamentally, relationships between related structures and sizes. Obviously the universe is full of those since an order does emanate in ours. So aliens probably also have math and even discovering the same relationships etc but that still won't make math an inherent part of the universe to me. The universe doesn't care for math, it just is. Intelligent beings want to describe and discuss it though so we keep inventing math in order to do so and speak a common language.
Personally I find this very simple and not controversial at all. Math was simply invented as a system for us to teach and jot down things so that we don't lose knowledge across generations or for example colleagues.
Right, mathematics is a language for very formally and precisely describe consistent relationships. Since the universe is persistent and consistent, it is useful to us such descriptions.
I may not be possible to know why the universe is this particular way, but I don't think the universe is consistent 'because of maths'. The universe is this way for unknown reasons, but languages don't define or create the things they describe.
To prove this, we can construct descriptions of things that do not or cannot physically exist. Frodo the Hobbit, for example, in English. I'm sure there are equivalent expressions in maths that don't relate to physical things. The description, and therefore the concept exist (same thing), but the thing itself does not. Another way to say it is that the description does not correspond to something that is physically real. So we can construct mathematical descriptions of unreal or hypothetical things, and we can construct English language descriptions of such things. That's just a feature of languages.
The mathematical universe hypothesis says reality is mathematics. Not just that math can model reality, but that the universe is a mathematical structure.
That isn't really at odds with what you are saying though, it's just a lower level.
The universe is compatible with math not because the math is part of it, but because the universe is what math was invented to describe. Most fundamentally, relationships between related structures and sizes. Obviously the universe is full of those since an order does emanate in ours. So aliens probably also have math and even discovering the same relationships etc but that still won't make math an inherent part of the universe to me. The universe doesn't care for math, it just is. Intelligent beings want to describe and discuss it though so we keep inventing math in order to do so and speak a common language.
Personally I find this very simple and not controversial at all. Math was simply invented as a system for us to teach and jot down things so that we don't lose knowledge across generations or for example colleagues.