Models. Humans hold models of the world in their minds, math helps you understand and create more complex and consistent models. You always exist in a simulation of your own construction to make sense of the universe.
My feeling is that no model can ever fully capture a complete description of reality, the information isn't compressible to such a degree that approximations or abstractions can be lossless.
Most of what we consider to be invention is merely combinatoric novelty.
The universe is not a nice place. It never was, and never will be. This universe is merely a proving ground for the strong to conquer, and the weak to perish. You either offend, or be offended.
How we express math is particular to us, though it'd be commonly decipherable. Math is more and more globally standardized as more of it gets globally acknowledged as "the most useful" way to do math. E.g. place holder 0 vs Roman Numerals. Ratios are conceptually universal to any species that bothers measuring. Quantification maybe less so. Especially if their comprehension of advanced sciences/engineering is somehow intuitive instead of formally calculated.
If a space faring species has a concept of proportions/ratios, but not individual identity of numbers, presenting Meters as a portion of the speed of light might be a universal way discern the rest of our math. Water as Liters might be more accessible, depending on how they think of water.
Sets and Axioms are purely conceptually representative and so viable as long as they're capable of symbolic abstraction at all.
Math is definitely universal. The math behind things in science wouldn't suddenly change on different alien planets. Take things like V = IR. That relies on multiplication and division. It's gonna be the same on other planets. The units, notation, etc. will be different but the concepts would be the same.
I'm no STEM major, so I may be way off, but this is how I see it.
V = IR isn't math. It's a way of defining the relationship and outcome of two specific physical qualities. It says that we combine the resistance of a medium ( R) with the current flowing through it (I) into another joint emergent quality we call voltage (V). We do this because it makes our understanding of the physical world easier to manage since this relationship has helpful applications.
Math is simply patterns in the relationships of quantities. It excludes any physical units or qualities. In other words, math is the art of counting.
I think you're misunderstanding my point. I'm not saying the relationship of V = IR means math exists, what I'm saying is that because that relationship factually exists aliens would have a way to quantify that relationship. Because of that they would have a way to express the concepts of multiplication and division.