Maybe maths could help us understand biology or other non-maths fields better!
(Extra mystery: Why did we evolve phase-invariance?)
On the other hand, at a lower level of abstraction, the most fundamental theories of physics known do tend to involve real numbers and continuous functions – from my limited understanding, that applies even to quantum mechanics in many cases, even though it’s known for discretizing quantities that were continuous in classical mechanics. However, it’s unknown – unknowable, even, at some point – whether these infinities are “real”, or themselves approximations of even more fundamental laws.
"Why did your ear, the outer part and the inner bones and the canal and the fluids and the brain, all evolve together in a way that grants Fourier analysis for free? Coincidence? "
No, we model physical systems using math, so you should expect that a physical system involving dynamic systems to use Fourier transforms to effectively model that system. But the efficacy of math does not imply that mathematical objects exist.
"Maybe maths could help us understand biology or other non-maths fields better!"
Um, clearly. Math is extremely successful at describing many aspects of many sciences. But this does not imply mathematical objects exist and are describing the reality of what is occurring, despite providing accurate outputs.