It seems what you are saying is that math should be considered emergent, along with the processes and patterns it models, but this does seem to go against the culture of the field, where it is implicit, if not explicit, that math is platonic ideals.
If it models the emergent, than it is descriptive, rather than explanatory.
For example, epicycles were effectively predictive, because the geocentric point of view is what we experience and that was what was modeled. Yet in trying to explain it, the crysalline spheres were poor physics. So while what was observed was described, it wasn't explained.
Now consider General Relativity as describing gravity, with spacetime as the explanation.
As we exist on earth and a geocentric cosmology modeled that, we are mobile organisms, necessitating this sequential process of perception, in order to navigate. Consequently our experience of time is as the point of the present, moving past to future. Which is codified as measures of duration, in order to be correlated with measures of distance, in order to produce spacetime.
Yet the evident reality is that change turns future to past. Tomorrow becomes yesterday, because the earth turns. Duration is the present, as the events come and go.
There can be no literal dimension of time, because the past is consumed by the present, to inform and drive it. Causality and conservation of energy. Cause becomes effect.
Time is asymmetric, because it is a measure of action and action is inertial. The earth only turns one direction.
Different clocks can run at different rates simply because they are separate actions. Think metabolism.
Entanglement is required to synchronize them, the consequence is a larger entity. Added together, the parts becomes one. Two sets of one, become one set of two. Ingredients of a cake become a cake.
Organisms synchronize, ecosystems harmonize.
The node settles into equilibrium while the network stretches to infinity. Galaxies are energy radiating out, as mass/form coalesces in.
Energy is conserved, because it is the present, it creates time, as well as temperature, pressure, color, and sound. Time is frequency, events are amplitude.
As present and process, energy goes past to future, while the patterns it generates go future to past.
In terms of the wave, energy drives it, passing through the medium, as the fluctuations rise and fall, future to past.
As consciousness goes past to future, while thoughts go future to past.
Though it is the digestive, respiratory and circulatory systems processing the energy driving us, feeding that flame, while the central nervous system sorts the forms precipitating out, signals from the noise.
Consequently we tend to define reality in terms of order and chaos, rather than energy and form. Yet unfocused, redundent and excess signals revert to noise. Too much information is chaos.
So not only is math emergent, but if not properly calibrated, it defeats the purpose of clarity.
Thus it needs to be pointed out that this culture of idealism defeats the function of the field, when it generates too much excess information.
For example, the field with the broadest and most basic application of math is accounting and in accounting, it is considered bad form to simply write in a figure and call it "dark money," whenever there is a gap in the books, because it is understand that as a tool and model, the complexities can obscure as easily as clarifiy, so there has to be oversight, because it will serve subjective interests to obscure what is happening.
Which is to say, there are many more layers to that onion you are starting to peel.
