Mathematics is nothing more than a method based on the human discovery that things can be counted.
The reification of mathematical concepts is one of the earliest of superstitions (think Pythagorous) and the most fundamental of logical fallacies. That this pathetic superstition still has a market is incredible.
The mistake the earlier Platonists made was to postulate some sort of world of ideal forms over and above the physical world. That was indeed mysticism. Modern Platonism only postulates that the mathematical world and reality are one and the same. This is not mysticism, because the mathematical forms are located in the physical world.
My advice to you to go take a rudimentary course in the nature of rationality and the scientific method.
The whole basis of science and philosophy is the idea that there is a wider reality than the one we can currently directly observe. Then we use critical thinking and indirect evidence to try to reason our way to ideas about this deeper reality. Eventually we figure out a way to directly observe this deeper reality and our conception of reality is broadened.
Given objective reality and given that the mind can grasp it, scientists are perfectly justified in assuming that there is some degree of direct correspondence between things that are in their models and unobservables in reality, if they have a strong rational understanding of the principles underpinning the parts of reality under study.
Not being able to tell the difference between concepts (mathematics) used to describe those aspects of reality that can be counted and measured and reality itself is the same as not being able to tell the difference between monopoly money and the real thing.
Circular reasoning Regi old boy. You've simply pre-supposed a complete distinction between a model of reality and reality itself. You're saying that scientists can't know things in themselves. That is also, by the way, is the philosophy of Kant.
How do you know in advance what is and is not a part of concrete reality? The nature of reality is what are trying find out. We shouldn't presuppose in advance which things are merely 'devices' and which are concrete observables.