Hi, Pedro, and thanks for your comments.
Your suggestion that maths studies structure, or pattern, or "coherent realities" of all forms, and that physics is one of these, and that the universe in which we live is another, is certainly popular among mathematicians and mathematical scientists. But it does seem to displace the central question in favour of even harder questions! These include the following. Why should physics be coherent - why not be too difficult for us to understand, or not coherent at all? Must the universe be coherent for life of any kind to arise? Is there a hidden anthropic principle in this line of argument, requiring a vast array of unknowable parallel universes?
You might be able to sense that while I find your "answer" appealing, I also think that it raises harder and more troubling questions!