Question

Good holiday!
The Chazon Ish formulated a responsum (it was printed on Tohorot and censored) to the question of what the cause of God is: just as a mathematical formula exists even if there is no material world and will always be true—that is, it is not subject to the limitations of space-time and therefore not to causality either (and as I understand it, he means physical rather than logical causality, and from here we get to the problem of induction and Leibniz's question of why there is anything at all, and this is not the place to elaborate)—that is, it has an ideal status of truth, so too God is an eternal entity not subject to material limitations.
And my question is this: seemingly, the Chazon Ish simply assumes that mathematics has an essential eternal status that exists even without a material reality, and if so he is basically assuming, like Plato, that there are ideal concepts (true, he spoke about essences such as good and evil and all categories of thought, but seemingly the same applies here as well. And by the way—what is the status of music? Does it have an ideal status, or is it only a description translated into sound of the interactions of matter?). But if we assume, like Aristotle, that all essences and properties are merely categories that describe matter and nothing more, then if there is no world there is no mathematics either, and seemingly no truth either (for according to him, truth is only a relation of correspondence and nothing more), since there is no such eternal abstract reality—and consequently the Chazon Ish's definition would not apply?
Another question: according to Plato there is a 'world of ideas' that is not attached to material existence, and I do not understand: where is it? In what sense does it exist? Is it an ontological being?
Thank you very much!