It would be idiotic, therefore, and thus can only be assumed that one must go out into the natural world and observe its contingent properties in order to know that truths about numbers are true. Sensory observations can provoke recognition of facts like how negative numbers exist as logically necessary concepts despite how there could never be a hole in the ground with negative amounts of square feet. No collection with a negative number of cars, to give just one example, can be found because this is already logically impossible. The metaphysical and epistemological dependence of scientific matters on mathematics is not because numbers and logical facts about them are just a part of science. They transcend science altogether and can of course to some extent can be discovered and grasped without any sensory experience at all [1].
For this reason, there is also no such thing as a correct "mathematics applicability argument" for God's existence, since it is numeric truths that exist as logically necessary facts in the absence of God and not the other way around [2]. If there was no God, there would be zero deities, but there would. There is an uncaused cause and this is demonstrable from reason [3], and if there was no God there could be no cosmos, yet God does not make mathematics apply to the physical world. Any physical world that exists could only exist if it was governed by what cannot be false. It would still be true and could only be true that 127 is not 3,016 and that three added to three equals six.
It is neither because the natural world grounds mathematical truths, as if there would be none if not for the existence of matter and they are only true of physical things, nor because the mind of God makes them true. Mathematical truths are numeric subsets of logical truths, which are necessarily the case in themselves, instead binding God and the cosmos alike. Nothing can be true that violates logical necessity, so God and nature are not above or outside of them. On the contrary, they dictate the nature of all other things, including the divine mind (for instance, one God is one God, no matter what Trinitarians pretend; it either has multiple personalities within one single divine consciousness or there are multiple gods if there is a "Trinity"), physical phenomena, and mental conceptions of them.
Mathematics is but a subcategory of reason that specifically pertains to matters of quantity, which has ramifications for things like geometry (which is about shapes and not just numbers). Yes, logical axioms, while there are mathematical truths about them, such as that there are multiple logical axioms--the existence of truth, the inherence of things following or not following from others, and so on--must be true in order for anything to be true about numbers or their binding relationship on all else. For instance, that a thing is what it is is self-evident, for otherwise whatever else it is would be what it is, and thus it is true in itself like other axioms. However, it is not that 1 is 1 that is self-evident. This hinges on what can be called the law of identity already being true. A number could not be itself without the law of identity, but the law of identity is true prior to and apart from any example of a category or thing it could be true of beyond logical axioms themselves. Science cannot possibly be what dictates or reveals mathematical truths instead of numeric truths and broader and more foundational logical truths dictating and revealing scientific ideas and experiences.
[2]. See here for more elaboration:
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