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Here is my reasoning:

Physics supercedes, or at the very least, is parallel to math. Math is not something that produces meaningful results on its own. Math is merely abstracted physics; it's never really led the pack in terms of revolutionizing scientific knowledge. Any great math discovery seems to be paired with a great physics advancement. Therefore, the math was simply the language of the physics discovery itself. It was not a separate thing.

And with that said, the hypercube, as I understand it, is not a shape that exists. There may be some equations that point to more than 3 spatial parameters, such as the Kaluza-Klein, but I intuitively feel that this is misunderstood. This is an abstraction gone astray. It cannot mean 4 literal spatial dimensions.