i think mathematics is an extraordinarily powerful tool for making various models of reality but for that I credit the power of Fourier for providing a handy bridge between analog and digital (continuous and discrete) along with computing which provides a structured 2nd order logic methodology which can handle what 1st order could not, by sacrificing full provability. (True=False being perfectly valid in untyped Lambda calculus is my favorite example of that).
Could you build a universe-like thing with mathematics? Sure, just as you can also create a realistic cartoon or drawing, or make a movie that approximates reality. But it’s still not reality but a part of it and also not.