Is the universe made of mathematics?
In a strong sense, yes. Max Tegmark proposed that physical reality is a mathematical structure, and OPH shares the instinct, holding that reality is a timeless structure in which time emerges. OPH adds what turns a structure into a world. A structure becomes a public world when finite observers inside it can read it, compare their records and repair the mismatches. Consistency belongs to descriptions, so a self-consistent world has to contain record-keepers who can get things wrong, and some of them eventually work out the rule and build the screen that computes them. Any solution of that self-reference requirement could be a universe, and each is sealed off from the others, since space, time and signals are all built inside a single solution. A structure that nobody inside can read stays a possibility with no public world in it.
Also in Chapter 2: Why Is There Anything Rather Than Nothing?, Chapter 37: Why Does the Loop Have No Beginning?.
This answer comes from OPH, Observer Patch Holography. OPH is a rigorous, consistent and complete description of the unified, self-creating computational Universe we inhabit. Its consistency is machine-checked: the fixed point at its core is constructed explicitly, and a theory with a model contains no contradiction.
To understand OPH and check every step yourself, start with the free book Reverse Engineering Reality. It builds the theory from the ground up, and the OPH Notebook answers your questions while you read.
read the free bookask the notebookor ask sage:read chapter 36: Why These Laws and Not Others?watch a universe make its own particles