Why does mathematics describe nature so well?
Because nature contains nothing except the kind of thing mathematics is about. Take the world apart into its basic entries and each one is a rate, a count, a rank, a cost or a commitment, with no substance underneath. Distance is a count of comparisons between observers. Charge is the residue a loop of records carries home. The strength of electromagnetism comes out as the one number at which two readings of the same cell of an observer's record surface agree, so nobody chose it any more than anybody chose the square root of two. The world runs on rules acting on records, and the consequences of rules belong to nobody. A description built from such consequences fits because there is nothing else in the world for it to fit.
Also in Chapter 36: Why These Laws and Not Others?, Chapter 40: Does It Feel Like Anything, and What Is Left to Decide?, Chapter 12: Why Is the World Made of Relations and Not of Things?.
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 35: What Is Anything Made Of?watch a universe make its own particles