The unreasonable effectiveness of mathematics - explained

Eons ago my peers used to puzzle over the unreasonable effectiveness of mathematics. Back in the 1960s an essay on the topic by Merci Cooper ended with this conclusion …

… The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve….

Why is it that the “the great book of the universe is written in the language of mathematics” (Galileo Galilei)?

In a recent In Our Time programme on Mathematics' Unintended Consequences I heard, from one guest, a personally persuasive explanation. It’s a fundamentally anthropic explanation that goes something like this:

1. Entities that can do mathematics arise as a consequence of natural selection.
2. Natural selection can only occur in regions of a universe that have interacting and persistent patterns (perhaps including recursion).
3. So a universe containing mathematicians will also be a pattern-based universe.
4. Mathematics is a process for describing and manipulating patterns.
5. Therefore mathematics is a language that can describe pattern-based universes, including our own.

I’m good with that.