But rivers have been mathematical for only something less than ~60 years, no? Mandelbrot's paper on the length of the coastline of Albion was in the mid 60s or so, and the math that made rivers mathematical (fractals, chaos theory) came after that (within my lifetime!).

Rivers are mathematical only because we have so improved our mathematics in recent times (when my parents were born, they were random and non-deterministic, mysterious).