Why are rivers so mathematical?

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).

Rivers form fractal shapes just like how Iterated Function Systems[1] and L-systems[2] form: by simple branching, carried out at varying levels of scale. A gentle reminder that fractals are nature's favorite building block.

[1] https://en.wikipedia.org/wiki/Iterated_function_system

[2] https://en.wikipedia.org/wiki/L-system

This is backwards cause-effect

Mathematical axioms are derived from sensory experience in this physical reality

The math is actually river-like

"THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES" https://webhomes.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf