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).
Mathematical axioms are derived from sensory experience in this physical reality
The math is actually river-like
* humans are still unsure of exactly how much detail reality contains, or even if it's a constant, but we can be sure that all observable natural phenominon adhear to the laws of nature at the finest level that exists, and so in another article about "electric rain" it is shown that each drop of water in a cloud has a charge and can be considered as a physical component of lightning, and if left undischarged goes on to corrode cars, or interact in unknown ways as it becomes part of a river, to which I suggest getting some much higher, much bigger math to figure it out. Or ask a fish.