Math, the hash function use magic numbers which in turn initialize and eventually map to a specific Galois Field, they are also called finite fields.

You have a set field size as you go over it, it loops and so output fields are never unique, you have a 1:infinite relationship. That property to determinism, there are problems computers cannot solve but we can. A computer requires determinism to do work, which in effect is that 1:1 state->next state mapping on the state graph. There's a lot of computer science theory and literature on this if you want to dig deeper. MIT has an OCW course in signals and systems.

Anywhere you see modulus math happening, its working with finite fields.