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Applying this new form of mathematics to study changes of physical phenomenon, Newton discovered that the concept of motion follows very strict mathematical laws; this essentially was the discovery of the laws of physics. The laws of physics have since then always come to us in the form of differential equations (or generalizations thereof).

To make a long story short, differential equations - or any abstractions thereof or of descriptive functions where the input and outputs reside in the same space - are the prototypical mathematical implementation (or 'mathematization') of the concept of determinism.

My question is, is anyone familiar with other forms of determinism which can definitively not be reduced to or be shown to be equivalent to differential equations in any sense, not even in principle?