So what is your opinion on pure math vs applied math, and how do you think it might play into determinism?
Pure mathematics is the study of viable language constructions where viable is defined as logical consistency and applied mathematics is the use of those constructions in external fields of study.
In the logical case, in order for a logical construction to be consistent it seems necessary that results logically determine other results and that all results have a logical pathway to initial assumptions/axioms.
More generally the law of causality has escaped the grasp of mathematicians as it relates to intersection between it and foundational axioms so I will not try to rectify this here as I have no satisfying answer.
In the case of systems application, applied mathematics allows us to model memory (both past and future) of systems and this is generally what we generally mean when we speak determinism in the context of physics.
Okay, thank you.