if computer science were primary and mathematics emerged later, the distinguishing features of mathematics would be:
- systematic minimization of operational detail
- pursuit of invariant structure independent of representation
- explicit separation of syntax from semantics
- construction of theories where all permissible transformations are closed under a small set of axioms
- maximal generalization such that the same formal object applies across many computational regimes
- preference for proofs that eliminate reliance on procedural execution
- focus on completeness, consistency, decidability, and other global properties not tied to any particular computational model
in such a sequence, mathematics would appear as a discipline that abstracts away from machines, encodings, and resource bounds, producing structures that unify rather than implement. it would specialize in identifying the minimal information required for a property to hold, and in characterizing spaces of possible computations rather than any concrete computation itself.