> I think the difference here is, and I don't think this is a subject that has been thought about quite enough, is that mathematics typically describe calculation, while code describes a superset of calculation, computation.
This statement is correct, but probably not for the reason you think it is.
The set of math proofs is isomorphic to the set of programs that terminate [1].
There are useful non-terminating programs (operating systems, for example), but all of the useful CS theory lies in the common subset. Data structures can completely described in math, including mutable ones.
Comments
> I think the difference here is, and I don't think this is a subject that has been thought about quite enough, is that mathematics typically describe calculation, while code describes a superset of calculation, computation.
This statement is correct, but probably not for the reason you think it is.
The set of math proofs is isomorphic to the set of programs that terminate [1].
There are useful non-terminating programs (operating systems, for example), but all of the useful CS theory lies in the common subset. Data structures can completely described in math, including mutable ones.
[1] See the Curry-Howard isomorphism.