That's a little extreme. I think most computations are best¹ written in a way that is amenable to mathematical treatment, and most of the useful ones can be. Just because a counter-example exists doesn't mean we should give up hope.
I find constructing programs mathematically makes life easier in the common case and possible in nearly all others, unless you insist on things like proof-of-termination for programs which do not (I do not.)
1. 'best' because it gives us the means to reason about the code, and we know what kind of transformations we can perform on it, and do them abstractly without having to simulate it, potentially for infinite inputs, etc., etc. You know the drill.
I find constructing programs mathematically makes life easier in the common case and possible in nearly all others, unless you insist on things like proof-of-termination for programs which do not (I do not.)
1. 'best' because it gives us the means to reason about the code, and we know what kind of transformations we can perform on it, and do them abstractly without having to simulate it, potentially for infinite inputs, etc., etc. You know the drill.