Sure, and I'm not claiming that you must unify them. Or that you can't. I'm also not saying that the language of mathematics is a formal language, but instead that it shares structure with them. The very notion of the interplay between a theory and its model is not dissimilar.
I'm not trying to absolve a cultural gap. Nor am I trying to claim that if you dropped a mathematician into a programming role they would thrive, or visa versa.
I'm simply trying to claim that there is a whole lot of similarity between the two and refutations of that are silly. Seeking a clear-cut demarcation between fields is a little silly as an exercise.
Finally, exploiting the similarity is powerful. Both fields benefit from this fact already and the more widespread the idea is the better.
I'm not trying to absolve a cultural gap. Nor am I trying to claim that if you dropped a mathematician into a programming role they would thrive, or visa versa.
I'm simply trying to claim that there is a whole lot of similarity between the two and refutations of that are silly. Seeking a clear-cut demarcation between fields is a little silly as an exercise.
Finally, exploiting the similarity is powerful. Both fields benefit from this fact already and the more widespread the idea is the better.