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 t

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.