Okay, 94 points and still no comments, I'll bite.<p>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 <i>calculation</i>, while code describes a superset of calculation, <i>computation</i>.<p>When we spend all our time working with the more expansive set, computation, we sometimes forget that calculation is in many ways less expressive and has fewer ways to express a thing. Many of the ideas in the article seem to be about getting over things we take for granted in computation, and understanding how to operate in the more limited framework offered by calculation, and/or understanding that even if things look kind of alike (what's a good word for this concept? a homoscript?) in computation vs. calculation they can be subtly different with a range of pitfalls.