Absolutely. Most of the code being produced around me is of the "When button X is clicked, send an XML message to service Y letting it know the contents of textbox Z."
I'm sure this can be modelled mathematically, but I'm not convinced this would help.
I'm not sure. The OP raise the fact the SQL is modeled after set theory. I happen to have learnt set theory a very long time ago, and to use SQL as much as any web developper around. Then I read a book about foundations of SQL, and found out it can and should be seen as an implementation of the set theory.
And you know what? It was like a revelation to me. It is incredibly helpful. And, by the way, it make me laughing inside each time I query MySQL (because MySQL is sadly /not/ a correct implementation, while PostgreSQL is). The "dots connecting" between set theory and SQL made also much clearer to me the NULL "mess" and why it has to be like that.
So, on this part I'd push the same way as the author, and would go as far as saying that doing correctly a "button X pushed -> notify API Y + persist the action to Z" simple glue code thing /is/ requiring a mental activity that (probably) uses the same parts of your brain as any mathematics and the use them the same way.
However I don't get why the author seem to be ranting against Test Driven Development. In my experience it is unrelated to how you model you data and interactions, except TDD will do exactly as the author is advocating: it will force you to write stateless atomic functions, to make them testable.
NB: From all I have read about mathematics on HN, it seems to me possible that we are not talking about the same thing. Maybe you and many other refer to some "sin a + sin b = cos sin ..." memorization exercise, and some multiple choice questions one have to check as fast as possible in order to get some good enough ranking.
I am talking about a teacher spending around 20 hours a week during several years in front of young people, telling them step by step how the world can be described, analyzed, understood with their brain. It started with: first predicate, there is something, at least one thing. Let's take this thing in your hand, and nothing else: you have a set. In your other hand let's take nothing: you hold now another set, the empty one. Then you have two different things. And on this the teacher built the set theory. (I was educated in France, when math were still on their pedestal).
"""I'm sure this can be modeled mathematically, but I'm not convinced this would help."""
Why would a mathematically modeled system of key-value observing would not help? For one, it would enable one to prove and examine all kinds of assumptions about the model working correctly.
I'm sure this can be modelled mathematically, but I'm not convinced this would help.