>I’m ashamed to admit, but I have an engineering background and I never "noticed" that approach in my studies. Are there more axioms in engineering than in math?

Well, probably one more, 2+2=4 +/- 0.002 :)

I know some engeneers, and knew some engineering students, and used some of their textbooks - that's where I noticed this sort of approach. Of course it's not a rule. I've even known one economist who was a hell of a programmer.

But then I'm also not saying all mathematicians make good programmers. I've known some colleagues who were learning differential geometry or function theory not really trying to understand the under-the-hood stuff. I'm actually amazed they eventually graduated :)