Yes, because civil engineer = architect + math, what a good analogy (hint: no, it's not, until people that have studied civil engineering and not architecture start winning the Pritzker regularly).

Do you also think the difference between a doctor and a biomedical engineer is math?

P.S.: I agree with your first point, but the analogy you chose is really bad. Self-taught coder isn't to a software engineer what an architect is to a civil engineer.