You can make easy parallels with "traditional" engineering fields. Very few electrical engineers understand Maxwell equations, and if they do, it is because of their extra-curricular curiousity. The one who needs to understand it is a scientist; all engineer does is applying it to solve concrete problems. At the opposite end of the spectrum is an alectrician, who does not know what Maxwell equations are and would not be able to read them if shown.
Similarly, the one proving a convergence of some algorithm or pushing some elements of the (algebraic) lattice theory is a computer scientist. At the other end of the spectrum are pogrammers, and softare enginners in between.
The issue of whether some activity is engineering is unfortunately confounded with accreditation. Even if you were to graduate from a non-accredited school, you can call yourself an engineer if you completed the coursework. However, I may not rely on you if others I respect --- the association giving accreditation to schools (remember accreditation is not from a divine body) does not back up your claims.
THe same is with the state: a consumer, or employer, may have extra confidence if you are licensed. However, if the FDA does not approve a product for disrtibution, that produce does not cease to be a drug (it may simply have side effects). An engineer not approved by the state is sill an enginner.
THe problem, therefore, is largely psychological and is easily solved: an licensed engineer can put that word, "licensed," on his business card. That's all.
The problem is also irrelevant: since mid-1980s it became popular for hotels to call janitors "engineers." I recall a toilet misfunctioning and, upon my report, the fron desk told me, "OK, I'll send an engineer right away." I remember chuckling to myself: when you cannot use the bathroom, the last thing you need is someone with a calculator making estimates and building a prototype of a new toilet. I needed a janitor, not an engineer! You will notice that we have no salespeople any longer: we have "sales asscotiates." Outsourced programmers, who are not asked any kind of advice and were intially referred to as "contract programmers," have become "consultants" --- just like those who advise senior management on the fate of the company. In our civil society, the "feel-good-about-yourself" approach makes everyone into a general.
“Very few electrical engineers understand Maxwell equations, and if they do, it is because of their extra-curricular curiousity. The one who needs to understand it is a scientist; all engineer does is applying it to solve concrete problems”
If an engineer were solving “concrete problems” he’d likely be a civil engineer, not an electrical engineer, in which case, I’d agree, maxwells equations would not be important.
(kiddin’ of course)