There was an interesting discussion on HN last week that brought up the fact that mathematics has its own crises, namely a communication crises. It was brought up that the proofs can be so dense that errors will be published and go unchecked for a long time. The interesting part is that everything that's needed for "replication" is literally within the paper and the errors still fall through the cracks.
There is still an awful lot of engineering that is model-based without strong deductive proofs. (Mechanical failure theory comes to mind). But the actual origin of "profession" comes from professing an oath to the public good. Meaning the traditional professions (law, medicine, engineering) aren't necessarily aimed at creating new knowledge, but applying knowledge to the betterment (or profit) of society. Sometimes that butts up against problems without known solutions that requires adding knowledge to the field, but that's not really the primary goal, unlike something like mathematics.
There is still an awful lot of engineering that is model-based without strong deductive proofs. (Mechanical failure theory comes to mind). But the actual origin of "profession" comes from professing an oath to the public good. Meaning the traditional professions (law, medicine, engineering) aren't necessarily aimed at creating new knowledge, but applying knowledge to the betterment (or profit) of society. Sometimes that butts up against problems without known solutions that requires adding knowledge to the field, but that's not really the primary goal, unlike something like mathematics.