This is from the view of a software person or must be, because formal definitions of math, chemistry, physics, engineering, the English language, etc. have existed for centuries. There are entire college curricula, formal dictionaries, exact specifications for equations and how to apply them to basically all fields of engineering.

Like... other fields exist, this is incredibly myopic. What is specific to software is it is all language based, and the people making the tools happen to be familiar with it so they know how to train it, but that's about it.