Related: the article "They Write the Right Stuff", about the software engineers who worked on the Space Shuttle [1].
In the United States, the National Council of Examiners for Engineering and Surveying (NCEES), which is the organization of engineering licensing boards in all states, recognizes Software Engineering as a discipline of Professional Engineering [2]. Our industry does not ordinarily require certification as a professional engineer, and it is not normally required by law; however, if you look at the topics that the certification exam covers [3] -- intended for people with 4 years minimum industry experience -- they are all ones that I'd expect senior software engineers to have down pat.
[1] https://www.fastcompany.com/28121/they-write-right-stuff
[2] https://ncees.org/engineering/pe/software/
[3] https://ncees.org/wp-content/uploads/2015/07/SWE-Apr-2013.pd...
Programming is a vague term that seems to simply refer to the act of using a descriptive and functional language to describe a problem set intended to be solved by a computer. But then how is that different from any other area of applied mathematics?
This ongoing debate seems needlessly pedantic. Someone will write some new academic paper, or book, or tweet which future generations will point back to and say "that was where the term computer humptyfucker came from to describe my job." A bunch of neckbeards will then buck the trend and start writing op-ed pieces about how we aren't humptyfuckers because we don't apply the rigidity that traditional certified and legal humptyfuckery requires.