It seems like you are talking about software engineering vs programming vs maths. While there are exceptions, I'm seeing that people, who were able to teach th

It seems like you are talking about software engineering vs programming vs maths. While there are exceptions, I'm seeing that people, who were able to teach themselves programming, make good software engineers lot, lot more frequent. Same for maths. The same for programmers with good understanding of fundamentals vs hobbyists who never tried to look at the basics. There are always exceptions, yes, but for me it looks like these exceptions are rare. But very often I see dissatisfied people who spent years of time and some good money but are unable to get any kind job/internship. They are not engineers and they did not become programmers either.