I don't know. To me, any programmer looks a little insane, no matter of their motivation. Because how can you write code 5 days a week and stay alive?
I do program but I treat is a nessesary evil which has to be done to solve some issue I have. I won't be able to write a codebase which may or may not be deployed in a year
Just tell people you're a mathematician in a logician's role. They'll assume you're a maths teacher, doing amateur magic to make money.
Not most of the super programmers I have met, they have always seem like they are bit off to me.
coding as a job look normal? Right now they would look like an Indian engineer, kind of like me. So if that's not normal, then probably not.