>Math, physics, late night debugging sessions, repairing electronics/cars, overall hacking... Is this the skillset of an artist or a programmer?
Yes.
>Painting, playing instruments, creative writing, pottery... Is this the skillset of an artist or a programmer?
And yes.
To meet their goal they're each going to carry out a 1000 step process where everything builds on what went before (many many thousands of steps) and (regardless) too many false steps you are out.
A musician may have a piece memorized or may be using sheet music. They may have composed the piece or even be improvising as they go along. But one false step and people may say hey what a sour note.
Some notes more sour than others.
A programmer may implement a familar algorithm from memory or may be copying & pasting. They might have an appropriate one of their own or come up with something excellent as they go along. But one false step and people could say hey you've got a serious bug there.
Some bugs more offensive than others.
Depending on your gear at the time, different steps may or may not be automated or manually carried out.
There's not much room for error in a 1000 step process.
Obviously most people aren't cut out for it anyway.