A teacher's job is not to teach. It's to provide a space in which a student can learn. A focus is useful for this, but the focus doesn't need to be an abstract subject. It's a MacGuffin; it can be anything.
As I understand, classifying classes into "disciplines" is for the convenience of administrative systems, like university deans. This classification is not a law of the universe, nor of the human mind. One can imagine the negatives of fitting learning into hierarchical administrative models.
Donald E. Knuth lived two separate lives in the late 1950s. During daylight he ran down the visible and respectable lane of mathematics. During nighttime, he trod the unpaved road of computer programming and compiler writing. Both roads intersected! -- as Knuth discovered while reading Noam Chomsky's book Syntactic Structures on his honeymoon in 1961. "Chomsky theories fascinated me, because they were mathematical yet they could also be understood with my programmer's intuition. It was very curious because otherwise, as a mathematician, I was doing integrals or maybe was learning about Fermat's number theory, but I wasn't manipulating symbols the way I did when I was writing a compiler. With Chomsky, wow, I was actually doing mathematics and computer science simultaneously."
Which makes you wonder, what kind of person reads this stuff on the honeymoon.
I was always into computers and tech but never really programming.
I was a math major in college, however, and after graduating I started programming. The transition was almost seamless, I picked up programming really quickly, it was surprising to me how much the "ways of thinking" are alike.