That is a good analogy, except programming languages are formal languages, not natural languages.

> they are readily mapped to mathematical models

With code we are not talking about something that is mapped to mathematical models. Code is not modelled by mathematics, it is defined by mathematics (denotational semantics and operational semantics).

"Code is math" is true in a theoretical sense. Practically, coding doesn't always feel like what is commonly thought of as "doing mathematics", but it is essentially mathematical.

https://en.wikipedia.org/wiki/Formal_language

https://en.wikipedia.org/wiki/Semantics_(computer_science)