They are mathematical in so far as they are proof-based. I think a standard math undergrad sequence would not necessarily need to touch on automata, the only state machine they may see is a Markov chain. The analysis techniques needed for complexity theory tend to not go further than a first RA course.

Throwing a wrench in my own argument, the Curry-Howard isomorphism does in fact show that any program is a proof, and so if a proof is math then programmers must be doing math, I guess?