>>107047369 (OP)
Without having watched her video and heard her argument, I would tend to disagree. Functional and logic programming seem much closer to doing math, to the point where programming in some languages, e.g. Coq, Lean, etc is *literally* doing math. Imperative and object-oriented programming in say, python or C feels quite different, but some of the same of reasoning is still there. Regardless, there are aspects of programming that bare a strong relation mathematics, but I wouldn't say therefore that programming *is* math.
I haven't studied linguistics in any detail but from bits I've picked up here and there I can't say it bore much similarity to programming at all.