Don't you lump math in there, math is 99% human language. The symbol pushing you learned in HS is just advanced arithmetic. Math is more like legalese with some very loose additional notation than a formal language.
> In the particular cases being discussed, there's no ambiguity: "is a" means "member of" and "is the" means equals.
Yes, and fitting just those cases would result in a model that handled other cases incorrectly, because idioms inconsistent with that rule exist. (“Jodie is the bomb” has a meaning distinct from the individual words taken separately which is not stating a reflexive equivalency, for instance.)
Even before computers we created formal languages (mathematics, logic equations) precisely because human language is too often ambiguous.