My intuition is that there is some overlap between understanding language and symbolic mathematics (e.g. algebra). The rules of algebra are somewhat like grammar, and the step-by-step arguments get you something like a narrative. If one buys this premise, it might be worth training an AI to do algebra (solve for x, derive this equation, etc).
Moreover, when variables represent "real" numbers (as seen in physics, for example) algebraic equations describe the real world in an abstracted, "linear," way somewhat similar to natural language.
Finally, there are exercises in algebra, like simplifying, deriving useful equations, etcetera which edge into the realm of the subjective, yet it is still much more structured and consistent than language. It seems like this could be a stepping stone towards the ambiguities of natural language.
Can anyone speak to whether this has either (1) been explored or (2) is a totally bogus idea?