> Learning a language is _not_ like learning math.

I disagree. As a mathematician, looking at the language learning problem from a very "structural" perspective helped me a lot to grasp languages much better. Unluckily, most language learning textbooks are written by people who are not very "mathematically-minded", thus making their method of teaching overly complicated for me.

PhD students in mathematics told me that my explanations of languages make so much more sense than how the foreign language is taught at the language course at the university. On the other hand, from people who are more "humanities-minded", I often get reactions that my way of explaining languages is deeply confusing and has no value.