Not sure how this study actually shows that mathematics is the same as or similar to natural language. I doubt very much that it is, in fact, though it's one of those bits of "common sense" that crops up all over the place. I've not yet decided how much damage might be done in K-12 mathematics education through this error, assuming it is one, but my instinct is to err on the side of caution here and not assume mathematical thinking operates similarly to linguistic thinking or that mathematics is like natural language. Absent a lot more evidence than this study seems to offer, I'm not moved.