In the old days (i.e. just a few decades ago) candidates had to know a foreign language in order to become a PhD. Very sly students, like my macroeconomics professor, were able to maneuver through this requirement by convincing their superiors that mathematics is a language. Until I heard that story, I didn't know the idea was taken that seriously. Actually, I have never heard a mathematician or scientist argue otherwise. A quick Google search for the phrase "mathematics is not a language" as of this date returns a paltry 26 results, and even some of those are conditional. The opposite and more familiar statement returns 14,500 results. Saying that mathematics is a language sounds all nice and poetic, and it's possible for one to wax philosophically on the subject, but I'm not looking for philosophy or poetry here. Please no philosophizing in this thread. This is the math section. I'm looking for a mathematical argument showing that mathematics is a language. After all, if the proposition is true, then shouldn't it be possible to use mathematics to prove it? If it's not true, can we use mathematics to disprove it? Even if one could show that it couldn't be proved or disproved, one should still be able to state the proposition mathematically. Has that ever been done? I have never seen that little. Until the statement is formalized, I'm afraid the idea is pseudo-mathematics. Remember, please no philosophizing. Conjecture or postulate instead, if you must. I just request that you make it a mathematical argument.