Some juxtapositions are indeed funny, but on the whole the article's tone is quite apologetic. Secondly, I wonder what the author may think of programming languages. This said, the whole argument of comparing contradictory meanings of math terms becomes vacuous. Some of the examples quite plainly have nothing to do with mathematics. Or, turning again to the number story, consider the plain English The crowd was small in number.
Some terminological problems transcend barriers between sciences.
However, one does not need a microscope to convince oneself on inspection that neither of the two has a really simple structure. By the end of the last century the fact has been recognized in Mathematics. Thus, one may assume that the need for conscientiously accurate word usage has been recognized long ago by both scientist and pedagogs in Mathematics as much as in other sciences. Being the first to recognize the necessity of specifying the language, mathematicians may be expected to lead the effort of instilling this idea in the rest of the populace. If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.