Those without substantial mathematical training often take mathematics to mean just numbers and formulas (and possibly things that have to do with calculus). This article gives an excellent example of why this is not the case, in a way that people without mathematical training can approach, and be convinced. It is of course a great read to the mathematically trained as well.
D. Gale and L. S. Shapley, "College admissions and the stability of marriage." (1962)