ABSTRACT
We select 10 inequality problems that have appeared in the Monthly over the past half century. We will encounter many familiar characters, among them: Cauchy's inequality, L'Hôpital's monotone rule, Majorization and Convexity, Hilbert's identity, Hardy's inequality, and differential equations. What makes our trip worthwhile is the realization that these old chestnuts still have something new to tell us. They all appear here in novel and surprising ways and you should add them to your inequality tool box.
