Solving equations. The problems, techniques, and viewpoints are our legacy. One theme throughout this lecture is that classical and modern mathematics are tightly intertwined, that contemporary mathematics contributes real insight and techniques to understand traditional problems. This is a considerably expanded version of a lecture---intended for undergraduates---that I gave at both the University of Montreal and the University of Pennsylvania. I thank R.~Horn and H.~Wilf for valuable suggestions. A shorter version appeared in the {\it American Math.~Monthly}, {\bf 105}, Jan.~1998, pp.~1--21.}