My recent research deals with billiards in rational polygons. The elementary questions posed in this area are connected to many branches of modern mathematics. More broadly, we can motivate the problem as follows: Some natural phenomena are “chaotic” (i.e. unpredictable). These are often studied by statistical methods. Others are “integrable” (i.e. predictable and regular). Other phenomena fit somewhere in between. The polygonal billiard system, is a good model of intermediate behavior. As such it has been studied extensively in physics as well, in particular in connection to “quantum chaos.”