appeared in: Amer. Math. Monthly, 107(2000), 185-188. Cake-Cutting Algorithms: Be Fair If You Can. By Jack Robertson and

As I grow older, I find myself yearning more and more for a connection between my work and the complex problems facing the world. And unlike most people, I am in a profession where I have the flexibility to choose what I do. Should this yearning influence the kind of research that I pursue? Should it affect how and what I teach my students? At the very least I should vigilantly ponder these questions. Because of this yearning, I have taken up the challenge of a problem motivated by the social sciences—the problem of fair division. Mathematically, it is a very rich subject with many applications and a variety of open questions, ranging from very deep problems to accessible ones that my undergraduates can pursue. A very nice survey of the subject can be found in Cake-Cutting Algorithms, by Jack Robertson and William Webb. The basic question—how to cut a cake fairly?—is surely an ancient one. However, Robertson and Webb’s book demonstrates that the subject has evolved considerably in the fifty years since Steinhaus [10] first posed the question as a serious mathematical endeavor. Now much more than a collection of ad hoc results, the subject has matured, exhibited fertile connections with many areas of mathematics, and proved itself practical in social applications [4], [8]. The question is loaded with terms that must be made precise. In today’s theory, “cake” could mean any desirable set of goods (or burdens, or mixtures of goods and burdens), each with various properties (such as being divisible or indivisible) and restrictions (such as the number of goods a player may get). The word “cut” refers to kinds of divisions that can be carried out in practice, such as discrete procedures or continuous moving-knife schemes for real cakes, and compensation procedures for the division of estates (using money as a