Eating a non-uniform cake together as friends can be difficult. Two people might want a single cherry, or someone might prefer to have no chocolate chips. Is it possible to cut up the cake in such a way that everyone is pleased?

The problem of cake eating is one example of a fair division problem. In this talk we will begin by describing some of the different types of fair division and transition to a more detailed explanation on problems of subjective preferences. We will then discuss a topological proof of the existence of a fair division which results in interesting extensions of well known theorems such as Sperner's lemma, Brouwer's fixed point theorem, and the KKM theorem.