The surface of the human brain is topologically equivalent to a sheet that has many folds that vary in their size, shape and extent across individuals. This variability makes it difficult to compare similarities and differences in the functional processing of the brain between subjects. As a result, there is great interest in trying to "unfold" and flatten the cortical surface so that the entire surface of the brain can be visualized. I will discuss a method that uses an area of mathematics called circle packings to produce maps of the cortical surface that are approximations to the conformal (angle-preserving) map. I will present examples of these maps and discuss some of the topological and computational difficulties that arise.