The cortical surface of the human brain can be reconstruction from magnetic resonance imaging (MRI) scans. This surface is where the majority of the functional processing of the human brain occurs. As a result, neuroscientists are interested in 2D, surface-based analysis tools for localizing and analyzing brain function with anatomy. Using results from the Riemann Mapping Theorem, and recent results from the area of Circle Packings, I will show how we are creating discrete, quasi-conformal "flat" maps of the cortical surface. I will discuss the method of circle packing, show examples of brain maps that we have created in the Euclidean, hyperbolic and spherical geometries and describe some of the mathematical and computational challenges involved in reconstructing cortical surfaces and defining coordinate systems on cortical regions which have been implicated in depression and schizophrenia.