Although intense research effort is seeking to address which brain areas fire and connect to each other to produce complex behaviors in a few living primates, little is known about their evolution, and which brain areas or facets of cognition were favored by natural selection. By developing statistical tools to study the evolution of the brain cortex at the fine scale, we found that rapid cortical expansion in the prefrontal region took place early on during the evolution of primates. In anthropoids, fast-expanding cortical areas extended to the posterior parietal cortex. In Homo, further expansion affected the medial temporal lobe and the posteroinferior region of the parietal lobe. Collectively, the fast-expanding cortical areas in anthropoids are known to form a brain network producing mind reading abilities and other higher-order cognitive functions. These results indicate that pursuing complex cognition drove the evolution of Primate brains.