Primates brains stand apart from other mammals due to frontal cortex shape changes. Highest evolutionary rates of brain shape change occur in Homo sapiens and Neanderthals. Catarrhine monkeys evolved brains faster than other mammals. Primate brain evolution features enlarging frontal cortex starting in early primates. Anthropoids show fast expansion in posterior parietal cortex alongside prefrontal. Homo genus adds expansion in medial temporal lobe and posteroinferior parietal lobe. Fast-expanding areas in anthropoids form network for theory of mind and higher cognition. Prefrontal cortex enlargement characterizes all primate brain evolution. Anthropoid fast-expansion zones cover 36% of endocast versus 19% in other mammals. Homo fast-expansion zones cover 41% of endocast. dmPFC expansion aids emotion management and understanding others in primates. PPC expansion links to decision-making and social cognition across primates. DMN-related areas underwent special selection in anthropoid evolution. Theory of mind emerges in catarrhines and strengthens in hominoids. Human DMN expands uniquely to include IFG, angular gyri, and MTL. Primate prefrontal cortex has granular layer and dense neurons absent in other mammals. Anthropoids have unusually high cortical neuron counts and more areas. Complex sociality and Machiavellian intelligence selected for DMN expansions. Human brain shows strongest covariation among cortical areas versus other primates. dmPFC-to-PPC connections develop strongest in humans.