The human brain contains multiple regions with distinct, often highly specialized functions, from recognizing faces to understanding language to thinking about what others are thinking. However, it remains unclear why the cortex exhibits this high degree of functional specialization in the first place. Here, we consider the case of face perception using artificial neural networks to test the hypothesis that functional segregation of face recognition in the brain reflects a computational optimization for the broader problem of visual recognition of faces and other visual categories. We find that networks trained on object recognition perform poorly on face recognition and vice versa and that networks optimized for both tasks spontaneously segregate themselves into separate systems for faces and objects. We then show functional segregation to varying degrees for other visual categories, revealing a widespread tendency for optimization (without built-in task-specific inductive biases) to lead to functional specialization in machines and, we conjecture, also brains.