Modern mammals, birds, and reptiles (squamates, turtles and crocodiles) share their developmental and evolutionary origins in the ancestral, stem amniotes of 300 million years ago. This study explores how the brains of amniotes diverged in their neuronal composition. The systematic analysis of a large dataset on the cellular composition of the major parts of the brain of 242 amniote species shows that it is not the case that a general theme in amniote evolution is the proportional expansion of the telencephalon or pallium, for such expansion only happened in owls, in primates, and in the largest mammalian species. Instead, the brains of extant mammalian, avian, and reptile species are characterized by signature proportions of numbers of neurons across the brain divisions. Reptile brains, with few exceptions, are characterized by having fewer than 10 million neurons in each brain division, with about 1.5 neurons in the telencephalon and 0.5 neuron in the cerebellum to every neuron in the rest of brain. In contrast, the brains of the closely related birds are characterized by much larger numbers of neurons that occur at a higher, fixed proportion of 4.5 neurons in the cerebellum to every neuron in the rest of brain, with variable ratios of pallial neurons. The brains of mammalian species, in turn, are characterized by larger numbers of neurons that occur at an average 4 neurons in the cerebellum to every neuron in the pallium regardless of numbers of neurons in the rest of brain. There is a striking continuity in the scaling of the pallium (or telencephalon) of extant mammalian and squamate brains that argues for a quantitative continuum between the two groups and dispels the mistaken notion that mammalian brains evolved with a qualitative change or an addition of structures to the reptilian brain. The shared scaling rules between mammalian and squamate brain structures also allow for predicting the composition of early synapsid brains in amniote evolution.