Although intelligence should theoretically evolve to help animals solve specific types of problems posed by the environment, it is unclear which environmental challenges favour enhanced cognition, or how general intelligence evolves along with domain-specific cognitive abilities. The social intelligence hypothesis posits that big brains and great intelligence have evolved to cope with the labile behaviour of group mates. We have exploited the remarkable convergence in social complexity between cercopithecine primates and spotted hyaenas to test predictions of the social intelligence hypothesis in regard to both cognition and brain size. Behavioural data indicate that there has been considerable convergence between primates and hyaenas with respect to their social cognitive abilities. Moreover, compared with other hyaena species, spotted hyaenas have larger brains and expanded frontal cortex, as predicted by the social intelligence hypothesis. However, broader comparative study suggests that domain-general intelligence in carnivores probably did not evolve in response to selection pressures imposed specifically in the social domain. The cognitive buffer hypothesis, which suggests that general intelligence evolves to help animals cope with novel or changing environments, appears to offer a more robust explanation for general intelligence in carnivores than any hypothesis invoking selection pressures imposed strictly by sociality or foraging demands.