Significance Intelligence presents evolutionary biology with one of its greatest challenges. It has long been thought that species with relatively large brains for their body size are more intelligent. However, despite decades of research, the idea that brain size predicts cognitive abilities remains highly controversial; little experimental support exists for a relationship between brain size and the ability to solve novel problems. We presented 140 zoo-housed members of 39 mammalian carnivore species with a novel problem-solving task and found that the species’ relative brain sizes predicted problem-solving success. Our results provide important support for the claim that brain size reflects an animal’s problem-solving abilities and enhance our understanding of why larger brains evolved in some species.