Cortical layers seem to play a significant factor - wrinkles affect the surface area of the cortex, but layers seem to dictate the level of abstraction a species can comprehend - it's one of the biggest differences between reptiles, mammals, birds, and amphibians. While only mammals have a cortex, in other species, like birds, there are layered structures that can approximate cortical function. Animals that lack a layered cortex or analogous feature, or that have fewer layers in the structure, are demonstrably less intelligent. Birds have an advanced pallum, which is what gives them the edge over reptiles.

The last 4-5 years have been wonderful for neural biology.

Interestingly corvid brains are smooth.