It is usually considered a paradox that the human brain, although smaller than elephant and cetacean brains, is the most cognitively able. The concept that humans are more encephalized than all other mammals appeared in the 1970s as a solution to that paradox: humans have a brain that is much larger than expected from their body mass. Such an "excess brain mass" would provide increased cognitive abilities across species, thus explaining our cognitive superiority. However, behind the paradox lies the assumption that large mammalian brains are scaled-up versions of smaller brains, always containing more neurons than smaller ones--an assumption that we have recently shown to be invalid. Here, it is proposed that the absolute number of neurons, irrespective of brain or body size, is a better predictor of cognitive ability--in which case, the cognitive superiority of humans would come as no paradox, surprise, or exception to evolutionary rules.