Recently, it has become commonplace to interpret major transitions and other patterns in the Palaeolithic archaeological record in terms of population size. Increases in cultural complexity are claimed to result from increases in population size; decreases in cultural complexity are suggested to be due to decreases in population size; and periods of no change are attributed to low numbers or frequent extirpation. In this paper, we argue that this approach is not defensible. We show that the available empirical evidence does not support the idea that cultural complexity in hunter-gatherers is governed by population size. Instead, ethnographic and archaeological data suggest that hunter-gatherer cultural complexity is most strongly influenced by environmental factors. Because all hominins were hunter-gatherers until the Holocene, this means using population size to interpret patterns in the Palaeolithic archaeological record is problematic. In future, the population size hypothesis should be viewed as one of several competing hypotheses and its predictions formally tested alongside those of its competitors.This article is part of the themed issue 'Major transitions in human evolution'.