At the upper end of spectrums, males outperform females in mathematical cognition (i.e., processing information relevant for understanding the physical world) and females outperform males in social cognition (i.e., processing information relevant for understanding the social world). To be precise, sex differences in thinking about physical problems are observed in top-tier scientific environments, whereas sex differences in thinking about social problems are observed under more interpersonal, empathetic circumstances. One idea is that these differences are due to biologically based cognitive capacities that would differ between males and females. Here we would like to challenge this view and argue that biologically based motive drives principally underlie disparity in mathematical and social ability between the sexes. These motive drives are produced by the sexually dimorphic neuroendocrine system, and presently we highlight the role of the gonadal hormone testosterone. Testosterone is omnipotent in all sex differences in brain and behaviour, first because this male type hormone by itself and by way of its metabolite, the female type hormone oestradiol, builds both male and female brains. Moreover, testosterone influences our motive drives in such a way that we want to understand the mechanical world and the hormone improves performance under highly challenging conditions. Finally, testosterone conveys no affiliative motives or motives to understand people as its affinity with sociality purely depends on sex, money or status. The largest hormonal difference between the sexes is observed for testosterone, thus the hormone's specific motivational properties may well explain sex differences in mathematical and social cognition.