Human capital is embodied in people of different generations whose lifetimes are finite. We show that the finiteness of people's lives precludes human capital accumulation from driving long-run aggregate economic growth unless sufficiently strong externalities from aggregate human capital are introduced. Two possible channels for carrying forward such externalities are (i) knowledge spillovers and (ii) public education spending. Our findings shed new light on the foundations of the Uzawa–Lucas growth model. We also show that the cross-sectional Mincer equation, generated by a linear human capital accumulation equation at the individual level, does not carry forward to aggregate data.