This research empirically establishes and interprets the hypothesis that the relationship between population aging and inventive activity is hump-shaped. We estimate a reduced form, hump-shaped relationship in a panel of 33 OECD countries over the period 1960–2012, as well as in a panel of 248 NUTS 2 regions in Europe over the period 2001–2012. The increasing part of the hump may be associated with various channels including the acknowledgement that population aging requires inventive activity to guarantee current and future standards of living, or the observation that older educated workers are more innovative than their young peers. The decreasing part may reflect the tendency of aging societies to lose dynamism and the willingness to take risks.