Generative AI (genAI) has expanded the scope of artificial intelligence, raising both hopes and fears that it could rapidly change the structure of the economy, reduce employment in many occupations, and increase productivity. There remains great uncertainty, however, over both the time frame for the economic effects of genAI and the magnitude of its ultimate impact on the economy. In this paper, we assess genAI through the lens of productivity. Some new technologies, such as the lightbulb, temporarily raise productivity growth as adoption spreads, but the impact fades when the market saturates. Others, such as the electric dynamo, spur ongoing innovation and induce sustained growth in productivity. Such general-purpose technologies (GPTs) are defined by three characteristics: broad diffusion, the ability to spur knock-on innovations, and ongoing core innovation (Lipsey, Carlaw, and Bekar 2005). Another breed of technologies, inventions in the method of invention (IMIs), have longer-lasting impacts on productivity through increased R&D efficiency via observational, analytical, communicational, and organizational improvements (Whitehead 1925). We conclude that there are clear signs that genAI is both a GPT and an IMI and, thus, can be expected to have a sustained positive impact on productivity. However, the time frame for this increase to happen is lengthy.