Artificial intelligence (AI) can perform core research tasks such as generating research questions, processing data, and solving problems. We shift the focus from AI as a "worker" to ask whether, how, and when AI can also "manage" human workers who perform such tasks. Focusing on the context of crowd science, we find examples of algorithmic management (AM) in five key functions highlighted in prior organizational literature: task division and task allocation, direction, coordination, motivation, and supporting learning. These applications benefit from the instantaneous, comprehensive, and interactive capabilities of AI, and reflect several more general underlying functions such as matching, clustering, and forecasting. Quantitative comparisons show that projects using AM are larger and more likely to be associated with platforms than projects not using AM, pointing to potentially important contingency factors. We conclude by outlining an agenda for future research on algorithmic management in scientific research.