Leading the crowd in open collaboration for discovery: The informational role of emotions under radical uncertainty

Open collaboration is increasingly used to advance scientific discovery, yet sustaining participation remains difficult when leadership is informal and problems are open-ended. We study projects from Polymath—a large-scale open collaborative initiative in which mathematicians jointly work on unsolved mathematical problems under conditions of extreme epistemic and social uncertainty. Drawing on public online discussion data from four Polymath projects and using computerized text analysis, we examine how leaders' emotional expressions facilitate continued participation. We find that leaders' emotional expressions are associated with higher crowd participation. This effect does not happen through emotional contagion but through cognitive inference. Participants interpret leaders' emotions as informational cues that help them contribute despite radical uncertainty. The relationship weakens when leaders' emotions are framed as questions rather than affirmative statements, suggesting that clarity in emotional signaling matters for sustaining participation. These findings show how emergent epistemic leadership operates as leaders shape collective inquiry not through formal coordination but by signaling meaning and direction through emotions.