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We develop a quantitative framework for understanding the class of wicked problems that emerge at the intersections of natural, social, and technological complex systems. Wicked problems reflect our incomplete understanding of interdependent global systems and the systemic risk they pose; such problems escape solutions because they are often ill-defined, and thus mis-identified and under-appreciated by communities of problem-solvers. While there are well-documented benefits to tackling boundary-crossing problems from various viewpoints, the integration of diverse approaches can nevertheless contribute confusion around the collective understanding of the core concepts and feasible solutions. We explore this paradox by analyzing the development of both scholarly (social) and topical (cognitive) communities — two facets of knowledge production studies here that contribute towards the evolution of knowledge in and around a problem, termed a knowledge trajectory — associated with three wicked problems: deforestation, invasive species, and wildlife trade. We posit that saturation in the dynamics of social and cognitive diversity growth is an indicator of reduced uncertainty in the evolution of the comprehensive knowledge trajectory emerging around each wicked problem. Informed by comprehensive bibliometric data capturing both social and cognitive dimensions of each problem domain, we thereby develop a framework that assesses the stability of knowledge trajectory dynamics as an indicator of wickedness associated with conceptual and solution uncertainty. As such, our results identify wildlife trade as a wicked problem that may be difficult to address given recent instability in its knowledge trajectory.