A central component of the scientific record is the output of university professors publishing research papers in peer-reviewed scientific journals. But what research isn't being done due to the current inefficiencies of the scientific ecosystem? We apply a diverse array of computational and mathematical methods to begin to answer this question. First, we show how hierarchies in faculty hiring and retention shape the US academic ecosystem, quantifying the stark inequalities in faculty production, prestige, retention and gender across PhD-granting institutions in every field. Then, we will show the consequences of these inequalities on demographic diversity and knowledge production, examining why working at a more prestigious environment leads faculty to become more productive. Lastly, we present a model for scientific productivity based on a random walk, drawing from the results to suggest simple policy interventions to potentially foster more creative and risky science.