What do mathematical concepts and mathematicians' names have to do with each other? Can deception and trickery serve the greater mathematical good? Do universal truths allow for insiders and outsiders? In the mid-1930s, a radical group of French mathematical reformers launched a project to build the conceptual foundations of mathematics anew. As a mark of their radicalism, they invented a shared mathematical name, Nicolas Bourbaki, a refugee from the invented country of Poldavia. Over rambunctious meals in a Princeton cafeteria, an early group of Bourbaki admirers concocted for him a countryman, Ersatz Stanislas Pondiczery. The two Poldavian impostors' impostures, committed in their names by a somewhat-shifting cast of conspirators, offer a window onto the conditions and compromises that made the mid-twentieth century such a dynamic period of transformation in mathematics, for better and for worse. Through their stories, I will examine the changing meaning of authorship and abstraction, the links between philanthropic and mathematical foundations, and the social, political, and intellectual consequences of pseudonymous mathematics in the 1930s and 1940s, including a published proof of the Riemann Hypothesis that captured the attention of the world's leading mathematicians in the 1950s and was never definitively refuted.