The geographic reach and international integration of modern mathematics expanded dramatically in the wake of the Second World War. I examine the political and logistical achievement of intercontinental mathematics in this period by following the travels of José Luis Massera of Uruguay, Leopoldo Nachbin of Brazil, and Laurent Schwartz of France. The interlocking efforts of mathematicians and bureaucrats in universities, governments, philanthropies, and new postwar formations like the United Nations Educational, Scientific and Cultural Organization to build mathematical institutions in Latin America operated with partial information, competing prerogatives, and costly exchanges of materials and personnel, each of which reflected the shifting economic and political constraints of the global Cold War. Drawing primarily on fellowship files and institutional archives, I situate these undertakings in the mechanics and ideals of twentieth-century scientific colonialism, development, and modernization. I explain how the seemingly nontechnical bases for such exchanges related to the specific mathematics being taught and researched by accounting for the particular success of Schwartz’s theory of distributions in Latin America, which owed both to circumstantial coincidences and to a mixture of several of the theory’s superficial, technical, and conceptual features. My analysis stresses the complex, ambivalent, but nonetheless consequential personal and institutional negotiations underwriting midcentury intercontinental mathematics while pointing to the importance of such phenomena for explaining the form and effects of the period’s broader array of global scientific exchanges.