This paper accounts for the intercontinental elaboration of French mathematician Laurent Schwartz’s theory of distributions in the years immediately following World War II by tracing how mathematicians explained the theory to each other, advanced new interpretations, and reconciled existing ones. Situating distributions in mathematicians’ changing contexts of funding, travel, and publication, especially in connection with the postwar reconstruction of international science, I argue that wordplay and suggestive comparisons—often termed “abuses of language”—helped tie communities of scholars together across disparate geographies and fields of study. Material limits and linguistic ambiguity, here, offered important resources for asserting relevance and unity in a fragmented and heterogeneous discipline. I show in particular how reinterpretations and puns of the calculus technique of integration by parts helped advocates of Schwartz’s theory create a far-reaching community of students and researchers that was itself partially integrated—with distributions’ scholars believing themselves to be using a common theory while understanding and using that theory in considerably different (if sometimes mutually recognizable) ways. If exponents of modern mathematical research and pedagogy tend to emphasize settled theories and stabilized innovations, the history of these activities demands a converse emphasis on the variable and ongoing labor required to reconcile techniques and concepts—a labor that often hinges on theories’ instability, pliability, and susceptibility to play.

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.