Distributions in Postwar Mathematics

Abstract

Distributions in Postwar Mathematics examines the intertwined histories of French mathematician Laurent Schwartz’s theory of distributions and the American-hosted 1950 International Congress of Mathematicians in order to explain how mathematicians in the Second World War’s wake rebuilt a discipline newly capable of and dependent on intercontinental exchanges of people and texts. Schwartz’s theory, first formulated in 1944-1945, offered a new way to study differential equations for non-differentiable functions using topological vector spaces and an analogy to the basic calculus technique of integration by parts. Drawing on archives from three continents, Distributions in Postwar Mathematics shows how elite mathematicians joined with agents of government, philanthropic, and other institutions to foster a theory and a discipline across what would come to be called the First, Second, and Third Worlds. This account connects abstract theories to their communities of users, technologies of investigation and exposition, and social, political, and institutional contexts, casting mid-century mathematics as a heterogeneous enterprise sustained through a range of resource-intensive and partially integrated means of coordination.

Chapter 1 details European and North American mathematicians’ efforts from the turn of the century through World War II to organize their discipline across national and regional scales, refracted through the Americans’ two failed attempts to host interwar International Congresses of Mathematicians. These developments set the institutional and geopolitical background for Schwartz’s endeavors, discussed in chapter 2, to promote distributions between 1945 and 1949. Chapters 3 and 4 offer a close analysis of American mathematicians’ postwar struggles to organize the 1950 International Congress, tying their challenges to postwar reconstruction and the emerging Cold War. Both Schwartz and the ICM’s organizers, in their separate contexts, used shifting and ambivalent formulations of, respectively, techniques of mathematical analysis and ideals of internationalism, to coordinate a range of interests and entities across great distances. Chapter 5 then develops this account of coordination through polysemy and ambiguity into an explanation of distributions’ intercontinental presence following the 1950 Congress, linking the theory’s adoption and adaptation to postwar institutional configurations by tracing the theory to new venues in and beyond South America, North America, and Europe.