The phrase “truly international” recurs significantly in the organisational paper trail of the 1950 International Congress of Mathematicians, hosted at Harvard University by the American Mathematical Society. The 1950 ICM was organised without the coordinating presence of an International Mathematical Union, whose formal postwar reconstitution was initially linked and then subtly dissociated from the 1950 Congress. Mathematicians negotiated what a “truly international” congresss would mean from a variety of perspectives, representing national communities and national institutions in a variety of capicities while doing so. My presentation will contrast how mathematicians spoke for nations and national institutions in these negotiations, what values they espoused, and how these affected the congress that transpired. I draw particular contrasts between the postures of mathematicians and their national institutions in comparatively central and peripheral countries, manifesting significant differences in access to information and in conditions of mobility.

This paper focuses on a scientific dispute between Georges-Henri Halphen (1844-1889), a French career military-man, and Hermann Schubert (1848-1911), a German high-school teacher based in Hamburg. Both men made key contributions to the emerging field of enumerative geometry throughout the 1870s, though one class of theorems caused much division between them. These theorems lay at the heart of Schubert’s landmark book Kalkül der abzählenden Geometrie (1879), wherein he developed a groundbreaking and much-acclaimed geometrical calculus.

Yet, Halphen held that those very theorems were all simultaneously refuted by an argument he had published in 1876, albeit only in French periodicals and in very concise notes.
The dispute initially unfolded within personal correspondences, with a few other actors playing important roles as mediators and arbiters: those included German leading mathematician Felix Klein (1849-1925) and the Danish geometer Hieronymous Zeuthen (1839-1920), widely recognized to be an expert in such questions. By 1880, however, the disagreement blew up in the open, with Halphen convincing Schubert to pen a retraction of his theorems for the Bulletin de la Société Mathématique de France and finally circulating his own arguments in full and outside France–in particular, via a memoir for Klein’s Mathematische Annalen.

Building on Halphen’s and Klein’s scientific archives and extant correspondences, I will retrace the international negotiation of mathematical (dis)agreement that took place during those months. I will stress the role played by a range of scientific institutions (societies, journals, and academies) and key leaders thereof in validating, diffusing, and safeguarding mathematical assertions.

In 1922 Bryn Mawr College hosted an international celebration for Charlotte Angas Scott, the first woman to direct a graduate program in mathematics. The guest list was a veritable who’s who of mathematicians in the United States. At the party, letters of congratulations poured in from Europe and Alfred North Whitehead made the transatlantic journey for the sole purpose of delivering the keynote address. Complementing the better known logistics of the International Congresses, details of this more intimate gathering embellish the landscape of international mathematics after World War I. In addition, the relative prominence of Bryn Mawr College helps to clarify the distinct situation for international exchange among women mathematicians in the early-twentieth century.