This paper explores German statistical discourse at a crucial moment when, especially after 1945, mathematically trained statisticians increasingly challenged the authority of then dominant social and economic statistics. Drawing on archival material of the German Statistical Association’s annual meetings and statistical textbooks, I argue that ‘mathematisation’ in statistics was a particular discourse in the language of contemporary statisticians. The first part of the paper utilises the idea of ‘boundary disputes’ (Gieryn 2001) to show how statisticians used the ‘mathematisation’ discourse to (re-)order knowledge within their discipline in intellectual (sampling theories, formulas) and institutional (education and training of statisticians) terms. Social statisticians (the ‘Frankfurt School’) defended their factual logic but struggled to keep their discipline ‘pure’ from advancements in probability theory. Mathematical statisticians (the ‘Munich School’), by contrast, translated ‘mathematisation’ into matters of methodical proficiency with the aim of expanding the epistemic authority of their field.

The main part will focus on how ‘mathematisation’ played out differently with regard to measurement issues, their cognitive boundaries and to claims for statistical objectivity. I will show how ‘Frankfurt’ statisticians defended an autonomous space for the social world essentially demanding the logical definition of elements to be counted; their ‘social arithmetic’ involved conceptual work, similar to that in contemporary social sciences. Social statistics were seen as a method of mass observation essential for the study of society precisely because of the diversity of individuals. By contrast, for mathematically trained statisticians, ‘mathematisation’ first and foremost helped to demarcate a space for statistical practice based on probability calculus which, other than ‘social arithmetic’, served as a unifying, overarching perspective that could be applied infinitely to any research field. The mathematical language thus functioned as a formula to foster agreement among all those who had mastered its procedures while excluding all those who did not. This language – almost entirely incomprehensible to Frankfurt social statisticians – helped set numerical ‘rules’ that established when and how judgments could be made on the basis of partial or uncertain information; a matter for which ‘Frankfurt’ statisticians had nothing but their ‘sure instincts’.