ESHS/HSS Annual Meeting

“Göttingen, we have a problem!” – Rethinking Listing and Institutionalization of Problems in Modern Mathematics

• In Event: Transformations of Mathematics in the 20th Century

English Abstract

The modernisation of mathematics is conventionally associated with major problems and the lists that assemble them. Yet, cloaked in epistemic neutrality, such lists rarely receive critical attention. Although the supposed objectivity of problems may signal the institutionalisation of modern mathematical epistemologies, problem lists are far from neutral “black boxes” (Latour); they function as agents that shape mathematical practice and generate the structural images (Corry) underpinning modern mathematical development. They embody the epistemic and social interests of programme-driven “list-makers” and institutional “list-keepers” (incl. their “archivists”), and they project an image of mathematics as a unified organism. As such, they not only model (challenging Mehrtens) the imagined anatomy and growth of mathematics but also organise the social and political geographies of the international mathematical community.
This paper unboxes the epistemic and social nature of problem lists during the early twentieth-century phase of Western mathematical modernisation, tracing their relations to parallel structures such as mathematical bibliography and institutionalised heuristic practices. It seeks to illuminate how different types of problems and problem lists, functioning as hybrid epistemic objects, participated in major transformations of modern mathematics in the early twentieth century Europe.

Author

• Jan Vrhovski, University of Edinburgh