Welcome to the website of the project “Purity and Abstraction in Modern Geometry: Historical and Philosophical Perspectives“, an FWF-funded research project at the University of Vienna (Project Number M 2803-G).

The aim of the project is to investigate a cluster of historical, philosophical, and mathematical problems in relation to a central program in modern axiomatic geometry, which aimed at the elimination of numbers from the foundations of geometry. Historically, the most influential instance of this research program is David Hilbert’s axiomatization of Euclidean geometry presented in Grundlagen der Geometrie (1899). Philosophically, the program aimed at providing a novel answer to an ancient problem in the philosophy of geometry, i.e., to define the role that numbers must play in the foundation of geometry. For details, see the Project description.

The project runs from February 2020 to January 2022 and is led by Dr. Eduardo N. Giovannini as the principal investigator.