Article ID: CBB044087153

David Hilbert and the foundations of the theory of plane area (2021)


This paper provides a detailed study of David Hilbert’s axiomatization of the theory of plane area, in the classical monograph Foundation of Geometry (1899). On the one hand, we offer a precise contextualization of this theory by considering it against its nineteenth-century geometrical background. Specifically, we examine some crucial steps in the emergence of the modern theory of geometrical equivalence. On the other hand, we analyze from a more conceptual perspective the significance of Hilbert’s theory of area for the foundational program pursued in Foundations. We argue that this theory played a fundamental role in the general attempt to provide a new independent basis for Euclidean geometry. Furthermore, we contend that our examination proves relevant for understanding the requirement of “purity of the method” in the tradition of modern synthetic geometry.

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Authors & Contributors
Hallett, Michael
Toepell, M.-M.
Gauthier, Yvon
Hilbert, David
Majer, Ulrich
Pejlare, Johanna
Historia Mathematica
Archive for History of Exact Sciences
Kwartalnik Historii Nauki i Techniki
Perspectives on Science
Journal for General Philosophy of Science
Intellectual History Review
Kluwer Academic
Walter de Gruyter
University of British Columbia (Canada)
Gangemi Editore
Birkhäuser Basel
Philosophy of mathematics
Hilbert, David
Kant, Immanuel
Schur, Friedrich Heinrich
Kronecker, Leopold
Brodén, Torsten
Riemann, Georg Friedrich Bernhard
Time Periods
19th century
20th century, early
18th century
20th century

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