Husserl on Hilbert’s 1902 "Memoir" Mirja Hartimo

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Husserl on Hilbert’s 1902 “Memoir”

Mirja Hartimo

In Hilbert’s famous Paris list of problems, the fifth challenge was to formulate Lie’s concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group. To solve the problem Hilbert wrote a short memoir on the foundations of geometry ‘Über die Grundlagen der Geometrie’ during the winter 1901/02, and published as an appendix of the English translation of the Foundations of Geometry in 1902, and separately, in more detail, in Mathematische Annalen in 1903. In the memoir Hilbert partially solves the fifth problem using group theory, Cantor’s set theory and the notion of Jordan curve. (To distinguish the Memoir from Hilbert’s 1899 Grundlagen der Geometrie, I will call the 1903 published paper ‘Memoir’ and the 1899 foundations ‘Festschrift’.) Husserl took detailed notes on the Memoir which were published in Husserliana XXI. The objective of this paper is to explain Husserl’s interest in Hilbert’s Memoir. It will be argued that Husserl’s interest is a continuation of his long-standing concern about analytic geometry and in particular Riemann and Helmholtz’s approach to geometry. In his notes Husserl also displays understanding of group theoretical notions for the first time. Thus it may have motivated Husserl in his subsequent work on eidetic intuition.

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