Hilbert's early work on the axiomatic method is an important part of the context of Zermelo's axiomatisation. Hilbert developed a particular version of the axiomatic approach to fundamental mathematical theories in his work on geometry in the period 1894–1904 (see Hallett and Majer 2004). This was to be seen as a distinct alternative to what Hilbert called the ‘genetic approach’ to mathematics. (For a short, historically informed description, see Felgner 2010: 169–174.) Ebbinghaus's book on Zermelo makes it very clear how embedded Zermelo was in the Hilbert foundational circle in the early years of the century.[8]  This is not meant to suggest that Zermelo adopted Hilbert's approach to the foundations of mathematics in all its aspects. Indeed, Zermelo developed his own, distinctive approach to foundational matters which was very different from Hilbert's, something which emerges quite clearly from his later work. Nevertheless, there are two elements of Zermelo's procedure which fit very well with Hilbert's foundational approach in the early part of the century. The first element concerns what might be called the programmatic element of Hilbert's treatment of the foundations of mathematics as it emerged in the later 1890s, and especially with regard to the notion of mathematical existence. And the second concerns proof analysis, a highly important part of Hilbert's work on Euclidean geometry and geometrical systems generally. These matters are intricate, and cannot be discussed adequately here (for fuller discussion, see both Hallett 2008 and 2010a). But it is important for understanding Zermelo's work fully that a rough account be given.