These von Neumann ordinals had, in effect, been developed before von Neumann's work. The fullest published theory, and closest to the modern account, is to be found in Mirimanoff's work published in 1917 and 1921 (see Mirimanoff 1917a,b, 1921), though he doesn't take the final step of identifying the sets he characterises with the ordinals (for an account of Mirimanoff's work, see Hallett 1984: 273–275). It is also clear that Russell, Grelling and Hessenberg were close to von Neumann's general set-theoretic definition of ordinals. But crucially Zermelo himself developed the von Neumann conception of ordinals in the years 1913–1916, (for a full account, see Hallett 1984: 277–280 and Ebbinghaus 2007: 133–134). Zermelo's idea was evidently well-known to the Göttingen mathematicians, and there is an account of it in Hilbert's lectures ‘Probleme der mathematischen Logik’ from 1920, pp. 12–15.[37]