Abstract

Zermelo’s research on set theory and the foundations of mathematics was concentrated in two periods: 1901 to 1910 and 1927 to 1935. They correspond to two specific periods of research on the foundations of mathematics by David Hilbert and his collaborators in Göttingen. In the first period Hilbert elaborated his early axiomatic program, and Zermelo’s work is clearly along the lines proposed by Hilbert, it is pro Hilbert. The second period falls into the time when Hilbert developed his proof-theory which was, because of its finitistic character, flatly rejected by Zermelo. His work at that time was contra Hilbert.