Naive set theory
Ernst Zermelo published a set theory in 1908. It uses axioms to define sets, and very much limits the ways in which sets can be made. Together with   Abraham Fraenkel he is one of the creators of Zermelo–Fraenkel set theory, the set theory that was used for the much of the 20th century. Because of Gödel's incompleteness theorems this can only be proved for finite sets, though.