 In the following years, Giuseppe Peano gave a more superficial (but also more famous) treatment of the natural numbers, employing the new symbolic language of logic, and Gottlob Frege elaborated his own ideas, which however fell prey to the paradoxes. An important book inspired by the set-theoretic style of thinking was Hilbert’s Grundlagen der Geometrie (1899), which took the “mathematics of axioms” one step beyond Dedekind through a rich study of geometric systems motivated by questions concerning the independence of his axioms. Hilbert’s book made clear the new axiomatic methodology that had been shaping up in connection with the novel methods of set theory, and he combined it with the axiomatic trends coming from projective geometry.