The text Grundlagen der Geometrie ( Foundations of Geometry ) was published by Hilbert in 1899 . It proposed a formal set , Hilbert 's axioms , instead of the traditional axioms of Euclid . The text Grundlagen der Geometrie ( tr . : Foundations of Geometry ) published by Hilbert in 1899 proposes a formal set , the Hilbert 's axioms , substituting the traditional axioms of Euclid .