Hilbert's axioms

Other well-known modern axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff.

The original monograph, based on his own lectures, was organized and written by Hilbert for a memorial address given in 1899.

This translation incorporates several revisions and enlargements of the later German editions by Paul Bernays.

Other major contributions to the axiomatics of geometry were those of Moritz Pasch, Mario Pieri, Oswald Veblen, Edward Vermilye Huntington, Gilbert Robinson, and Henry George Forder.

Mathematics in the twentieth century evolved into a network of axiomatic formal systems.

A 2003 effort (Meikle and Fleuriot) to formalize the Grundlagen with a computer, though, found that some of Hilbert's proofs appear to rely on diagrams and geometric intuition, and as such revealed some potential ambiguities and omissions in his definitions.