Hilbert's axioms

Summary

Hilbert's axioms are the axiom system for Euclidean geometry that David Hilbert gave in his book Grundlagen der Geometrie of 1899. They speak of points, lines and planes and of the relations of incidence, betweenness and congruence, and they fall into five groups. They fill the gaps of Euclid's Elements. They made it possible to prove that geometry is consistent if the real numbers are. They also made it possible to prove the independence of single axioms, such as the parallel postulate.