Hilbert's axioms

Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie[1][2][3][4] (tr. The Foundations of Geometry) as the foundation for a modern treatment of Euclidean geometry. Other well-known modern axiomatizations of Euclidean geometry are those of Alfred Tarski and of George Birkhoff.

  1. ^ Sommer, Julius (1900). "Review: Grundlagen der Geometrie, Teubner, 1899" (PDF). Bull. Amer. Math. Soc. 6 (7): 287–299. doi:10.1090/s0002-9904-1900-00719-1.
  2. ^ Poincaré, Henri (1903). "Poincaré's review of Hilbert's "Foundations of Geometry", translated by E. V. Huntington" (PDF). Bull. Amer. Math. Soc. 10: 1–23. doi:10.1090/S0002-9904-1903-01061-1.
  3. ^ Schweitzer, Arthur Richard (1909). "Review: Grundlagen der Geometrie, Third edition, Teubner, 1909" (PDF). Bull. Amer. Math. Soc. 15 (10): 510–511. doi:10.1090/s0002-9904-1909-01814-2.
  4. ^ Gronwall, T. H. (1919). "Review: Grundlagen der Geometrie, Fourth edition, Teubner, 1913" (PDF). Bull. Amer. Math. Soc. 20 (6): 325–326. doi:10.1090/S0002-9904-1914-02492-9.