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Lecture delivered before the International Congress of Mathematicians at Paris in 1900 and subsequently published in the Bulletin of the American Mathematical Society Vol. 8 (1902), 479-481.

2Foundations of Geometry

By David Hilbert

The German mathematician David Hilbert was one of the most influential mathematicians of the 19th/early 20th century. Hilbert's 20 axioms were first proposed by him in 1899 in his book <em>Grundlagen der Geometrie</em> as the foundation for a modern treatment of Euclidean geometry. <br><br> Hilbert's axiom system is constructed with six primitive notions: the three primitive terms <em>point, line</em>, and <em>plane</em>, and the three primitive relations <em>Betweenness</em> (a ternary relation linking points), <em>Lies on</em> (or Containment, three binary relations between the primitive terms), and <em>Congruence</em> (two binary relations, one linking line segments and one linking angles).<br><br> The original monograph in German was based on Hilbert's own lectures and was organized by himself for a memorial address given in 1899. This was quickly followed by a French translation with changes made by Hilbert; an authorized English translation was made by E.J. Townsend in 1902. This translation - from which this audiobook has been read - already incorporated the changes made in the French translation and so is considered to be a translation of the 2nd edition.