Foundations of Geometry

By David Hilbert

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Episodes: 42

Description

Discover the profound impact of the German mathematician David Hilbert, a towering figure in the landscape of mathematics during the 19th and early 20th centuries. In his groundbreaking work, Grundlagen der Geometrie, published in 1899, Hilbert introduced 20 axioms that laid the groundwork for a modern approach to Euclidean geometry. His innovative axiom system is built around six primitive notions, including the essential concepts of point, line, and plane, along with relations such as Betweenness, Lies on, and Congruence. This monograph, which was inspired by Hilberts own lectures for a memorial address, quickly gained traction through a French translation that incorporated his revisions. An authorized English version by E.J. Townsend followed in 1902, making this audiobook a significant resource as it reflects the insights and updates from both the original and French editions.

Episode Date
042 - Appendix
Mar 17, 2026
041 - Conclusion
Mar 16, 2026
040 - Criterion for the possibility of a geometrical construction by means of a straight-edge and a transf
Mar 15, 2026
039 - The representation of algebraic numbers and of integral rational functions as sums of squares
Mar 14, 2026
038 - Geometrical constructions by means of a straight-edge and a transferer of segments
Mar 13, 2026
037 - Analytic representation of the co-ordinates of points which can be so constructed
Mar 12, 2026
036 - The demonstation by means of the theorems of Pascal and Desargues
Mar 11, 2026
035 - Proof of the two propositions concerning Pascal's theorem Non-pascalian geometry
Mar 10, 2026
034 - The commutative law of multiplication for a non-archimedean number system
Mar 09, 2026
033 - The commutative law of multiplication for an archimedean number system
Mar 08, 2026
032 - Two theorems concerning the possibility of proving Pascal's theorem
Mar 07, 2026
031 - Significance of Desargues's theorem
Mar 06, 2026
030 - Construction of a geometry of space by aid of a desarguesian number system
Mar 05, 2026
029 - The totality of segments regarded as a complex number system
Mar 04, 2026
028 - Equation of straight line based upon the new algebra of segments
Mar 04, 2026
027 - The associative law of multiplication and the two distributive laws for the new algebra of segments
Mar 04, 2026
026 - The commutative and associative law of addition for our new algebra of segments
Mar 04, 2026
025 - Introduction to the algebra of segments based upon the Desargues's theorme
Mar 04, 2026
024 - The impossibility of demonstrating Desargues's theorem for the plane with the help of the axioms of
Mar 04, 2026
023 - Desargues's theorem and its demonstration for plane geometry by aid of the axiom of congruence
Mar 04, 2026
022 - Equality of content and the measure of area
Mar 04, 2026
021 - The measure of area of triangles and polygons
Mar 04, 2026
020 - Parallelograms and triangles having equal bases and equal altitudes
Mar 04, 2026
019 - Equal area and equal content of polygons
Mar 04, 2026
018 - Equations of straight lines and of planes
Mar 04, 2026
017 - Proportion and the theorems of similitude
Mar 04, 2026
016 - An algebra of segments based upon Pascal's theorem
Mar 04, 2026
015 - Demonstrations of Pascal's theorem
Mar 04, 2026
014 - Complex number-systems
Mar 04, 2026
013 - Independence of the axiom of continuity Non-archimedean geometry
Mar 04, 2026
012 - Independence of the axioms of congruence
Mar 04, 2026
011 - Independence of the axioms of parallels Non-euclidean geometry
Mar 04, 2026
010 - Compatibility of the axioms
Mar 04, 2026
009 - Group V Axiom of Continuity Archimedes's axiom
Mar 04, 2026
008 - Consequences of the axioms of congruence
Mar 04, 2026
007 - Group IV Axioms of congruence
Mar 04, 2026
006 - Group III Axioms of Parallels Euclid's axiom
Mar 04, 2026
005 - Consequences of the axioms of connection and order
Mar 04, 2026
004 - Group II Axioms of Order
Mar 04, 2026
003 - Group I Axioms of connection
Mar 04, 2026
002 - The elements of geometry and the five groups of axioms
Mar 04, 2026
001 - Preface Contents and Introduction
Mar 04, 2026