Episode Synopsis "07 - Irrationality and Transcendence of Certain Numbers"

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More episodes of the podcast Mathematical Problems by David Hilbert

• 00 - Introduction
• 01 - Cantor's Problem of the Cardinal Number of the Continuum
• 02 - The Compatibility of the Arithmetical Axioms
• 03 - The Equality of the Volumes of Two Tetrahedra of Equal Bases and Equal Altitudes
• 04 - Problem of the Straight Line as the Shortest Distance Between Two Points
• 05 - Lie's Concept of a Continuous Group of Transformations Without the Assumption of the Differentiability of the Functions Defining the Group
• 06 - Mathematical Treatment of the Axioms of Physics
• 07 - Irrationality and Transcendence of Certain Numbers
• 08 - Problems of Prime Numbers
• 09 - Problems 9 - 11
• 10 - Extension of Kronecker's Theorem of Abelian Fields to Any Algebraic Realm of Rationality
• 11 - Impossibility of the Solution of the General Equation of the 7th Degree by Means of Functions of Only Two Arguments
• 12 - Proof of the Finiteness of Certain Complete Systems of Functions
• 13 - Problems 15 and 16
• 14 - Expression of Definite Forms by Squares
• 15 - Building up of Space from Congruent Polyhedra
• 16 - Are the Solutions of Regular Problems in the Calculus of Variations Always Necessarily Analytic?
• 17 - The General Problem of Boundary Values
• 18 - Proof of the Existence of Linear Differential Equations Having a Prescribed Monodromic Group
• 19 - Uniformization of Analytic Relations by Means of Automorphic Functions
• 20 - Problem 23 and Conclusion