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.
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1:
00 - Introduction
2:
01 - Cantor's Problem of the Cardinal Number of the Continuum
3:
02 - The Compatibility of the Arithmetical Axioms
4:
03 - The Equality of the Volumes of Two Tetrahedra of Equal Bases and Equal Altitudes
5:
04 - Problem of the Straight Line as the Shortest Distance Between Two Points
6:
05 - Lie's Concept of a Continuous Group of Transformations Without the Assumption of the Differentiability of the Functions Defining the Group
7:
06 - Mathematical Treatment of the Axioms of Physics
8:
07 - Irrationality and Transcendence of Certain Numbers
9:
08 - Problems of Prime Numbers
10:
09 - Problems 9 - 11
11:
10 - Extension of Kronecker's Theorem of Abelian Fields to Any Algebraic Realm of Rationality
12:
11 - Impossibility of the Solution of the General Equation of the 7th Degree by Means of Functions of Only Two Arguments
13:
12 - Proof of the Finiteness of Certain Complete Systems of Functions
14:
13 - Problems 15 and 16
15:
14 - Expression of Definite Forms by Squares
16:
15 - Building up of Space from Congruent Polyhedra
17:
16 - Are the Solutions of Regular Problems in the Calculus of Variations Always Necessarily Analytic?
18:
17 - The General Problem of Boundary Values
19:
18 - Proof of the Existence of Linear Differential Equations Having a Prescribed Monodromic Group
20:
19 - Uniformization of Analytic Relations by Means of Automorphic Functions
