Mathematical Problems cover

Mathematical Problems

David Hilbert (1862-1943)

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
21. 20 - Problem 23 and Conclusion

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Summary

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.