Mathematical problems

About this eBook

Author

Hilbert, David, 1862-1943

Title

Mathematical Problems : Lecture delivered before the International Congress of Mathematicians at Paris in 1900

Original Publication

Lancaster & New York: The Macmillan Company, 1902.

Credits

Laura Natal Rodrigues (Images generously made available by The Internet Archive.)

Language

English

LoC Class

QA: Science: Mathematics

Subject

Mathematics

Category

Text

Project Gutenberg

eBook-No. 71655

Release Date

September 15, 2023

Copyright

Public domain in the USA.

Contents

1. 1.MATHEMATICAL PROBLEMS
2. 2.Untitled
3. 3.CONTENTS
4. 4.Untitled
5. 5.1. CANTOR'S PROBLEM OF THE CARDINAL NUMBER OF THE CONTINUUM.
6. 6.2. THE COMPATIBILITY OF THE ARITHMETICAL AXIOMS.
7. 7.3. THE EQUALITY OF THE VOLUMES OF TWO TETRAHEDRA OF EQUAL BASES AND EQUAL ALTITUDES.
8. 8.4. PROBLEM OF THE STRAIGHT LINE AS THE SHORTEST DISTANCE BETWEEN TWO POINTS.
9. 9.5. LIE'S CONCEPT OF A CONTINUOUS GROUP OF TRANSFORMATIONS WITHOUT THE ASSUMPTION OF THE DIFFERENTIABILITY OF THE FUNCTIONS DEFINING THE GROUP.
10. 10.6. MATHEMATICAL TREATMENT OF THE AXIOMS OF PHYSICS.
11. 11.7. IRRATIONALITY AND TRANSCENDENCE OF CERTAIN NUMBERS.
12. 12.8. PROBLEMS OF PRIME NUMBERS.
13. 13.9. PROOF OF THE MOST GENERAL LAW OF RECIPROCITY IN ANY NUMBER FIELD.
14. 14.10. DETERMINATION OF THE SOLVABILITY OF A DIOPHANTINE EQUATION.
15. 15.11. QUADRATIC FORMS WITH ANY ALGEBRAIC NUMERICAL COEFFICIENTS.
16. 16.12. EXTENSION OF KRONECKER'S THEOREM ON ABELIAN FIELDS TO ANY ALGEBRAIC REALM OF RATIONALITY.
17. 17.13. IMPOSSIBILITY OF THE SOLUTION OF THE GENERAL EQUATION OF THE 7TH DEGREE BY MEANS OF FUNCTIONS OF ONLY TWO ARGUMENTS.
18. 18.14. PROOF OF THE FINITENESS OF CERTAIN COMPLETE SYSTEMS OF FUNCTIONS.
19. 19.15. RIGOROUS FOUNDATION OF SCHUBERT'S ENUMERATIVE CALCULUS.
20. 20.16. PROBLEM OF THE TOPOLOGY OF ALGEBRAIC CURVES AND SURFACES.
21. 21.17. EXPRESSION OF DEFINITE FORMS BY SQUARES.
22. 22.18. BUILDING UP OF SPACE FROM CONGRUENT POLYHEDRA.
23. 23.19. ARE THE SOLUTIONS OF REGULAR PROBLEMS IN THE CALCULUS OF VARIATIONS ALWAYS NECESSARILY ANALYTIC?
24. 24.20. THE GENERAL PROBLEM OF BOUNDARY VALVES.
25. 25.21. PROOF OF THE EXISTENCE OF LINEAR DIFFERENTIAL EQUATIONS HAVING A PRESCRIBED MONODROMIC GROUP.
26. 26.22. UNIFORMIZATIOM OF ANALYTIC RELATION'S BY MEANS OF AUTOMORPHIC FUNCTIONS.
27. 27.23. FURTHER DEVELOPMENT OF THE METHODS OF THE CALCULUS OF VARIATIONS.

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