Mathematical Problems. David Hilbert

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       David Hilbert

      Mathematical Problems

      Published by Good Press, 2021

       [email protected]

      EAN 4064066449285

      Table of Contents

       Mathematical Problems

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

       1. Cantor's problem of the cardinal number of the continuum

       2. The compatibility of the arithmetical axioms

       3. The equality of two volumes of two tetrahedra of equal bases and equal altitudes

       4. Problem of the straight line as the shortest distance between two points

       5. Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group

       6. Mathematical treatment of the axioms of physics

       7. Irrationality and transcendence of certain numbers

       8. Problems of prime numbers

       9. Proof of the most general law of reciprocity in any number field

       10. Determination of the solvability of a diophantine equation

       11. Quadratic forms with any algebraic numerical coefficients

       12. Extension of Kroneker's theorem on abelian fields to any algebraic realm of rationality

       13. Impossibility of the solution of the general equation of the 7-th degree by means of functions of only two arguments

       14. Proof of the finiteness of certain complete systems of functions

       15. Rigorous foundation of Schubert's enumerative calculus

       16. Problem of the topology of algebraic curves and surfaces

       17. Expression of definite forms by squares

       18. Building up of space from congruent polyhedra

       19. Are the solutions of regular problems in the calculus of variations always necessarily analytic?

       20. The general problem of boundary values

       21. Proof of the existence of linear differential equations having a prescribed monodromic group

       22. Uniformization of analytic relations by means of automorphic functions

       23. Further development of the methods of the calculus of variations