Editing Hilbert's problems (section)

== List of Hilbert's Problems ==

The following are the headers for Hilbert's 23 problems as they appeared in the 1902 translation in the [[Bulletin of the American Mathematical Society]].<ref name=Hilbert_1902/>

:1. [[Continuum hypothesis|Cantor's problem]] of the cardinal number of the continuum.
:2. The compatibility of the arithmetical axioms.
:3. The equality of the 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 (The "[[Riemann hypothesis|Riemann Hypothesis]]").
:9. Proof of the most general law of reciprocity in any number field.
:10. Determination of the solvability of a [[Diophantine equation]].
:11. [[Quadratic form]]s with any algebraic numerical coefficients
:12. Extensions of [[Kronecker's theorem]] on Abelian fields to any algebraic realm of rationality
:13. Impossibility of the solution of the general equation of 7th 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 calculus|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 (Boundary value problems in PD)
:21. Proof of the existence of linear differential equations having a prescribed [[monodromy]] group.
:22. Uniformization of analytic relations by means of [[Automorphic function|automorphic functions]].
:23. Further development of the methods of the calculus of variations.