Definition:Hilbert 23

Definition
The Hilbert 23 is a list of $23$ at-the-time unsolved problems in mathematics published by during $1900$.

They are as follows:

9: General Reciprocity Theorem in Algebraic Number Field
Find the most general law of the Reciprocity Theorem in any algebraic number field.

10: Algorithm to determine whether Polynomial Diophantine Equation has Integer Solution
There is no algorithm to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution.

11: Quadratic Forms with Algebraic Numerical Coefficients
Solving quadratic forms with algebraic numerical coefficients.

12: Extension of Kronecker-Weber Theorem to any base Number Field
Extend the Kronecker-Weber Theorem on abelian extensions of the rational numbers to any base number field.

13: Solution of 7th Degree Equations using Two Parameter Functions
Solve all 7th degree equations using functions of two parameters.

14: Proof of Finiteness of certain Complete Systems of Functions
Proof of the finiteness of certain complete systems of functions.

15: Rigorous foundation of Schubert's Enumerative Calculus
Rigorous foundation of Schubert's Enumerative Calculus.

16: Topology of Algebraic Curves and Surfaces
Topology of algebraic curves and surfaces.

17: Definite Rational Function as Quotient of Sums of Squares
Expression of definite rational function as quotient of sums of squares.

18a: Existence of Non-Regular Space-Filling Polyhedron
There exists a non-regular, space-filling polyhedron.

19: Solutions of Lagrangians are Analytic
Are the solutions of Lagrangians always analytic?

20: Existence of Solutions of Variational Problems with certain Boundary Conditions
Do all variational problems with certain boundary conditions have solutions?

21: Existence of Linear Differential Equation with prescribed Monodromic Group
Proof of the existence of linear differential equations having a prescribed monodromic group.

22: Uniformization of Analytic Relations by means of Automorphic Functions
Uniformization of analytic relations by means of automorphic functions.

23: Further Development of the Calculus of Variations
Further development of the calculus of variations.