Cantor's problem of the cardinal number of the continuum
The compatibility of the arithmetical axioms
The equality of two volumes of two tetrahedra of equal bases and equal altitudes
Determine how many natural numbers are  very, very, very large
Problem of the straight line as the shortest distance between two points
Lie's concept of a continuous group of transformations without the assumption of the differentiability of the functions defining the group
Whether there are enough small numbers to meet  the many demands made of them
Mathematical treatment of the axioms of physics
Proof of unjustness of  all governments
Irrationality and transcendence of certain numbers
Problems of prime numbers
Proof of the most general law of reciprocity in any number field
Inequality between eternal happiness and peanut butter  sandwiches
Determination of the solvability of a diophantine equation
Quadratic forms with any algebraic numerical coefficients
Equality of scary holidays and  end-of-year religious holidays
Extension of Kroneker's theorem on abelian fields to any algebraic realm of rationality
Impossibility of the solution of the general equation of the 7-th degree by means of functions of only two arguments
Proof of the finiteness of certain complete systems of functions
Rigorous foundation of Schubert's enumerative calculus
Equality of a sheet of  writing paper to a lazy dog
Problem of the topology of algebraic curves and surfaces
Expression of definite forms by squares
Building up of space from congruent polyhedra
Are the solutions of regular problems in the calculus of variations always necessarily analytic?
The general problem of boundary values
Proof of the existence of linear differential equations having a prescribed monodromic group
Likelihood of outragous things  happening given a large enough sample
Uniformization of analytic relations by means of automorphic functions
Further development of the methods of the calculus of variations
