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HIL-012

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Hilbert's 12th Problem: Extension of Kronecker-Weber Theorem

Extend the Kronecker-Weber theorem on abelian extensions of the rationals to any base number field....

Hilbert's 16th Problem: Topology of Algebraic Curves and Limit Cycles

Determine the maximum number and relative positions of limit cycles for polynomial vector fields of degree $n$, and investigate the topology of real a...

Hilbert's 6th Problem: Axiomatization of Physics

Develop a mathematical framework that axiomatizes physics, particularly mechanics, thermodynamics, and probability theory....

Hilbert's 13th Problem: Seventh Degree Equations

Prove that the general equation of the seventh degree cannot be solved using functions of only two variables....

Hilbert's 7th Problem: Transcendence of Certain Numbers

If $\alpha$ is algebraic and irrational, and $\beta$ is algebraic and irrational, is $\alpha^\beta$ transcendental?...

Hilbert's 9th Problem: Reciprocity Laws

Generalize the reciprocity law of number theory to arbitrary number fields....

Hilbert's 11th Problem: Quadratic Forms over Algebraic Number Fields

Extend the theory of quadratic forms with algebraic numerical coefficients....

Hilbert's 14th Problem: Finite Generation of Rings

Is the ring of invariants of a linear algebraic group acting on a polynomial ring always finitely generated?...

Hilbert's 15th Problem: Schubert's Enumerative Calculus

Rigorously justify Schubert's enumerative geometry....

Hilbert's 17th Problem: Expression of Definite Forms

Can every non-negative rational function be expressed as a sum of squares of rational functions?...

Hilbert's 18th Problem: Polyhedra and Space-Filling

Are there only finitely many essentially different space-filling convex polyhedra? Is there a polyhedron which tiles space but not in a lattice arrang...