Unsolved Problems

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

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

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

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

Do smooth solutions to Navier-Stokes equations exist globally in 3D? Or do finite-time singularities occur?...