Hairy Ball Theorem
Somewhere on the sphere must be a point or region to which hair is brushed creating a tuft or from which the hair is brushed away creating a bald patch.
More exactly the theorem states that on a sphere there does not exist an everywhere nonzero tangent vector field.
A result of this is that somewhere on the surface of the Earth, there is always somewhere a point with zero horizontal wind velocity.
It is however possible to comb the hair on a torus to be smooth all over.