Comb a tennis ball flat and a tuft stands up somewhere. That sounds like a fact about hair rather than a theorem. In topology it is the statement that no everywhere nonzero exists on the 2-sphere, and it has a consequence for the planet.
Yes, always. The hairy ball theorem implies that somewhere on the surface of the Earth there is a point with . It follows from the shape of the sphere rather than from the weather, so no arrangement of winds anywhere can avoid it.
The hairy ball theorem states that no everywhere nonzero tangent vector field exists on the 2-sphere. In plainer terms, a sphere covered in hairs cannot be combed flat everywhere, and a has to appear somewhere.
The planetary version follows at once. Treating horizontal wind at the surface as a tangent vector field, the theorem implies that somewhere on the surface of the Earth there is a point with zero horizontal wind velocity.
Note how little the claim depends on. Nothing about pressure systems, oceans or seasons enters the argument, only the shape of the surface the field lives on.
The result also generalizes by dimension. The n-sphere has a nonzero tangent vector field if and only if n is odd, so the obstruction is specific to rather than to spheres in general.
wat. The planet always has one still point, by geometry rather than luck.
wat wat
A claim about today’s weather falls out of a fact about surfaces, with no measurements involved.
How do we know?
Wolfram MathWorld states the theorem, its consequence for horizontal wind, and the generalization to spheres of other dimensions.
What is still unknown
It guarantees that such a point exists, and says nothing about where it is or how long it stays there.
Learn something?
Where to next
Why is there always one point in the coffee that did not move?topology
What do you get if you cut a one-sided surface down the middle?topology
Which walk through a city turned out to be impossible?topology