The Stern-Gerlach experiment is notoriously counter-intuitive. The official explanation has it that the spin remains always aligned with the magnetic field such that the directions of space would be quantized: A fermion can only have its spin up or down. But that theory is based on several blatant mathematical errors in the way it (mis)treats spinors and group theory. We present here a mathematically rigorous theory for a fermion in a magnetic field, which is all but beyond human intuition. It is based on an understanding of spinors in SU(2) which as explained in [1] is only Euclidean geometry. Contrary to what everybody has been reading into the Stern-Gerlach experiment , the directions of space are not quantized. The energy V = −µ·B is a statistical average. It is not a potential energy and it is not valid for individual fermions.