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 \cite{spinors} is only Euclidean geometry. Contrary to what everybody has been reading into the Stern-Gerlach experiment, the directions of space are not quantized. The new and corrected paradigm is that the fermions precess around the magnetic-field lines just like Einstein had conjectured, but that despite the presence of the many different possible angles $\theta$ between the spin axis ${\mathbf{s}}$ and the magnetic field ${\mathbf{B}}$, the electrons can only have two possible energies $m_{0}c^{2}\pm\mu B$. The values $\pm\mu B$ are at variance with the continuum of values $-\mu B \cos\theta$ Einstein had anticipated. He was wrongfooted by the surprising fact that the energy $V= -{\boldsymbol{\mu\cdot}}{\mathbf{B}}$ is a statistical average over a large ensemble of electrons distributed over the two energy states $\pm\mu B$, and as such not valid for individual fermions. The two states are devoid of potential energy, but they are stable, just like a precessing spinning top without friction in a gravitational field is stable. We also spell out the mathematically rigorous meaning of the spin-up and spin-down spinors. They represent left-handed and right-handed frames, such that everything is now intuitively clear.