Wolfgang Pauli, working at the University of Hamburg, seeks to explain the doublet structure of alkali spectra and the failure of Larmor's theorem in the anomalous Zeeman effect. He concludes that these anomalies are due to an additional quantum property of the electron, "of a classically non-describable kind of ambiguity" (in his own words), which adds a fourth quantum number to the three already known (principal, orbital, and magnetic). He then formulates the general principle: in an atom, two electrons can never share exactly the same four quantum numbers; if an energy level is completely non-degenerate, a single electron is enough to "close" it; any state contradicting this postulate must be excluded. Pauli does not propose in 1925 any physical interpretation for this fourth quantum number — indeed, when months later Uhlenbeck and Goudsmit propose the idea of electron spin as that physical interpretation, Pauli initially rejects it. The exclusion principle immediately explains the shell structure of atoms and, therefore, the entire logic of the periodic table, in addition to laying the foundation of what is today known as fermionic statistics (as opposed to bosonic statistics, which does not respect it). It is one of the founding pillars of modern quantum mechanics.