  We discuss the content and significance of John von Neumann's quantum ergodic
theorem (QET) of 1929, a strong result arising from the mere mathematical
structure of quantum mechanics. The QET is a precise formulation of what we
call normal typicality, i.e., the statement that, for typical large systems,
every initial wave function $\psi_0$ from an energy shell is "normal": it
evolves in such a way that $|\psi_t> <\psi_t|$ is, for most $t$,
macroscopically equivalent to the micro-canonical density matrix. The QET has
been mostly forgotten after it was criticized as a dynamically vacuous
statement in several papers in the 1950s. However, we point out that this
criticism does not apply to the actual QET, a correct statement of which does
not appear in these papers, but to a different (indeed weaker) statement.
Furthermore, we formulate a stronger statement of normal typicality, based on
the observation that the bound on the deviations from the average specified by
von Neumann is unnecessarily coarse and a much tighter (and more relevant)
bound actually follows from his proof.
