  Existence of the upper critical dimension d_{c2}=4 for the Anderson
transition is a rigorous consequence of the Bogoliubov theorem on
renormalizability of \phi^4 theory. For dimensions d\ge 4, one-parameter
scaling does not hold, and all existent numerical data should be reinterpreted.
These data are exhausted by results for d=4,5 from scaling in
quasi-one-dimensional systems, and results for d=4,5,6 from level statistics.
All these data are compatible with the theoretical scaling dependencies
obtained from self-consistent theory of localization by Vollhardt and Woelfle.
The critical discussion is given for a widespread point of view that
d_{c2}=\infty.
