The theorem of Hohenberg and Kohn and the works by and Lieb are beautiful mathematical treatments. Importantly, the basic concept that the ground-state electron density determines everything often enables decisive physical insight. The often misleading assumption is that the above laid out, exact algorithm "ρ(r) → ground-state energy (and even everything)" can be expressed in terms of a closed mathematical expression. Approximating the algorithm by a mathematical functional, i.e., by a DFA, suffers from the severe problem that the range of validity of this functional is typically unclear: We can test its accuracy only by comparing results with experiments or high-level wave-function theories. We trust the reliability for systems that we believe (!) are "similar" to the tested ones, but we don't know about the accuracy for untested systems. And the term "similar" is not even defined.