  The importance of the Lieb-Simon proof of the relative exactness of
Thomas-Fermi theory in the large-Z limit to modern density functional theory
(DFT) is explored. The principle, that there is a specific semiclassical limit
in which functionals become local, implies that there exist well-defined
leading functional corrections to local approximations that become relatively
exact for the error in local approximations in this limit. It is argued that
this principle might be used to greatly improve the accuracy of the thousand or
so DFT calculations that are now published each week. A key question is how to
find the leading corrections to any local density approximation as this limit
is approached. These corrections have been explicitly derived in ridiculously
simple model systems to ridiculously high order, yielding ridiculously accurate
energies. Much analytic work is needed to use this principle to improve
realistic calculations of molecules and solids.
