  In the early 1980s, Schwinger made seminal contributions to the semiclassical
theory of atoms. There had, of course, been earlier attempts at improving upon
the Thomas--Fermi model of the 1920s. Yet, a consistent derivation of the
leading and next-to-leading corrections to the formula for the total binding
energy of neutral atoms, $$-\frac{E}{e^2/a_0} = 0.768745Z^{7/3} -
\frac{1}{2}Z^2+0.269900Z^{5/3} + \cdots\,,$$ had not been accomplished before
Schwinger got interested in the matter; here, $Z$ is the atomic number and
$e^2/a_0$ is the Rydberg unit of energy. The corresponding improvements upon
the Thomas--Fermi density were next on his agenda with, perhaps, less
satisfactory results. Schwinger's work not only triggered extensive
investigations by mathematicians, who eventually convinced themselves that
Schwinger got it right, but also laid the ground, in passing, for later
refinements --- some of them very recent.
