  Following the death of Baron Lor\'{a}nd von E\"{o}tv\"{o}s in 1919, his
collaborators Desiderius Pek\'{a}r and Eugen Fekete co-authored a paper in 1922
containing the results of a series of earlier experiments testing the identity
of inertial and gravitational mass, the Weak Equivalence Principle (WEP).
Although the so-called "EPF" paper made no claim for any WEP violations, a
subsequent 1986 reanalysis of the EPF paper revealed a pattern in their data
suggesting the presence of a new ("fifth") force in nature. Although the EPF
data, and the 1986 reanalysis of these data, present fairly compelling evidence
for such a fifth force, many contemporary experiments have failed to detect its
presence. Here we summarize the key elements of this "E\"{o}tv\"{o}s paradox,"
and suggest some possible paths to a resolution. Along the way we also discuss
the close relationship between E\"{o}tv\"{o}s and Einstein, and consider how
their respective contributions may have been influenced by the other's.
