  We present new spectroscopic observations of the detached late-type
double-lined eclipsing binary YY Gem, a member of the Castor sextuple system
and one of the benchmarks for the comparison between observations and stellar
evolution theory in the lower main-sequence. In addition, we have re-analyzed
existing light curves in several passbands using modern techniques that account
for the conspicuous presence of spots. This, combined with the spectroscopy,
has yielded a very precise determination of the absolute dimensions of the
components, which are virtually identical to each other. We obtain mean values
of M=0.5992+/-0.0047 Mo, R=0.6191+/-0.0057 Ro, and Teff=3820+/-100 K. Both the
mass and the radius determinations are good to better than 1%. A re-analysis of
the Hipparcos transit data for Castor AB has yielded an improved parallax for
the system of 66.90+/-0.63 mas. With this, we have estimated the age (~370 Myr)
and metal abundance ([Fe/H]~0.0) of YY Gem from isochrone fits to Castor A and
B. We have compared the observations of YY Gem with a large number of recent
theoretical calculations, and we show that all models underestimate the radius
by up to 20%, and most overestimate the effective temperature by 150 K or more.
Both of these trends are confirmed by observations of another similar system in
the Hyades cluster (V818 Tau). Consequently, theoretical ages for relatively
low-mass objects such as T Tauri stars derived from the H-R diagram may be
considerably biased. If the radius is used directly as a measure of evolution,
ages could be underestimated by as much as a factor of 10 in this mass regime.
In view of these discrepancies, absolute ages from essentially all current
models for the lower main sequence must be viewed with at least some measure of
skepticism. (abridged)
