  We present the most precise constraints to date for the mass and age
distributions of single ultracool dwarfs in the solar neighborhood, based on an
updated volume-limited sample of 504 L, T, and Y dwarfs within 25 pc. We
develop a Monte Carlo approach using the $\langle V/V_{\rm max}\rangle$
statistic to correct for incompleteness and obtain a space density of
$(1.83_{-0.15}^{+0.16})\times10^{-2}$ pc$^{-3}$ for spectral types L0-Y2. We
calculate bolometric luminosities for our sample, using an updated
"super-magnitude" method for the faintest objects. We use our resulting
luminosity function and a likelihood-based population synthesis approach to
simultaneously constrain the mass and age distributions. We employ the fraction
of young L0-L7 dwarfs as a novel input for this analysis that is crucial for
constraining the age distribution. For a power-law mass function $\frac{dN}{dM}
\propto M^{-\alpha}$ we find $\alpha=0.58_{-0.20}^{+0.16}$, indicating an
increase in numbers toward lower masses, consistent with measurements in nearby
star-forming regions. For an exponential age distribution $b(t) \propto
e^{-\beta t}$ we find $\beta=-0.44\pm0.14$, i.e., a population with fewer old
objects than often assumed, which may reflect dynamical heating of the Galactic
plane as much as the historical brown dwarf birthrate. We compare our analysis
to Kirkpatrick et al. (2021), who used a similar volume-limited sample.
Although our mass function measurements are numerically consistent, their
assumption of a flat age distribution is disfavored by our analysis, and we
identify several important methodological differences between our two studies.
Our calculation of the age distribution of solar neighborhood brown dwarfs is
the first based on a volume-limited sample.
