  To understand the nature of supernovae and neutron star (NS) formation, as
well as binary stellar evolution and their interactions, it is important to
probe the distribution of NS masses. Until now, all double NS (DNS) systems
have been measured to have a mass ratio close to unity (q $\geq$ 0.91). Here we
report the measurement of the individual masses of the 4.07-day binary pulsar
J0453+1559 from measurements of the rate of advance of periastron and Shapiro
delay: The mass of the pulsar is 1.559(5) $M_{\odot}$ and that of its companion
is 1.174(4) $M_{\odot}$; q = 0.75. If this companion is also a neutron star
(NS), as indicated by the orbital eccentricity of the system (e=0.11), then its
mass is the smallest precisely measured for any such object. The pulsar has a
spin period of 45.7 ms and a spin derivative of 1.8616(7) x$10^-19$; from these
we derive a characteristic age of ~ 4.1 x $10^9$ years and a magnetic field of
~ 2.9 x $10^9$ G,i.e, this pulsar was mildly recycled by accretion of matter
from the progenitor of the companion star. This suggests that it was formed
with (very approximately) its current mass. Thus NSs form with a wide range of
masses, which is important for understanding their formation in supernovae. It
is also important for the search for gravitational waves released during a
NS-NS merger: it is now evident that we should not assume all DNS systems are
symmetric.
