  The exotic Borromean nucleus $^{20}$Mg with $N$ = 8, located at the proton
drip-line provides a unique testing ground for nuclear forces and the evolution
of shell structure in the neutron-deficient region. We report on the first
observation of proton unbound resonances together with bound states in
$^{20}$Mg from the $^{20}$Mg($d$,$d'$) reaction performed at TRIUMF.
Phenomenological shell-model calculations offer a reasonable description.
However, our experimental results present a challenge for current
first-principles nuclear structure approaches and point to the need for
improved chiral forces and {\it ab initio} calculations. Furthermore, the
differential cross section of the first excited state is compared with
distorted-wave Born approximation calculations to deduce a neutron quadrupole
deformation parameter of $\beta_n$=0.46$\pm$0.21. This provides the first
indication of a possible weakening of the $N$ = 8 shell closure at the proton
drip-line.
