In the so-called island of inversion, for very neutron-rich nuclei, the N = 20 shell gap narrows appreciably, allowing the lowest (fp)2 configuration to compete with the normal sd-shell structure at low excitation. It is thought that this intruder could even dominate the ground state (gs) in some nuclei. Of course, this lowering of the fp shell into the low-excitation region is already well known for N ~ Z nuclei, but, perhaps not quite to the same extent. For example, in 38Ar, which has N = 20, the presence of three low-lying 0+ states in an excitation region where only one sd-shell 0+ exists has long been taken as evidence of excitations into the fp shall (see Ref. 1 and references therein). An important nucleus in this region is 32Mg, whose gs has been reported to possess several puzzling features. Here, we briefly review the history as it relates to 32Mg.