Earnshaw’s theorem states that a static configuration of electrical charges and/or ferromagnets cannot be stable.  A small displacement will cause them to collapse and stick together in contact. This theorem  challenges our understanding of the stability of ordinary matter, which only quantum mechanics including Fermions can address.

However, for diamagnetism it is possible to have a stable non-contact configuration of magnets.  You cannot appreciate this, unless you have worked long and hard to produce a stable configuration of ferromagnets.  In diamagnetism the external magnetic field produces a repulsive magnetic field in the target material.  So a magnetic well may be created to capture and suspend a diamagnet as shown to the left.  The four gold colored magnets alternate top north and south poles to create a strong magnetic field gradient that captures the pyrolytic carbon diamagnet.