  The theory of hole superconductivity explains high temperature
superconductivity in cuprates as driven by pairing of hole carriers in oxygen
$p\pi$ orbitals in the highly negatively charged $Cu-O$ planes. The pairing
mechanism is hole undressing and is Coulomb-interaction driven. We propose that
the planes of $B$ atoms in $Mg B_2$ are akin to the $Cu-O$ planes without $Cu$,
and that the recently observed high temperature superconductivity in $Mg B_2$
arises similarly from undressing of hole carriers in the planar boron $p_{x,y}$
orbitals in the negatively charged $B^-$ planes. Doping $Mg B_2$ with electrons
and with holes should mirror the behavior of underdoped and overdoped high
$T_c$ cuprates respectively. We discuss possible ways to achieve higher
transition temperatures in boron compounds based on this theory.
