  If light sterile neutrinos are needed to understand the neutrino puzzles, as
is currently indicated, a major theoretical challenge is to understand why its
mass is so small. It is a more serious problem than understanding the small
mass of the familiar neutrinos. We discuss a new way to solve this problem by
identifying the sterile neutrino as gauge neutral fermion propagating in the
bulk of a higher dimensional theory, with bulk size of order of a millimeter.
The smallness of its mass is then a consequence of the size of the extra
dimension and does not need the introduction of new symmetries. We present a
realistic model for neutrino masses and mixings that implements this idea.
