  The problem of constructing maximal equiangular tight frames or SICs was
raised by Zauner in 1998. Four years ago it was realized that the problem is
closely connected to a major open problem in number theory. We discuss why such
a connection was perhaps to be expected, and give a simplified sketch of some
developments that have taken place in the past four years. The aim, so far
unfulfilled, is to prove existence of SICs in an infinite sequence of
dimensions.
