  We present five open problems in the theory of vertex rings. They cover a
variety of different areas of research where vertex rings have been, or are
threatening to be, relevant. They have also been chosen because I personally
find them interesting, and because I think each of them has a chance (the title
of the paper notwithstanding!) of being solved. In each case we give some
explanatory background and motivation, sometimes including proofs of special
cases. Beyond vertex rings per se, the topics covered include connections to
real Lie theory, formal group laws, modular linear differential equations,
Pierce bundles, and genus 2 Siegel modular forms and the Moonshine Module.
