  This article presents several challenges to nuclear many-body theory and our
understanding of the stability of nuclear matte r. In order to achieve this, we
present five different cases, starting with an idealized toy model. These cases
expose problems that need to be understood in order to match recent advances in
nuclear theory with current experimental programs in low-energy nuclear
physics. In particular, we focus on our current understanding, or lack thereof,
of many-body forces, and how they evolve as functions of the number of
particles . We provide examples of discrepancies between theory and experiment
and outline some selected perspectives for future research directions.
