  After more than 80 years from the seminal work of Weizs\"acker and the liquid
drop model of the atomic nucleus, deviations from experiments of mass models
($\sim$ MeV) are orders of magnitude larger than experimental errors
($\lesssim$ keV). Predicting the mass of atomic nuclei with precision is
extremely challenging. This is due to the non--trivial many--body interplay of
protons and neutrons in nuclei, and the complex nature of the nuclear strong
force. Statistical theory of learning will be used to provide bounds to the
prediction errors of model trained with a finite data set. These bounds are
validated with neural network calculations, and compared with state of the art
mass models. Therefore, it will be argued that the nuclear structure models
investigating ground state properties explore a system on the limit of the
knowledgeable, as defined by the statistical theory of learning.
