PAC Learnability of nuclear masses

After more than 80 years from the seminal work of Weizs\"acker and the liquid drop model of the atomic nucleus, theoretical errors over nuclear masses ($\sim$ MeV) are order of magnitudes larger than experimental ones ($\lesssim$ keV). Predicting the mass of atomic nuclei is with precision is extremely challenging due to the non--trivial many--body interplay of protons and neutrons in nuclei, and the complex nature of the nuclear strong force. This paper argues that the arduous development of nuclear physics in the passed century is due to the exploration of a system on the limit of the knowledgeable, defined within the statistical theory of learning.