  Understanding the origin and dynamics of hadron structure and in turn that of
atomic nuclei is a central goal of nuclear physics. This challenge entails the
questions of how does the roughly 1 GeV mass-scale that characterizes atomic
nuclei appear; why does it have the observed value; and, enigmatically, why are
the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD)
abnormally light in comparison? In this perspective, we provide an analysis of
the mass budget of the pion and proton in QCD; discuss the special role of the
kaon, which lies near the boundary between dominance of strong and Higgs
mass-generation mechanisms; and explain the need for a coherent effort in QCD
phenomenology and continuum calculations, in exa-scale computing as provided by
lattice QCD, and in experiments to make progress in understanding the origins
of hadron masses and the distribution of that mass within them. We compare the
unique capabilities foreseen at the electron-ion collider (EIC) with those at
the hadron-electron ring accelerator (HERA), the only previous electron-proton
collider; and describe five key experimental measurements, enabled by the EIC
and aimed at delivering fundamental insights that will generate concrete
answers to the questions of how mass and structure arise in the pion and kaon,
the Standard Model's NG modes, whose surprisingly low mass is critical to the
evolution of our Universe.
