The discussion centers on the feasibility of separating atoms into their subatomic particles, specifically electrons and quarks, with the consensus that while atoms can be split into protons and neutrons, the latter cannot be divided into quarks. Quarks were discovered through experiments like Deep Inelastic Scattering, which demonstrated their existence despite the inability to isolate them. The conversation highlights the importance of conserved quantities in physics, such as charge and lepton number, which guide theoretical predictions and experimental observations. These principles help scientists infer the existence of particles like quarks when discrepancies arise in expected outcomes. Overall, the dialogue emphasizes the complexity of atomic structure and the theoretical underpinnings that lead to our understanding of fundamental particles.