Following our spring seminar exploring the foundational connections between mathematics and pharmaceutical sciences, this second lecture—“Mathematical path illuminating pharmacy: 2nd story”—dives deeper into advanced quantitative frameworks and systems-level modeling. While the first part focused on core receptor occupancy theories and basic enzyme kinetics, this presentation addresses the remaining critical challenges in modern pharmacokinetics and pharmacodynamics (PK/PD). Specifically, we examine the limitations of conventional Michaelis-Menten approximations and introduce modified modeling approaches for accurate in vitro-in vivo extrapolation (IVIVE). Furthermore, we discuss advanced Physiologically Based Pharmacokinetic (PBPK) models, the challenges of handling correlated covariates using Full Random Modeling (FREM), and the implementation of machine learning into PK/PD via Mixed Effect State Space (MESS) models. By bridging mathematical systems theory with clinical pharmacology, this session aims to provide a comprehensive perspective on precision medicine and data-driven drug development.