75 Years of Mathematical Oncology

Mathematics has long provided a quantitative framework to interpret cancer biology and treatment. Driven by richer biological and clinical data, the field has evolved into a multidisciplinary and translational endeavor - giving rise to Mathematical Oncology. Yet, the field's strong interdisciplinarity obscures a comprehensive view of its evolution, as well as the boundaries between Mathematical Oncology and adjacent domains. Here, we address this gap through a comprehensive bibliometric analysis spanning 75 years of mathematical research in oncology. Using a manually curated corpus (~1,500 papers) and a large query-based dataset (~19,000 papers), we map the field's conceptual and collaborative development over time. Independent analyses reveal sustained growth, high impact, and pronounced interdisciplinarity, together with a gradual shift from fundamental cancer biology toward therapeutic modeling. This reorientation underpins the emergence of Mathematical Oncology as a distinct field, separate from Systems Biology and Pharmacokinetics / Pharmacodynamics. We show how diverse concepts interlace within Mathematical Oncology, bridging applied mathematics, optimal control, evolutionary theory, and imaging. Collectively, we demonstrate that Mathematical Oncology is not merely the application of mathematics to cancer, but the use of interpretable models integrating clinical, biological, and physical knowledge to improve screening, understand disease evolution, guide therapy, and strengthen forecasting.