Stop comparing spells: a defense of mechanistic reasoning in quantitative medicine

Mathematical methodology-spanning statistics, time series analysis, modeling, and AI-driven approaches-functions as a foundational language of biomedical research rather than a mere instrument, profoundly shaping the field by extracting structure from complex biological data. Yet as these methods grow more sophisticated, a quieter problem emerges: when the reasoning encoded in our methods is not made readable, scrutiny becomes harder-it grows more difficult to separate signal from artifact, mechanism from correlation, or insight from overfitting. The capacity for such distinctions is not lost to us; rather, the controls that data science has developed to enforce them are applied unevenly, and the expectation that quantitative methods remain legible to their users has eroded. We term this the "magicalization" of mathematics-the transformation of quantitative methods into oracular pronouncements accepted on faith or incantations rejected wholesale, rather than transparent arguments open to challenge. We treat this less as an accomplished verdict than as a tendency whose costs compound if current practice fails to correct it. This departs fundamentally from the vision of Poincaré and Wiener, who held that mathematics must function as a shared language sustaining dialogue between quantitative and domain experts. We readily concede that achieving operational understanding of mathematical constructs across disciplinary boundaries is inherently difficult; yet abandoning mutual intelligibility is neither scientifically sound nor methodologically neutral-it limits scrutiny and obstructs mechanistic understanding. We trace how magicalization manifests in clinical translation, black-box deployment, and research evaluation; identify its structural causes in complexity escalation, incentive misalignment, and disciplinary siloing; and argue that recovering mathematical interpretability serves as more than an academic luxury-it stands as a prerequisite for rigorous, mechanistically grounded biomedical science.