Mechanisms and Machines: On the Continued Relevance of Mathematical Modeling in Biological Sciences
Keywords:
Biological systems, mathematical modeling, Machine learning, Deep learning, Modern Biological InferenceAbstract
Mathematical modeling has long provided mechanistic insight and predictive power across biological scales, from the structure and dynamics of biomolecules to neural activity and even up to population dynamics and epidemics. With the rise of machine learning and large-scale data, its continued relevance is sometimes questioned. We argue that mathematical models remain indispensable: they support interpretability, causal insight, and principled generalization beyond what is commonly attainable with purely data-driven methods. At the same time, modern machine learning increasingly embeds mathematical structure, through geometric and graph-based learning, topological data analysis, and physics-informed networks, showing that progress in data-driven approaches often relies on theoretical foundations rather than replacing them.
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