Clinical scoring tables serve as structured frameworks for interpreting patient data, much like physicists rely on physical laws. However, unlike universal physical laws, healthcare knowledge is cohort-specific. Observation on one population may not apply to another. More than predictive tools, clinical scoring tables act as lenses for discovering new medical knowledge. To enhance these frameworks while preserving interpretability, we introduce LENS (Learning and Evolving Numerical Scores), a machine learning (ML) framework that fine-tunes established scoring tables while maintaining their familiar structure. LENS iteratively refines scoring components in a controlled manner, improving predictive accuracy without compromising usability or trust. Unlike traditional ML models that replace scoring tables, LENS adapts them based on cohort-specific insights. A key advantage of LENS is its ability to uncover new clinical patterns. For example, if LENS decreases a variable’s weight, it suggests reduced significance in a given cohort, while an increased weight indicates a shifting clinical focus. By systematically analyzing these refinements, clinicians can refine their understanding of disease risk and prognosis to their specific cohort of interest. Evaluations across multiple clinical scores and datasets show that LENS enhances predictive performance across discrimination, calibration, and reclassification metrics while maintaining interpretability. This work highlights a novel approach to using ML to advance human knowledge by refining existing tools rather than replacing them.