Pipeline leaks in the natural gas industry present multifaceted challenges, encompassing not only diminished product volume but also environmental degradation and potential catastrophic events such as explosions. Addressing these challenges requires a comprehensive approach, including the development and implementation of effective detection systems. Previous efforts have focused on physical surveys and the utilization of acoustic systems and pressure sensors to detect leaks promptly. However, recent advancements in technology have spurred interest in mathematical and machine learning models as potential solutions. This study delves into the comparative analysis of mathematical and machine learning models for leak prediction in gas pipelines, aiming to discern the most effective approach. Specifically, an existing mathematical model, derived from the Weymouth equation, is plotted against a machine learning algorithm—a random forest regressor, to be precise. Through rigorous evaluation, encompassing statistical error metrics, sensitivity analysis, and economic considerations, the study sheds light on the relative efficacy of these models. Ultimately, the findings not only contribute to enhancing leak detection capabilities but also underscore the transformative potential of machine learning in addressing complex industrial challenges.