Understanding the dynamics of pre-earthquake seismicity is crucial for advancing earthquake forecast and risk assessment. In this paper, we embark on a mathematical exploration of pre-earthquake seismic activity, aiming to elucidate the underlying patterns and mechanisms leading up to major seismic events. Leveraging probabilistic modeling techniques, we analyze historical seismic data to identify precursory signals and assess their predictive value. Our investigation encompasses the study of foreshock activity, preceding earthquakes, shedding light on the temporal and spatial characteristics of seismic activity prior to the main shock events. Through mathematical modeling and simulation, we aim to unveil the complex interplay of factors contributing to pre-earthquake seismicity, with implications for enhancing earthquake forecasting capabilities and disaster preparedness efforts. This research contributes to the ongoing endeavor to unravel the mysteries of earthquake occurrence, ultimately striving towards a more resilient and proactive approach to seismic risk management. This study introduces a novel mathematical framework for analyzing pre-earthquake seismic activity, leveraging a 15-day foreshock window and machine learning techniques to predict seismic events. The approach addresses gaps in existing methodologies by incorporating comprehensive feature engineering and a robust random forest classification model. Additionally, we draw upon insights from prior studies, such as Kumazawa et al. (2020) and Luo et al. (2023), which emphasize the significance of spatial-temporal dynamics and natural orthogonal expansion methods in identifying seismic precursors. By integrating interdisciplinary methodologies and advanced machine learning models, this study bridges critical gaps in real-time predictive capabilities, offering a tailored approach for region-specific seismic forecasting.