For more than a century, scientists and mathematicians have sought to understand and predict environmental change. Accurate forecasting is essential for improving preparedness for hurricanes and droughts, as well as anticipating shifts in food availability. In this lecture, I examine the mathematical tools—including systems of differential equations and numerical methods—that researchers use to study hurricanes, sea ice extent, temperature patterns, and precipitation changes, and to assess the resilience of these systems in a rapidly changing climate.