Climate research is faced with a multitude of scientific problems that originate from a wide range of scientific disciplines. Most often, climate research is associated intuitively with atmosphere-ocean science, yet this constitutes only the baseline. Studies of floods and droughts, for instance, require insight from Hydrology, and research into climate impacts'' calls for input from sociology, economy, and ecology. Mathematics has many different roles to play in this challenging research field. In this lecture I will discuss three examples that highlight very different types of contributions mathematics can and does make to deepen our understanding of geophyical fluid dynamics, to help extracting the essence behind complex observational and simulation data, and to support difficult interdisciplinary dialogues. Specifically, these examples involve multiple scales analyses of atmospheric motions, novel approaches to complex time series analysis, and a mathematical formalization of the notion ofvulnerabilty''.