Guest Lecture by Prof. Dr. Malte A. Peter: Modeling—Mathematics and Reality

Mathematical modeling refers to the representation of real-world (e.g., physical or financial) processes as mathematical structures, typically equations for process-relevant variables. The goal of modeling is to arrive at a meaningful mathematical formulation of the problem from which statements or predictions about the real-world process can be derived.

The task of (applied) mathematicians ranges from identifying the relevant processes and variables (typically in collaboration with users) to formulating systems of equations, performing their mathematical analysis and solving them (usually using a computer), and finally validating the models (typically again in collaboration with users). Wherever possible, established mathematical methods are employed. However, it is often necessary to develop new mathematical theories, which then represent a gain in knowledge even independently of the specific application problem.

A significant level of abstraction is required when the quantities to be determined are not finite (typically numbers) but rather functions (usually dependent on space and time). Here, the mathematically precise description of the infinite plays a crucial role, one that initially appears very counterintuitive. The lecture concludes by highlighting some current research questions.