Mathematical Modeling of Real World Processes

From the formation of galaxies to the evolution of the human cell mathematics aims to uncover the underlying abstract structures as an idealized model of reality on all spatial and time scales. Even earlier than writing, mathematics helped to organise and shape the world around us, such as keeping track of life stock, or the seasons to find food or grow crop, and nowadays penetrates each and every part of our lifes. In this talk I will illustrate i) how a mathematical model is conceived as an idealized structure that ii) is amenable to mathematical solutions and iii) allows a physical interpretation that can be validated against an experiment. I will discuss the importance of each step and address the challenges that needs to be overcome to arrive at a viable mathematical model.