Abstract

Many phenomena in engineering and the physical sciences are best described using mathematics: observable things in the real world become mathematical objects and the relationships between them become equations that these objects must satisfy. This approach, wildly successful in improving our understanding of the world around us and in making the technological advancements of the last century possible, has required the development of ever more sophisticated mathematical tools to mirror reality. As the tools become more complicated, so does their use, however, and care must be taken to ensure that we use them to draw the right conclusions. Applied analysts study and manipulate mathematical models and the objects which comprise them in order to better understand the original problems of interest. This talk will informally discuss what makes up a mathematical model, what kind of questions analysts are interested in answering, why non-mathematicians should sometimes care about their answers, and the value of mathematical rigour and proof in tackling these questions.