Abstract

The word abstraction often sounds daunting to many non-mathematicians, and probably also to some mathematicians. However, abstraction is all around us: not only in mathematics, but also in the way we form terms and concepts in our language. For example we all group together houses, schools, college chapels and skyscrapers under the word “building”. So if we know something that is common to all buildings (for example that they have to be maintained), then we know this for every building we meet without having to work it out anew in each case.

Mathematics builds heavily on abstraction. Some even say that abstraction is the main ingredient in mathematics. I will present some examples of mathematical concepts that arise as abstractions of well-known situations which every undergraduate has met. My research area – category theory – can be called the most abstract area of mathematics. We will try to explore the point of view and underlying principles that drive category theorists to their very abstract way of thinking.