What is category theory and why is it trendy?

Everyone thinks that mathematicians like numbers. However, this is not entirely true. Mathematicians like precision, clarity and, most of all, understanding structure. The sole reason why people associate the subject with numbers is because we like quantifying things. But what is not so clear to the general public is that we don’t quantify for the fun of it, we quantify to understand, organise, define. Numerical values attached to a mathematical concept help us understand the concept better. They also help us group things together that have the same, or similar enough, properties. For example, if we look at a triangle with two of the sides being equal to 7 centimetres and the third one being 12 centimetres, we can immediately say that it belongs to the family of isosceles triangles.

When I was writing my PhD thesis, my brother saw it and exclaimed — “Where are the numbers? This is just text and weird letters!”. By “weird” I think he meant all the Greek letters that were featuring in most equations written on the pages.

The deeper we dive into the ocean of mathematics, the fewer numbers we see. The reason for that is because mathematics is actually about explaining general phenomena. The letters mathematicians use are called “variables” and as the name implies, they can take different values, they “vary”. Plugging different numbers in an expression mainly defined by letters produces new examples. Working out various examples numerically can be quite helpful in spotting trends behind general phenomena and…