Over the course of 9 years of being a mathematics student/researcher, I had 1000s of conversations with people of all levels about mathematics. Some of the most common questions were:

  • What does maths look like beyond school?
  • Why do you enjoy it?
  • Is the enjoyment you get from it only accessible to people who have spent years studying maths?
  • Is it all just made up?
  • What’s the point of it (specifically pure maths/number theory)?

Ironically, now that I am no longer working in pure maths academia, I feel I have time to return to these questions and think about them a little more/write a few posts about maths. I hope some people find these posts interesting or helpful. There’s lots of fantastic places to learn maths at different levels, however my experience is often that the historical/expository information out there is often quite non-technical, so I want to try and connect concepts to actual mathematics. This might make for unhelpfully complex posts, but let’s just see!

My current plan is to roughly divide my writing into 3 sections:

  1. Concepts - These are intended to answer the first question of what mathematics looks like. Also, one of my stock comments in conversations is that a lot of the beautiful ideas in mathematics aren’t really about the notation or the esoteric setting in which they are applied, many are simply beautiful ways to think about something/find a new perspective. These posts are intended to try and demonstrate this.
  2. History of Maths - In my opinion, maths has been fundamentally shaped by the people who do it and the problems they have been drawn to. Many great areas of maths were brought about when a creative mathematician tried to tackle a specific problem in a new way, but often the maths lives on without the context of why it was considered in the first case. These posts are primarily intended as a conduit of learning for me too, as much of mathematical history is a mystery to me, and I hope to learn about it through these posts.
  3. Modern Mathematics - Now I’m no longer doing research, I need to keep up with modern mathematics in my own time, and hopefully will be able to communicate something about what is going on though some expository posts. (These might blur with both of the previous categories.)