Essays in this group are divided into six categories:

- the applicability of mathematics to solve both real and abstract problems
- the beauty of mathematics—eg geometry or fractal theory
- the elegance of mathematics in the proving of theorems—eg number theory
- the history of mathematics: the origin and subsequent development of a branch of mathematics over a period of time, measured in tens, hundreds or thousands of years
- the effect of technology on mathematics:
- in forging links between different branches of mathematics,
- or in bringing about a new branch of mathematics, or causing a particular branch to flourish.