To those who have studied it, mathematics is like a language. A language that allows complex ideas to be expressed with complete precision and clarity. It can be used to explain patterns and underlying structures that are not clear at first sight and, at its best, if one can find just the right 'turn of phrase’, it can do so with elegance and beauty. This is the mathematics we strive to write as mathematicians.

Given any new situation, I find something deeply satisfying about the process of learning and beginning to grasp its hidden patterns. As an intuitive understanding of a complicated problem starts to crystallise in my mind, this already comes with a feeling of accomplishment. However, as a mathematician I try to go further, to take this intuition and to use it to prove something about the situation. There follows a building sense of anticipation as I work, hoping that I get the right idea, that I can fit together what I know, until the structure of a mathematical proof takes shape. Finally, if everything holds together after tightening the screws and polishing the pieces, then there comes a supreme sense of achievement in being able to say, not just that something is probably the case, but that it is true and will always be true. And maybe, just maybe, the proof is a beautiful one!

Nathan Broomhead

Lecturer in Pure Mathematics