Reflections of a Mathematician
Mathematics quietly shapes the world around us.
Recently, a student asked me:
“When will I ever use this maths?”
As Head of Maths and Stats it was one of those simple questions that causes you to pause and reflect. My initial thought was:
“When don’t we use maths?”
From the phones we use hundreds of times a day, to farming, planting crops, cooking, and planning travel, maths is quietly embedded in almost everything around us. Much of it is so deeply woven into modern life that we barely notice it anymore.
One thing we often face in mathematics is an added layer of abstraction. Mathematics is foundational — ideas build on one another over time — and this can sometimes make the real-world application feel hidden beneath symbols, formulas, and unfamiliar language.
Take, for instance, trigonometry. You may remember learning “SOH-CAH-TOA” at school and understandably wondering what this had to do with real life. At first glance, it can feel like a strange collection of letters and rules.
However, if you look beneath the surface, trigonometry is fundamentally about understanding shapes, angles, distances, and relationships. It allows us to measure things we cannot easily reach or touch. From building and architecture to navigation, engineering, physics, graphics, and even video games, trigonometry quietly helps us describe and understand the world around us.
Statistics is another interesting example. Even without realising it, our brains constantly act as little statistical machines. Every day, we quietly estimate the likelihood of events based on prior knowledge and experience. We decide whether to take an umbrella, whether traffic might be heavy, whether someone is joking, or whether a situation feels safe — all using patterns and probabilities gathered over time.
Formal statistics simply provides tools to navigate uncertainty more carefully and reliably. Interestingly, modern artificial intelligence and large language models are also built upon this same probabilistic way of recognising patterns and predicting likely outcomes.
As mathematics and physics have evolved, the language used to describe ideas has naturally become more complex. Yet the underlying purpose remains surprisingly human: solving problems, recognising patterns, making predictions, and understanding how the world works.
However, just because a student does not immediately see how they will use a particular idea in everyday life does not mean that learning it has no value. Repeatedly engaging with challenging ideas helps develop persistence, logical thinking, problem-solving skills, and resilience. These habits of mind are often just as important as the content itself.
Learning mathematics is a little like building a toolbox. Not every tool is needed every day, and some may sit unused for long periods of time. However, when a new challenge appears, having the right tools — and knowing how to use them — can make an enormous difference. Mathematics gives students more ways to think, reason, estimate, analyse, and solve problems when life becomes unfamiliar or complex.
Not every student will use multiple parts of trigonometry in daily life, just as not every adult uses advanced algebra every day. But learning how to think mathematically equips students with tools to tackle unfamiliar problems and approach complexity with confidence.
At home, one of the most valuable things we can encourage is curiosity. Asking questions such as:
- “How does this work?”
- “Why does this happen?”
- “How could we figure this out?”
can help students see mathematics not simply as a school subject, but as a way of making sense of the world around them.
Sometimes the most important thing mathematics teaches us is not just how to find an answer, but how to keep exploring when the answer is not immediately obvious.
Lach Tantau
Head of Mathematics and Statistics