Hidden Everywhere: The Utility of Mathematics

By Jacob Ryan, Queensland University of Technology

“Wow you study maths, you can get a good job from that” is often a response myself and many maths students like me hear whenever we first introduce ourselves to strangers (well that or “do you want to be a maths teacher.”) Whatever the situation, most people I meet know of the importance of mathematics, yet the conversation rarely progresses past this.

I don’t expect everyone to know how to solve differential equations and there are numerous jobs I don’t have the first idea about but consider that everyone studies maths at school for as many as 12 years. In my experience, I didn’t really start to truly grasp the versatility of mathematics until I continued my studies at university.

For instance, my research with AMSI involved using differential equations (DEs) to model the behaviour of cells. For example, getting cut causes the cells in that area to be divided, leaving a gap that they will work to fill. Cells will also divide along the way, creating copies of themselves to continue the healing process. This system can be modelled with a DE known as Fisher’s equation, describing how cells move to fill space, while bumping into other cells around them and occasionally dividing in two.

This work has applications in cancer research as mutated cells will attempt to spread around the infected patient following these basic rules. In fact, research into the spread of Melanoma cells is where much of the original data that motivated this project came from.

Learning how to solve DEs for this project was not actually necessary for me. These types of equations exist everywhere which I discovered when I had an assignment last year to model how the flow of groundwater changed when a coal-seam-gas plant was built in the region, as this would remove water from the system necessary for the agriculture in the area.

It was in this class that I began to learn how to solve these more complex models that have a very specific and important application but one of the best parts of mathematics is how so many problems can be translated into something familiar. Groundwater does not behave like cells, but the same skills can be applied to solve both problems. I think this is something mathematics has over other fields which is why teaching it at school is so heavily emphasised.

I’ve heard someone refer to mathematicians in the workplace as ‘invisible people’ since they’re always working alongside professionals in engineering, IT and other industries even though they’re without the same training. This is a testament to the versatility of mathematics, from scheduling and transport modelling to biology and a plethora of other areas, the results of their work are far from invisible. The challenge for mathematicians moving forward is to do a better job at showing people.

Jacob Ryan was one of the recipients of a 2017/18 AMSI Vacation Research Scholarship.

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