As a child, I loved video games. I could spend all day just sitting in front of the computer screen with a mouse in hand. So naturally, I decided I would make video games when I grow up. If you had told me then that I would be spending a whole summer doing mathematics, reading papers on graph theory and drawing the same graphs over and over, well firstly I would tell you I do not know what a graph is, and secondly I would not understand why I would be doing mathematics while I could play video games instead.

Mathematics at school was taught to us in a rigid way, a constant cycle of memorising formulas and methods then applying it to a problem, repeated ad nauseam. Little was told in the textbooks about the application of maths, and so for me it was simply just a subject I needed to study to pass my exams. I put in a lot of effort and actually did quite well at it, but some of my peers were way better, and no matter how hard I tried I could never catch up. I figured I had neither the interest nor the brain for mathematics, so the plan was to end my short-lived and highly stressful journey in mathematics and leave it behind for good once high school is over.

It was not until I started seriously exploring programming and game development that I came across the fast inverse square root algorithm behind the lighting simulation in Quake III, one of my favourite games. The algorithm quickly estimates 1/sqrt(x), where x is a 32-bit floating-point number. Inverse square roots are used to compute angles of incidence and reflection in 3D graphics programs, so the algorithm was crucial at a time when floating-point processing lagged behind integer processing speeds. It started to dawn on me that underneath the beautiful graphics, there are computer science, linear algebra, and a huge amount of algorithms coming from computational mathematics. This realisation completely changed my perspective on mathematics, and after further research, I decided I would go on to study mathematics and computer science at university.

And here I am, reading papers on graph theory and drawing the same graphs over and over while I could be playing video games. But now I actually find it enjoyable to tackle the challenges that mathematics presents, and it feels great to know there is meaning in what you are doing. Mathematics is at the same time both fundamental and extensive, and regardless of your field of interest, you will encounter it sooner or later. These are the reasons that I am learning mathematics now, and hopefully will continue for years to come.

The VRS project has given me a clearer insight into the nature of mathematics research, and some of the difficulties that may arise. It is a great opportunity to improve my skills and definitely an experience I am glad to have. I would like to thank my supervisor, Murray Elder, for his support and patience in guiding me through the project, and thank everyone involved with the AMSI Vacation Research Scholarship for making this amazing opportunity possible.

John Cu
University of Technology Sydney

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