**By Jamie Owen, Queensland University of Technology
**

I have enjoyed science and mathematics from a young age, but several problems me want to become a mathematician.

The first problem I found when I was bored one afternoon sitting in a class in front of a brick wall. As my mind began to wander I wondered what would happen if you poured water into the gaps between the bricks to let it freely divide. It was just an idle thought at the time but it stuck with me gnawing a hole in my head until I sat down and worked it out linking it to a really interesting mathematical construction called Pascal’s triangle.

The second problem was again brought by a wandering thought in class, this one brought about due to my complete lack of talent in constructing physical models. I was interested in how to convert different types of motion into one another, and as such decided I wanted to make piston, a mathematical piston. Using some basic trigonometry and a lot of trial and error I accomplished my goal, I then plotted my solution and everything broke. Undeterred I did the maths again double checking everything and rebuilding my model from the ground up. I still had the same answer; slightly deterred at this point I looked more closely at the inputs I had chosen. It was at this point I realised that the values I had chosen for the proportions of the piston were impossible. After fixing this error the model worked perfectly or at least well enough that I didn’t want to probe it for any more errors.

The third problem was even more weird and esoteric that the previous two, as can be anticipated from the previous two occasions it came through a wandering thought. Why can we know if a number is even or a multiple of 5 just by looking at the last digit? This involved looking at the number system we used called decimal due to the 10 symbols that are used to represent all numbers. This question and variations of it stuck with me through the last two years of high school and through all of my undergraduate degree. I found the answer I was looking for not too long ago and how it is with so much of maths, Euler found it first.

*Jamie Owen was a recipient of a 2018/19 AMSI Vacation Research Scholarship.*