Abstract
How does one become interested in mathematics? There often seems to be a perception among the populace that those who pursue mathematics have a preternatural gift for it, are able to envisage complex calculations and ideas completely within their mind’s eye. Consequently, it is only natural that the pursue mathematics. Well, like many mathematicians before me, I would like to help dispel that notion.
Remainder
When I was much younger, though I am somewhat loathe to admit this as the origins of my inspiration, I watched a lot of Star Trek. I wanted to explore other worlds, and to do so I turned my attention towards the advancements in physics that would be necessary. In particular, the warp drive, or its ‘real world’ counterpart, the Alcubierre drive. More than loose concepts, I knew I would need to understand physics on a mathematical level to have any hope of making a worthwhile contribution; this was a daunting task given I frequently did not have the patience nor disposition for mathematical study (I even distinctly recall cheating on a math test in Year 1).
Eventually I began teaching myself calculus, and for the first time I came across the idea of a proof. For the unfamiliar, the equations you learnt in school (such as Pythagoras), are not determined experimentally such as physical laws like Newton’s equations. Instead, one takes certain mathematical statements as an absolute truth, and through pure logic deduces them with unshakeable reasoning. When described like that I admit that it might sound rather dry, but when it is done properly it is akin to pure thought: the distillation of an idea, a concept, to its rawest and most beautiful form. A proof like this is said to come from ‘The Book’, which is a figurative divine work that contains all of the most beautiful, intriguing, thoughtful proofs of every result to exist. Sounds a bit more interesting, right?
Beyond the obvious draw of this concept, what appealed to me about this was that my thoughts were not limited by the need for experimentation – all I needed was my mind. Subsequently I switched from physics and threw myself into mathematics, engaging in every learning opportunity I could find. It was a long process, but I’ve gotten better, and better, and better. I never won awards when I was younger, I was never a wunderkind, but now I study the kind of mathematics I dreamed of all that time ago. This project, in fact, is the first time I have constructed entirely new proofs. They are not worthy of The Book, but they are a contribution nonetheless. You might not have the time or desire to pursue mathematics in the way I have, but I would encourage you to think of it in this new light I’ve tried to frame it in – who knows? You might find you, like me, just weren’t studying the right kind of maths.
Chloe Markovic
Australian National University
