Mathematical research is unique in that it is physically accessible to anyone with pen and paper but also so abstract and dense that even understanding the motivation behind many modern problems requires years of education and toil. However, the AMSI VRS programme has given me a valuable insight into the world of research which differs so greatly from the years of coursework that we have come to associate with mathematics.
Throughout my schooling and undergraduate studies, I always found a sense of comfort and hope in knowing that a solution did indeed exist and it was my job to find my own way there. Be it course-work or competition, it’s akin to being told to run a pre-defined obstacle course where the path is clear and a clear goal in sight, all under the supervision of our teachers who are ready to help. It was always a controlled environment as you followed the tracks of the millions of people around the world who had gone through exactly what you were experiencing.
However, mathematical research at university felt like you were suddenly thrust outside the walled garden where you had played for your whole life. You find yourself in a beautiful but dense and dark forest where the new boundaries of mathematics are pushed. There is no chequered flag indicating the finish line, there isn’t even a place for you to begin! You must decide what path you will take not knowing if there even is an end or if it’s littered with great chasms that will drain all your time. The tangled roots and dense foliage of notation and jargon slow you down as you hack through it, re-contextualising the symbols on the page into concepts in your mind. Initially it feels rather daunting as you find yourself isolated and directionless as you take the first few steps into this new world.
However the wealth of knowledge that past explorers have left behind are beacons illuminating patches of the jungle, that guide you through what others in your shoes have done. Aside from their results, they provide valuable insight into the paths that others have taken and the way in which they approach the problems. One of the most satisfying experiences is drawing relationships to seemingly unrelated fields and using their results to look at your problem in a completely new light. The saying “we stand on the shoulders of giants” is particularly poignant in my experience and research as a whole.
Most of all, my supervisor, Assoc. Prof. Alexander Fish, was an invaluable guiding force in helping me navigate this world as his experience helped me understand how to approach such open problems. One of the key takeaways is that in research you are both the problem setter and solver so you are free to define your own goals and the methods you will use to approach them. Often he was able to see things that I could not and vice versa (although the converse was less so). Having my supervisor as a guide allowed me to explore much deeper into the forest than what I could have done on my lonesome and taught me how to avoid common pitfalls all the while being persistent.
Having had a taste of what mathematical research is like in this AMSI VRS project I’ve been able to stop fearing the depths of the forest and instead enjoy the beauty of all the fascinating creatures that we find lurking within. We have submitted a paper to a peer-reviewed journal and I hope that it may guide others onto something even greater.
The University of Sydney