Only three years ago, I never would have expected that I would end up studying pure mathematics. From the beginning, I originally only intended to study physics, as I never really tended to do very well with mathematics in school. Like many other new students of physics, I was quite interested in quantum mechanics in particular, and was excited at the possibility of learning more about it – and even potentially being involved in research. At this time, the possibility of doing mathematics research hadn’t even crossed my mind. That, however, changed as soon as I took my first pure mathematics course at the end of the first year of my undergraduate degree. This course on complex analysis served as my first minor exposure to the world of pure mathematics; I was immediately impressed by its elegance, as well as the feeling it gave of being able to understand everything in precise detail. Nothing felt particularly arbitrary or contrived!
As I continued through my degree, this appreciation deepened, especially with respect to areas such as group theory, representation theory and topology. I also became more invested in quantum mechanics as well, largely in part due to its treatment being a bit more mathematical than most other branches of physics. Indeed, much of the elementary theory of quantum mechanics is essentially nothing more than functional analysis! Unfortunately, physics is not often taught in a way that is mathematically satisfying; the underlying machinery often tends to be obfuscated for the sake of time. I still made it my goal to learn as much as I was able to about the formal mathematics behind the physical concepts I was being introduced to.
During one of my courses on quantum mechanics, I began to wonder what operators really were, as their treatment in undergraduate physics tends to be rather mysterious. This resulted in studying the theory of operator rings and algebras, as well as their basic history and how they brought life to the early algebraic formulations of quantum mechanics. This interest in the relationship between theoretical physics and pure mathematics has thus led me to where I am at the time of writing; having just finished an extremely interesting project with rather deep roots in theoretical physics, and with hopeful prospects of doing more pure mathematics research in the future!
The University of New South Wales