Abstract
Many students enter university with a passion for mathematics, only to find themselves disillusioned by its abstract and rigorous nature. Here, I reflect on my own experience of falling out of love with mathematics in my early university years, struggling with formalism, and eventually rediscovering its beauty through deeper intuition, collaboration, and a shift in perspective.
I did not love mathematics in my first few years of university. In fact, the mathematics courses I took were always the ones I dreaded going to and doing the most.
The mathematics I had fallen in love with seemed to vanish—or at least, it took on an unrecognisable form. The joy of simplifying a satisfying integral was replaced by the nightmare of epsilons and deltas, and instead of solving equations, I was now expected to prove statements that were obviously true.
My intuition for solving problems slowly became worse and worse, overwhelmed by formal definitions and rigorous proofs. Thankfully, it was comforting to know that I wasn’t alone—after all, as Terence Tao aptly puts it, transitioning to this new way of mathematical thinking “is well known to be rather traumatic”[1].
Many times during my first three years, I considered leaving pure mathematics for something else—computer science, physics, anything that was more relevant to engage with the real world. But perhaps I stuck with it because a small part of me still hoped math would one day excite me again, just as it had when my thirteen-year-old self first discovered trigonometry.
It wasn’t until I took an algebraic topology course that my intuition and rigour finally clicked—each reinforcing the other. I could visualise topological structures and reason through them using algebra, which in turn deepened my understanding of topology.
Only recently did I realise my perspective on studying mathematics had shifted. As I advanced, class sizes shrank—from packed lecture halls to intimate seminar-style discussions, where learning became more collaborative, and even the lecturer sometimes wrestled with the material alongside us.
And this made me think about how my motivations for doing mathematics had changed. In his reflection on the cultural aspects of mathematics, William Thurston notes that “what [mathematicians] really want is usually not some collection of ‘answers’” but “understanding”[2]. Wrestling with abstract concepts, making sense of new structures, and even embracing the uncertainty of not knowing has now become the reason why I love mathematics.
I no longer see mathematics as a rigid set of tools or a means to an end. Instead, I appreciate it as a collaborative effort—a way to build intuition, refine logic, and share insights with others who are equally lost but equally determined.
[1] https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/
Yangda Bei
Australian National University
