From Humanities to Pure Mathematics: My Odyssey of Rebellion and Awakening

❝ I remember standing at the university gate, filled with uncertainty. Having suspended my studies for a year and immersed in the humanities, mathematics felt like a foreign language to me. My father, a computer science Ph.D., walked beside me—his presence both comforting and intimidating. "Maybe I'll just get through this," I thought, never imagining that behind these gates awaited a revolution that would shatter and rebuild my entire worldview. Little did I know that this reluctant step would become the first note in a symphony of mathematical discovery that would consume my every waking thought. The humanities had taught me to ask "why," but mathematics would teach me to ask "why not"—and in that subtle shift, I would find my true intellectual home.

❝ They say you never truly understand something until you teach it. So I chose to teach the one subject that terrified me most: Linear Algebra. The night before my first lecture, I almost backed out. "What if I fail? What if they see through my facade?" But as I stood before my peers, explaining row reduction and vector spaces, something miraculous happened—the fog began to lift. In the process of deconstructing knowledge for others, I discovered a profound truth: the elegance of algebraic structures spoke to me in a way no historical narrative ever had. This wasn't just teaching; this was my mathematical awakening. I realized that the most terrifying challenges often conceal the most beautiful revelations, and that true understanding comes not from avoiding difficulty, but from embracing it with open arms and a curious mind.

❝ Standing at the astronomy conference, surrounded by brilliant physicists, I felt like an imposter. Professor Pang had given me everything—Python skills, research training, a path forward. Yet as I listened to talks about cosmic phenomena, my mind kept wandering back to the mathematical structures underlying them. The equations fascinated me more than their physical interpretations. That night, staring at the starry sky, I made the most difficult decision of my academic life: to abandon the security of applied research and pursue the treacherous path of pure mathematics. I was choosing beauty over utility, abstraction over application. In that moment of clarity, I understood that some callings cannot be ignored, even when they lead away from practicality and into the realm of pure, unadulterated beauty.

❝ The moment I understood Galois theory, I felt like I had discovered a secret language of the universe. While my peers struggled with the abstraction, I found myself intoxicated by it. Teaching commutative algebra became not just a duty, but a joy. Each lecture felt like unveiling a masterpiece—group theory's symmetry, field extensions' elegance, the heartbreaking genius of Galois' short life. One evening, after explaining the unsolvability of the quintic, a student asked, "But what's the practical use of this?" I smiled and replied, "Some beauty needs no justification." In that moment, I knew: I was no longer studying mathematics; I had become a mathematician. The abstract patterns and structures had become my native tongue, and I knew I could never go back to seeing the world in any other way.

❝ Listening to Professor Zhang recount his decades of solitary pursuit, I saw my future—and it terrified me. As he described working in isolation, driven only by mathematical intuition, I remembered my own lonely nights plotting prime number spirals, searching for patterns that might not even exist. His story wasn't just inspirational; it was a warning. Mathematics demands everything—your time, your relationships, your very identity. Walking back to my dorm, the weight of this realization crushed me. Was I prepared for such solitude? Did I possess that kind of courage? The prime numbers on my screen seemed to mock my uncertainty. Yet in that moment of profound doubt, I also found a strange comfort: if such beauty could emerge from solitude, then perhaps the loneliness was not a price to pay, but a sacred space to cherish.

❝ If the path didn't exist, I would build it myself. Frustrated by the lack of pure mathematics community, I decided to create one. Sending those first invitation emails felt more daunting than any exam. "Who would come? Was I qualified to lead this?" But as the room filled with curious faces, something shifted. Standing there, explaining Galois' genius to students from different backgrounds, I realized this was my answer to the solitude. We weren't just sharing knowledge; we were building a sanctuary for those who saw beauty in abstraction. My lecture on Galois theory, tracing the historical motivation to the unsolvability of the quintic, became a testament to how individual passion can ignite collective curiosity. Looking at the engaged audience, I understood: my journey was no longer about personal achievement, but about creating spaces where mathematical beauty could flourish and where solitude could transform into shared wonder.

❝ When I discovered category theory—"the study of mathematical objects through their relationships rather than their internal structure"—I felt I had finally come home. This was the mathematics I had been searching for all along! My previous understanding of group homomorphisms as "bridges" was merely a glimpse into the world of categories and functors. And when I encountered the Yoneda Lemma—"an object is determined by its relationships with all others"—it felt less like mathematics and more like revelation: reality is defined by connection, not isolation. I joined the seminar without hesitation, knowing I had found my true mathematical calling. In category theory, I found the perfect synthesis of my humanities background and mathematical passion—a discipline that values context, relationship, and the spaces between things as much as the things themselves.

❝ My journey from struggling student to Algebra Teaching Assistant completed a beautiful, unexpected cycle. Every week at the Help Center, I watched younger students wrestle with concepts I had once feared. Designing challenging problems and seeing that spark of understanding in their eyes—it brought me full circle. I was now paying forward the guidance that had once saved me, creating the supportive community I wish I'd had from the beginning. In helping others navigate the same mathematical labyrinths that once confounded me, I discovered that teaching is not just about transmitting knowledge, but about creating bridges between different stages of understanding—both for my students and for myself.

❝ Surrounded by the best mathematical minds at Westlake University, something in me caught fire and refused to be extinguished. Discussions with Professors Huayi Chen and Xing Gu about homotopy theory and academic futures opened horizons I hadn't dared to imagine. In that crucible of intellectual ferment, I understood with terrifying clarity: to grow, I had to leave the comfort of familiar shores and venture into the vast, uncharted waters of real mathematics. The summer school became a mirror reflecting both my current limitations and my boundless potential, forcing me to confront the gap between who I was and who I needed to become. I left not with answers, but with better questions—and the courage to pursue them wherever they might lead.

❝ Returning to Westlake as a visiting scholar, I stand at the edge of a new mathematical frontier. Diving into homotopy theory while mastering categorification and Lean, I feel not an ending, but a beginning. This is not convergence—it is emergence. Each abstract concept grasped, each proof formalized, feels like gathering supplies for a much longer journey ahead. I can now see the vast landscape of pure mathematics stretching before me, and I understand that everything until now has been but the prologue. The real odyssey—the one that will test my courage, deepen my understanding, and truly define my mathematical soul—is only just beginning to unfold beyond this horizon.