I’m just an ordinary undergraduate student in the School of Management and Engineering at Nanjing University, majoring in Industrial Engineering. To be honest, I don’t particularly enjoy most of what we learn in this program. As an interdisciplinary field, it involves a lot of things I can’t connect with.
Coming to this university wasn’t what I had envisioned, and not studying mathematics was something I regretted. I’ve wanted to study math since high school—not because I was head-over-heels in love with it, but because it was the only subject that could truly calm my mind. It was the only thing I could focus on deeply.
Back in high school, many of my classmates were obsessed with math. I followed along and learned a lot beyond the standard curriculum. That was one of the most enjoyable experiences in those years. I couldn’t picture myself working in a company, doing something I had no passion for. I just wanted to spend a lifetime studying mathematics.
But when I entered college, things changed. Due to my carelessness, I missed the opportunity to transfer into the math department. I lost the chance to become what people call a “proper” math student. I felt completely lost. I thought I’d just settle for any major where I could maintain a decent GPA, get a master’s degree, find a stable job, and live a decent life. But I wasn’t optimistic about it. As I said, I couldn’t imagine myself committing to something I didn’t enjoy—and that scared me.
At that time, my life felt directionless. I didn’t know what I wanted anymore. But then, I got lucky.
In my sophomore year, I met Professor Caihua Chen. He introduced me to optimization—a branch of mathematics I found incredibly interesting. From the very first paper I read about online LP, I was hooked. The process of proving bounds reminded me of the inequality problems I used to love solving in math competitions, even if I was never that successful at them. Of course, optimization was on a much deeper level, but the joy of bounding, the elegance of the proofs—it all felt so familiar and thrilling. And I really enjoy the idea behind acceleration algorithms or solving the different problem.
Even though I wasn’t a math major, I felt like I was finally getting closer to mathematics. I began learning about online optimization, first-order methods, and distributionally robust optimization. Each new topic felt exciting. And I was grateful for having read—out of sheer interest—some books on matrix theory, functional analysis, and real analysis. Although I only skimmed the surface, that prior exposure helped me better understand the concepts in optimization.
Speaking of that, back in high school, I was strangely fascinated by the name “algebraic topology.” I didn’t know what it was, but it sounded so advanced and mysterious.( Kind of funny by the way.) During my first year in college, I even tried reading a bit about it. Again, I understood very little, but even today, it’s something I remain curious about.
Gradually, I began to believe that pursuing a Ph.D. might be the right path for me. I’ll talk more about that later. But as I dove deeper into the literature, I became increasingly aware of my biggest limitation: my mathematical training is not systematic enough. I may know where a concept originates from, but I don’t fully understand its properties, its stability, or its deeper meaning. Take variational inequalities, for example. I’ve read definitions and seen them used in papers, but I’ve never actually solved an exercise. The more I learn, the more I realize how little I know. Recently, however, I have been reading a number of papers on monotone inclusions and variational inequalities, and I feel that I have begun to build a more solid foundation compared to before.
Sometimes I ask myself: when will I be able to say that I “understand” optimization? Honestly, I don’t dare make such a claim. All I hope is that one day, I can say: “I understand a little bit of it.”
During my work at HKUST with Prof. Sanyou Mei, I worked on problems in nonconvex–concave minimax optimization. What I found most valuable was not only learning the technical details, but also beginning to see where ideas for improving bounds actually come from. Through discussions and paper presentations, I realized that progress in optimization often emerges from rethinking assumptions, reformulating problems, and connecting with deeper structural insights, rather than just applying existing tools mechanically. This experience taught me how to approach research more independently, to ask why certain results hold, and to search for the underlying principles that can guide the development of new methods. It gave me confidence that I can grow into a researcher who contributes not just by solving problems, but also by shaping the way we think about them.
This journey has been a lonely one. I’m not in the math department, and I don’t have many peers who share my interests in optimization. But I want to stay on this path. I’ve come too close to mathematics to walk away now.
Just a few months ago, two professors from The Hong Kong Polytechnic University—Prof. Xiaomeng Guo and Prof. Guang Xiao—came to Nanjing University for a talk. Professor Juan Li arranged for me to meet them. They told me they had studied pure mathematics at Tsinghua and Peking University, but eventually moved away from theory. They said doing pure theory isn’t always realistic, and that finding a faculty position in optimization is extremely difficult. They encouraged me to think carefully.
I understand what they meant. Maybe someday, I’ll also walk away from theory. But not yet. I haven’t even had the chance to truly do mathematics. I’m not a math major—I haven’t really immersed myself in mathematical research. How could I already feel disillusioned? What they once had is still what I’m striving for.
In my department, I am required to take several management-oriented courses with a liberal arts emphasis—subjects that often feel foreign and distant to me. Sometimes I just want to run away. But I’m not brave enough to restart( just like we can stop the algorithm when it works not well and restart with the information, lol). I don’t have the courage to take the Gaokao again, just to pursue math from scratch. Optimization is the only path I’ve found to reconnect with mathematics. Even if I one day decide to let go, I don’t think I’ll regret walking this road.
At a recent sharing session, Professor Hongqiao Chen told me that I might be limiting myself too much. I think he’s right. But at the same time, this is the one thing I’m genuinely passionate about right now. Optimization is not a friendly field for students outside of math departments. It’s hard. But I really want to give it a try.
Now, I’m approaching the Ph.D. application season. I’ll soon be reaching out to professors and applying to schools. Why do I want to study abroad? Partly because I’ve always had high academic ambitions—I want to learn from the best, to be around the brightest minds, to explore the cutting edge of technology and knowledge. I’ve never left mainland China. I genuinely want to see more of the world.
Why not pursue a master’s degree first? Because it’s too expensive. Studying abroad without funding isn’t something I want, or can afford.
Lately, my life has been hectic. The pressure is intense. But I believe I can persevere. There was a time during college when I drifted aimlessly, even drank to escape reality and made a fool of myself more than once. But looking back, those were also part of the experience—moments I can smile at now.
I hope I can keep walking this path of optimization. I’m writing this post to encourage myself during one of the most important phases of my life. May I stay committed and keep fighting for what I truly want.
Wish me luck.