About mathematical research. Mathematical research differs from other sciences in several ways, notably in the timing of publishing results, which can take years. This is primarily because mathematics especially pure mathematics relies on abstract logical deductions rather than physical experiments. (This could lead to claims that math is not a science per Popper’s demarcation criterion.) Furthermore, pure mathematics is rooted in a proof-oriented approach where the complexity and depth of problems can impede even seasoned mathematicians from fully grasping research outside their own specialty. Developing an automated formal verification infrastructure that validates theorems built upon axioms could help break down barriers and allow mathematicians to focus on more creative work. The recently announced theme of the 2025 Joint Mathematics Meetings, “AI and Math,” underscores this current trend in mathematics. I’m proud that my mentor, Prof. Tom Hales, has been a pioneer in formal proofs long before it became the trend.
About mentorship. Another aspect that contrasts with other sciences is that undergraduate research in mathematics often resembles doctoral studies through one-on-one mentorship rather than group lab work. In math, students often have the opportunity to tackle original problems that match their current mathematical maturity and toolkit. Having a mentor who can pick the right problems for you really makes a difference, and I’m lucky because my mentor is widely recognized as a leading figure in discrete geometry – the field of my thesis research. Prof. Hales provided a profound sense of support and security, consistently affirming even my most naive, immature, and sometimes silly ideas and writings. He subtly yet effectively guided and nurtured my growth, understanding that students can truly open their minds and grow confident when they feel sufficiently respected and secure, making genuine learning and creative thinking possible.
About research presentation. From my experience, presenting research at conferences is not the primary goal, but it offers a great opportunity to see what others are up to and, of course, to explore new cities through reimbursed travel! At national events like the Joint Mathematics Meetings and the Mathematical Association of America’s annual MathFest, I’ve learned about current big changes in mathematics. At local events like the Pittsburgh MathFest, the Mathematics Department Colloquium, and the Honors College Research Symposium, I’ve had the chance to see the interesting projects my fellow undergrads are working on. Along the way I have received some awards, but that is not the main focus.
Lessons learned. What I’ve learned might sound cliché, but it’s important for those new to research or considering involvement. Don’t wait until you have the skills to start your project; your project will teach you the skills. Also, don’t wait until you have confidence to pursue what you want; confidence comes when you are doing it and it’s going well. Additionally, don’t try to do too much at once; time is limited. My own experience of taking several graduate-level courses, launching a new journal, the Pittsburgh Interdisciplinary Mathematics Review (drop by our homepage at pimr.pitt.edu), and managing a heavy teaching load pushed my physical health to its limits.
My next step. My undergraduate research experience with Prof. Hales has not only cemented my decision to go to graduate school in mathematics but has also helped me clarify specific directions I want to study next. I am sincerely grateful to the Chancellor’s Undergraduate Research Fellowship for the financial and honorary support provided.