About me... (TMI)

I am a mathematics Ph.D. student driven by a deep fascination with abstract and structural theories. My research explores the mathematical underpinnings of spatio-temporal analyses — particularly how concepts like Empirical Orthogonal Functions (EOF), cyclostationary analysis, and wavelets can be synthesized with neural networks to better understand complex climate patterns.

For over 9 years, I’ve immersed myself daily in academic discussions — not only in formal seminars but also through global conversations unfolding on YouTube and online platforms. I find inspiration in white-noise cafés, often accompanied by a notebook and a coffee — a habit that has surprisingly earned me Gold status at Starbucks for nine consecutive years.

My approach to mathematics is reflective and self-driven. I value both rigor and intuition, and I’m always seeking to connect seemingly distant concepts in novel ways.

Ever since my first and second year of high school, I was certain that either pure mathematics or mathematics education would become my lifelong path.

What I loved most about mathematics was that it gave me the freedom to think deeply and the joy of striving to solve problems on my own.

For instance, I often found myself questioning what textbooks simply asked us to accept.  

1) I was dissatisfied with how the notion of “mathematical closeness” was explained through examples like x approaching 0.1, 0.01, 0.001... and f(x) getting closer to a certain value. Was that really enough to define a limit?  

2) I didn't want to accept the Law of Large Numbers as just a rule that “things converge when n is around 30 to 60.” I wanted to know why.  

3) Above all, I realized that if you’re given a problem and repeat solving similar examples over and over, you eventually internalize an "optimized formula" — and then the problem no longer feels like a challenge.

Actually, I had two small publications during high school, reflecting my early curiosity and eagerness to explore mathematics:

- (151119) A Proof and Deep Dive into Euler’s Constant \(e\), and Its Applications  

  Centum High School, 6th High School Science Project Research Presentation

- (160911) Exploring the Relationship Between Geometry and Probability Through Buffon’s Needle Problem,  Centum High School, Mathematics Research Club

After entering the Department of Mathematics, I spent my undergraduate years continuously seeking balance between academic study, community life, and deep reading. In the beginning, I actively participated in various groups — including a mathematics enrichment circle, a reading club, and a campus church community. At the same time, I began to develop a conceptual fascination with foundational subjects like calculus and set theory, and for the first time since high school, I started asking genuine mathematical questions of my own.

Driven by the conviction that “I would pursue graduate studies anyway, so I should do what only undergraduates can do now,” I set out to read 450 books — primarily to understand 500 years of European intellectual history.

From my second year, I began a double major in philosophy and became deeply interested in the structural parallels between mathematics and philosophical thought. I immersed myself in courses like analysis, linear algebra, abstract algebra, and topology. Though the study of mathematics often felt isolating, I created and led several study groups with fellow classmates, which helped me make significant progress by articulating problems aloud. When I first encountered the proof of the Heine–Borel Theorem, I experienced firsthand the gap between abstract formalism and computational understanding.

By the third year, I started to view mathematics as a serious object of research. I studied real analysis independently and attended my first academic conference on Topological Data Analysis (TDA), which sparked my interest in topology. As I prepared for graduate school, I came to recognize both the solitude and the subtle joy that accompanies research. I also led study groups in linear algebra and topology, and served as the director of “Hamdeokshil,” a science college reading room — where I explored broader academic perspectives beyond mathematics.

In my final year, I experienced the intersection of theory and education: I studied complex analysis, abstract algebra, and topology problem-solving; tutored students through the Hyowon tutoring program; and worked as an undergraduate intern in a university research lab. Through the Undergraduate Research Program, I explored geometric ideas in two projects — one on the rotation of manifolds with fixed points (2019), and the other on understanding Riemann’s doctoral dissertation (2020). These experiences deepened my appreciation for mathematical rigor and ultimately led me to commit to graduate studies at my home institution.

From January 2020 to the end of 2021, I devoted myself to a group study on topology and believed — perhaps mistakenly — that I had worked through all the major problems. In September 2020, I entered the integrated B.S.–M.S.–Ph.D. program and began graduate coursework immediately, taking 12 credits in my first semester. Yet I quickly found myself struggling. I was a student who couldn’t fully grasp my advisor’s direction, often held firm to my own ways, and gradually began to lose sight of the distinction between “studying mathematics” and “doing research.”

Although I was active as a tutor in a campus reading program and joined a Riemannian geometry seminar as a tutee, I came to realize a major gap — not only in my conceptual understanding, but in my ability to express and communicate mathematical ideas clearly to others. I couldn’t verbally articulate even a basic definition of compactness, and I didn’t recognize that I had been relying on others in my study group to fill in the gaps I hadn’t grasped myself. I had failed to learn how to explain a proof, not just follow it. In hindsight, this was likely a reflection of missing practice during my undergraduate years.

A conversation with a Ph.D. student in complex geometry became a turning point. At the same time, I took a course in applied numerical analysis and faced, for the first time, the technical barrier of coding within mathematics. I began to ask myself: “What if this isn’t the right path for me?”

In early 2021, I made a pivotal decision to leave the complex geometry lab and shift toward a new research direction — one centered on data assimilation, time series decomposition, and applied mathematics for geoscience. It wasn’t a retreat, but a redirection toward a form of mathematics that suited both my strengths and my temperament. Since then, I’ve been presenting weekly in lab seminars and gradually deepening my understanding of methodologies such as Empirical Orthogonal Functions (EOF) and Cyclostationary EOF (CSEOF).

Starting in 2022, I entered a more stable phase of graduate study, transitioning from self-doubt to focused research. I learned how to write formal research proposals, passed comprehensive exams, and began working intensively on EOF and CSEOF methodologies. I revisited analysis with fresh eyes, started reading research papers systematically, and began presenting literature reviews weekly in lab seminars. During this time, I also engaged with data assimilation techniques such as 4D-Var, and gained exposure to scientific communication through assistant teaching roles in high school outreach programs.

In 2023, I deepened my analytical and computational skills. I solved all the exercises in *Data Science 01–07* using MATLAB, began learning information geometry, and explored links between time series analysis and probabilistic inference. Through various presentations — including the Sakura Exchange Program and Joint Mathematics Colloquium (JMC) — I introduced my research on sea ice variability, which I modeled using CSEOF decomposition. My internship at the Institute for Basic Science (IBS) helped me gain a deeper sense of ownership over my research.

By 2024, I was ready to formalize and articulate my academic vision. I began preparing my dissertation project, which focuses on the comparative analysis of EOF-Wavelet Neural Networks and CSEOF models in forecasting nonstationary geoscientific signals. I conducted regional-level simulations, developed hypotheses based on observed oceanic phenomena in the East Sea, and began compiling my theoretical framework through review-style manuscripts. As I explored digital twin frameworks, I also incorporated TDA (Topological Data Analysis) into my regional modeling pipeline.

In 2025, I am in the process of completing my dissertation and preparing my first formal research paper for archive submission. I have implemented hybrid neural architectures, refined the mathematical background of CSEOF, and presented my results at conferences including KSIAM and the Yeongnam Mathematical Society. I am also set to deliver an oral presentation at JSIAM, summarizing this multi-year comparative modeling effort as a unified mathematical approach to analyzing nonstationary spatio-temporal patterns in geoscience.