PRIMES: Junho Won's Story
Having read the experiences of other PRIMES students with the program and about their love for math, I can say that the way I became fond of mathematics is somewhat unique. Until in middle school, I had little exposure to pure mathematics. In fact, growing up in South Korea where the tradition of pure mathematics and its education are historically not as firmly established as in the United States which has dozens of leading institutes for mathematical research, I had few books and no persons or events early on that inspired me to pure mathematics. However, I had natural tendency to mathematics and mathematical sciences like other students at PRIMES. As long as I can remember I have spent most of my waking time reading books on physics and astronomy or the biographies of mathematical giants like Galois, Hardy, Ramanujan, and Erdős, and research of these mathematicians that were explainable to non-professionals. I self-studied analysis and number theory, which seemed the most accessible and interesting to me at the time, and delved into number-theoretic formulae including many eccentric and fascinating integrals by Ramanujan. I also recall trying to develop a not-so-rigorous theory of my own to explain the motion of an ideal rain drop under air resistance with success that I thought new and extraordinary, only to learn later about the theory of differential equations. Although I received many awards for competitions in sciences, what drove me in mathematics when I was young was the theory and thought exercises much more than contest problems.
Having this kind of unorthodox track for studying mathematics and fondness for building theory to explain mathematical structures or phenomena, I was elated to learn about PRIMES. Where else, I wonder, can high school students conduct original research with help from some of the leading professionals in the field? There are many math contests out there, but a year-long research program like PRIMES where very young students can make their own contributions to a field and learn so much mathematics is unique of its kind. Personally, I really loved the fact that I met with my graduate mentor, Chiheon, almost every week. We discussed so many problems and cases leading to some original results, but it was also simply awesome to build a strong personal relationship with someone who guided me so thoroughly and patiently through abstract concepts, and sometimes, just chatted (in Korean!) about random things. Also, given that combinatorial mathematics was rather new to me, he showed me why graph theory - the field for my project - is quite beautiful and initiated me to study topological graph theory. The problems we worked on were very simple-looking and yet sinisterly difficult due to the virtual non-existence of organized tools to tackle them (which were relatively young), but coming up with my own insights and ways to resolve problems was the day's delight. Although the transition to research mathematics has been rather tough, it slowly became part of me and changed me and my aspirations fundamentally, and now I can confidently say that I conceive of a career as a researcher.
All these said, if I am to pick the one most important lesson I learned from joining PRIMES, it is this: there are lots and lots of fascinating math problems out there (whatever you imagine, there are more) - and you can even make some of your own! Thank you PRIMES for showing me all these problems and the fun and beauty behind them at the level I could not previously imagine of. And if you really like problems, or contemplate on differential equations (rather than poetry) looking at rain drops, I invite you to join this extraordinary community of quirky, young mathematicians!
Junho Won worked on the project Highly non-convex graph crossing sequences under the mentorship of Chiheon Kim.
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