Discovering new ways to enjoy mathematics. Challenges driven by curiosity eventually lead to the next stage of learning.

Profile

From Koishikawa Secondary Education School, Tokyo

From a combined junior and senior high school that emphasizes science and mathematics, he went on to Keio University. He had been interested in numbers since childhood, to the point of memorizing the calendar layouts for each year, but with an eye on future employment, he entered the Faculty of Economics at Keio University. However, as he delved deeper into his studies, his interest in mathematics was rekindled, and he took on the notoriously difficult transfer examination. He is now in the Department of Mathematics, conducting research in "dynamical systems," a field of mathematics that originated from physics. While mathematics is often thought of as a solitary world of facing equations at a desk, he says that his image of it changed completely once he actually experienced it. We asked him about how he freely enjoys learning, including his self-taught mastery of Chinese, which he became interested in through a required second foreign language course, and his activities that make use of it.

[*] Academic year at the time of the interview (November 2020).

Thanks to the liberal school atmosphere, I had a lot of fun, dedicating myself to swimming and marathons while also exploring the city and having tea with friends after school. I also loved trains and other forms of transportation, so I enjoyed traveling alone with a map in hand, from Hokkaido to Kyushu. I might have studied a fair amount, but basically, every day was about immersing myself in what I loved.

When I returned to my alma mater for teaching practice to get my teacher's license after entering university, I was reminded that the school offered unique classes that fully reflected the teachers' personalities, rather than just following a set curriculum. Even when I was a student there, if I asked a teacher about something that went beyond the scope of the lesson, they would think about it with me during break time or let me do additional experiments. It was a school that responded to students' curiosity, which is why I think I naturally came to love studying independently.

In addition, I participated in the "Science Koshien," where teams of students from various high schools tackle problems in science, mathematics, and information technology. I also had opportunities to present research on combinatorics and geological strata in English under the guidance of a teacher. I believe the discussion and presentation skills I acquired through these activities have been quite useful in my undergraduate and graduate studies.

When I was in my second year of high school, my peers started thinking about entrance exams, so I went to a Juku and things like that, but I didn't really study for the exams very seriously.... I did get ahead of the class by studying on my own, and my friends who liked math and I would create and exchange problems, but that was just out of interest, not studying. I like to learn freely, but I lose motivation when I'm forced to do something, so it wasn't like I was intensely focused on "exam time!"

However, as part of my preparation for the national university entrance exams, I studied all five subjects and seven courses evenly. Among them, math and science didn't feel like studying; it was more an extension of my curiosity, because I liked them and wanted to know more. For the other subjects, I particularly liked world history, but I would read the textbook as a way to rest my brain, so I think I managed my time well. I can strangely concentrate better in a lively environment, so I often studied at a family restaurant or on a park bench (laughs).

To be honest, I was planning to apply only to a national university. I originally had no intention of attending a private university, so I had done almost no research, but I ended up taking the exam because I have relatives who graduated from Keio University and my parents encouraged me, saying the Faculty of Economics is strong for job hunting.

I ended up transferring from the Faculty of Economics to the Faculty of Science and Technology in my second year, so it turned out differently from my initial plan, but I was able to study in two different faculty environments and expand my personal network, so in the end, it was a very good thing. I think both faculties had an atmosphere that allowed for freedom in studying and extracurricular activities, which suited my personality.

I was in the Faculty of Economics for two years, and one of the triggers for my transfer was studying a field called "microeconomics." Learning how mathematical theories like calculus and linear algebra, which I had studied before, were applied in the real world paradoxically deepened my interest in mathematics itself.

I also took an elective course called "Introduction to Analysis," which involved intensive study of mathematics, and I really enjoyed that time. It was a small class, so I could ask the teacher questions immediately, whether during or after class, which might be similar to the environment in the Department of Mathematics. My desire to join a mathematics research group in the Department of Mathematics was firm even before I transferred, so I think my aspirations and my current research style were aligned from an early stage.

I had friends in the Faculty of Science and Technology who showed me their textbooks, and I had also audited classes there, so I was somewhat familiar with the study material. Since I was good at math, my friends from the Faculty of Science and Technology often asked me questions. I had already studied the physics and chemistry taught in the first year to some extent before transferring, so I only started studying for the exam the day before, basically reviewing my existing knowledge while looking at books in the library. Afterward, as I had hoped, I transferred from my second year in the Faculty of Economics to the second year in the Faculty of Science and Technology[*1], which led to my current research in "dynamical systems," a field of mathematics that originated from physics. The fact that I can conduct my research anytime, anywhere, as long as I have paper and a pen, really suits my lifestyle.

[*1] Second-Year Transfer Examination... This is a transfer examination for which Keio University students who have completed or are expected to complete their first year of study (excluding those in the Faculty of Science and Technology) and who are expected to be enrolled for at least one year after admission are eligible to apply. The application guidelines are usually released in early December, and the examination is held in February of the following year. For details, please see "Second-Year Transfer" on the Keio University Student Website.

I can't speak for the entire Faculty of Science and Technology, but my impression of mathematics changed significantly. I had always had a strong image of mathematics as something you study silently, hunched over a desk, but communication is very active among the people actually studying it. In particular, in the "common room," a shared space for the Department of Mathematics, discussions are lively, with everyone looking at equations, propositions, and their proofs written on the whiteboard, asking "Why is this?" or exclaiming "Oh, I see!" The common room brings together students specializing in various fields of mathematics (algebra, geometry, analysis, etc.), so when we need knowledge outside our specialty for research or reports, we can help each other out. It's reassuring, and it made me realize that mathematics is not necessarily something you do alone.

I'm studying Chinese, which I became interested in after taking it as a required second foreign language in my first year of my undergraduate studies. I already liked Chinese cuisine and Chinese music, known as C-pop, but when I traveled to China alone for the first time as a university student, I was thrilled that the Chinese I had learned was understood (laughs). I was also deeply impressed by the taste of authentic hot pot I ate on my trip, so after returning to Japan, I started working part-time at a hot pot restaurant where Chinese was spoken and at the bustling Tsukiji Market, which was popular with tourists, to combine my studies with practice. It was the perfect environment to learn a language while having fun. Before I knew it, I was even talking to myself in Chinese (laughs).

The second foreign language course only lasts for one year, but for those who want to learn more, there are classes at the Research Center for Foreign Language Education[*2] on Hiyoshi Campus. So, even after moving to Yagami Campus, I frequently commuted to Hiyoshi, and I am now learning Cantonese and Taiwanese in addition to Putonghua (Standard Chinese). I am also continuing to study Chinese by pouring my energy into on- and off-campus activities, such as launching the Keio University official club, the Chinese Language Society (HST), participating in the University Student Delegation to China, and reaching the finals of the All-Japan Chinese Karaoke Competition.

[*2] Research Center for Foreign Language Education... Established in October 2003, this organization aims to support and enhance foreign language education throughout Keio University. It meets the demands of students who want to study foreign languages more by offering "Special Courses," which can be taken regardless of one's faculty or graduate school, and "Open courses," which allow students to take foreign language courses offered by other faculties at Hiyoshi Campus. For details, please see the "Special Courses and Open Courses" page on the Research Center for Foreign Language Education website.

I am researching a field called "dynamical systems." In a dynamical system, where the state changes according to a set of rules, I investigate how numbers and points move over time. The "recurrence relations" you learn in second-year high school math are also a type of dynamical system, as the initial number increases or decreases according to the rule of the recurrence relation. Among these, I am particularly focused on a phenomenon called "chaos," where numbers and points appear to move randomly, like the roll of a die.

Basically, everything in our research group is self-directed. We each bring our own topics to every meeting, such as "I've researched this," or "I've read this paper." For a year and a half until September 2020, I was the only student in the research group, so I received one-on-one guidance from Associate Professor Takahashi, who is also my academic advisor.

Among my peers, dynamical systems seemed to be less familiar than other fields of mathematics, and there was an impression that its specific research content was not well understood, so very few people chose to specialize in it. The basis of the research is desk work with paper and pen, and we hold seminars about once a week to present what we've learned and deepen our discussions.

Recently, one more student joined, so our research group now has four members, including Associate Professor Takahashi and an assistant professor, but the style of each person writing what they've researched on the blackboard and sharing it for discussion remains the same. Unlike research groups in other graduate school majors, we don't need experimental facilities or equipment, so during the COVID-19 pandemic, I was reminded of the advantage of being able to do math research anywhere.

I'm still undecided between becoming a junior high or high school teacher and getting a job at a private company, so I'm still exploring my career path (laughs). However, I believe that the discussion and presentation skills gained in research, as well as the logical thinking process of forming and testing hypotheses, will be useful in any job. If I were to directly apply the mathematics I've studied for many years to my work, it would be as a teacher, but I'm also interested in the insurance and IT industries, as well as jobs related to railways, so I'm currently giving careful thought to my future path.