The mathematics of clear answers and the ambiguity of human society. Studying mathematics allows me to appreciate the merits of both.

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From Ohyu Gakuen Girls' Senior High School, Tokyo

During her junior and senior high school years, she loved learning about unknown fields and accumulated a wide range of knowledge and experience in both the liberal arts and sciences. When she considered her future path based on the joy of learning rather than her strengths and weaknesses, the path she chose was the world of mathematics. Her desire to learn continued after entering the Keio University Faculty of Science and Technology, and she enjoyed interacting with others beyond her department's framework, joining a debate club and studying abroad for a short period to avoid being confined to a science-only environment. She spoke to us about the encounters and discoveries during her university life that influenced her career path, such as her interest in social issues.

[*] Academic year at the time of the interview (August 2022).

My combined junior and senior high school had a liberal and open culture, so in addition to the artistic gymnastics club, I actively enjoyed experiences unique to student life, such as dancing in a volunteer group that transcended grade levels and club affiliations. I also shifted my focus to studying for entrance exams from my first year of high school, studying for about 15 hours a day on holidays, but it wasn't a hardship because I've always loved "knowing and noticing" things. I studied all subjects evenly, including those not used for exams like home economics and gardening, and I also visited museums when I could have hands-on experiences. I enjoyed connecting my knowledge with my experiences and accumulating them, and these experiences broadened my desire to learn, regardless of whether the subjects were in the liberal arts or sciences.

In terms of academic performance, my strengths were in liberal arts subjects like Japanese and English. However, I wanted to study subjects at university that would teach me the joy of learning. When I looked back on the subjects I had enjoyed most, the ones that stood out were mathematics and physics. I had heard from people around me that "in mathematics and science, the fields are clearly divided, so if you want to study what you're interested in, you should go to a place with a specialized professor." But I hadn't decided on a specific path—whether I wanted to study mathematics itself, use mathematics to study technology, or use mathematics to contribute to society. So, the Keio University Faculty of Science and Technology, with its many faculty members in various fields and its Gakumon system[*], was a great option. I also wanted to study at a comprehensive university where I could learn subjects other than science, such as Japanese and social studies, to develop the ability to think about things from a broader perspective. That's why I took the entrance exam for Keio University.

[*] The Gakumon system is a unique system at the Keio University Faculty of Science and Technology where students choose one of five "Gakumon" (academic fields) at the time of admission, gradually narrow down their areas of interest, and decide on their department when they advance to their second year. The Gakumon system was revised for students entering the Faculty of Science and Technology in the 2020 academic year, and some of the departments that can be chosen from each Gakumon have changed. Please refer to the link below for details on the Gakumon system.

University classes were a world apart from high school, so I feel it was important that I had a year to carefully consider my options under the Gakumon system. I chose "Gakumon 2 (now Gakumon C[*])," and I found the analysis classes to be incredibly enjoyable. I wanted to delve deeper into it, and my heart was already set on mathematics within two to three months of enrolling. The department is composed of people who are passionate about learning mathematics, so while I felt it was a different environment from what I was used to, the essence felt unchanged, perhaps because there were many passionate people in my junior and senior high school as well. Another characteristic is its small size, with only about 50 students in my year, compared to other departments. I feel that many of the students are like bundles of ambition, not satisfied with just one thing, but constantly thinking about knowing and exploring what lies beyond. [*] Gakumon 2... The "Gakumon" that, at the time of her enrollment in 2016, allowed students to advance to one of three departments: the Department of Mathematics, the Department of Industrial and Systems Engineering, or the Department of Information and Computer Science. The names and composition of each Gakumon were changed for students entering in the 2020 academic year.

I was a member of the Keio Debate Squad, an English competitive debate club. Since my junior and senior high school classes were all in English, speaking English had become a part of my daily life. However, I felt a gap between English as a school subject and English as a communication tool, so I was looking for a place to polish my English conversation skills. Also, since science majors have many required subjects and few opportunities to interact with liberal arts students, I thought that by choosing an environment with many liberal arts students, I would be better able to understand others' perspectives when looking at things. What was particularly impressive was when we were discussing social issues, there was someone who looked at the present day from a broad perspective, citing world history as a concrete example. I didn't know any world history at all and had to learn from the basics, like researching things on my own at night, but this stimulus also led to a desire to learn more about social issues.

In my second year of undergraduate studies, I participated in a four-week summer school at the University of Cambridge. The catalyst was my exposure to social issues in the competitive debate club. As I engaged in discussions, I realized I lacked a background understanding of social issues, so I applied for the study abroad program, seeing it as a chance to learn more practical things.

While studying abroad, I majored in "International Relations." I realized that mathematical thinking and approaches—such as clearly verbalizing the definitions I had learned to share preconditions and verifying things step-by-step to avoid leaps in logic—could be a kind of tool for thinking about social issues. Since I was interested not only in mathematics but also in society and people, the events during my time abroad became a catalyst for deciding my current path, as I realized I was interested in connecting mathematics and society. It was also an opportunity to be positively influenced, as I learned anew from the friends I met abroad that my opinions would not be understood unless I voiced them.

A class called "Basic Mathematics Seminar I" in my second year of undergraduate studies. We were randomly given practice problems in mathematics, such as calculus and algebra, which we then solved by consulting with our group and presented in front of everyone. For me, mathematics up to that point had been a passive process of solving practice problems on my own and having my answers checked on a test. But when it came to presenting, I needed the ability to explain things in a way that the listeners could understand. I learned anew in this class that understanding something yourself and conveying it to others are two different things, which has been useful in my current research. At the end of the presentation, we also had to answer any questions that were asked, so it was a good opportunity to develop the ability to respond flexibly.

I am researching a problem in number theory and algebraic geometry: "Calculating the proportion of equations in a specific family of equations that have rational solutions." To take one example, this includes problems like calculating the proportion of equations with rational solutions, such as x^2+y^2=1, within the family of equations ax^2+by^2=1, where a and b are considered over the range of all integers. In general, it is difficult to directly calculate the proportion of equations with rational solutions within a family of equations. However, for certain families of equations, the problem can be reduced to the proportion of those with local solutions. Therefore, in my current research, I am working on determining the proportion of equations with local solutions by focusing on the "periodic structure" of the equation family I am dealing with. The research process involves not only trial and error and hands-on work but also gathering evidence from books and papers and proceeding with the research based on opinions obtained through discussions with my academic advisor and lab members. In discussions, they properly pick up on aspects that I might lose sight of on my own, saying things like, "There's also this way of thinking," which leads to new discoveries. For me, conducting research may be close to the feeling of updating myself while incorporating the opinions and thoughts of various people.

I had taken Professor Bannai's classes before joining the lab, but the deciding factor was the topic of the "unit circle" that he talked about during my lab visit. I had known since high school that there are both a geometric approach, which involves drawing a diagram of the intersection of a line and a curve, and an algebraic approach, which involves solving a system of equations, to the equation of a unit circle. But it was a major discovery to learn that the same perspectives exist even in the advanced world of mathematics. I chose the Bannai Lab because I have loved being able to solve equations from a geometric approach since high school, and there were many things in number theory and algebraic geometry that I could only learn by joining his lab. I visited several labs, and all the faculty members looked so happy when they talked about their own research. I was reminded that being able to learn under people with such an atmosphere is one of the charms of the Keio University Faculty of Science and Technology. Professor Bannai also works at RIKEN, and I am now fortunate to be involved in research on operators using an algebraic approach there. Having such an experience after joining the lab has also been a valuable learning opportunity.

Having learned about examples of how knowledge of mathematical sciences is being applied to society during my study abroad and being strongly interested in being a "person who mediates change," I have chosen to pursue a career in the think tank industry. I sometimes hear stories of people with a mathematics background playing active roles in think tanks and other fields, and I hope that I, too, can create new approaches and organic reactions by using mathematical thinking. I believe the difference between liberal arts and sciences lies in how humans are involved. The ambiguous society in which humans are involved is built upon established theories, and both have their merits. I think society could become more prosperous if I can demonstrate that "this kind of math is used in places where people live comfortably."