Students who are selected by the Japan Society for the Promotion of Science (JSPS) for a Research Fellowship for Young Scientists receive research subsidies and/or fellowship grants (Grants-in-Aid) for a period of two to three years. The research grants can be used for any purpose, and fellows can receive a maximum of 1.5 million yen per year by applying for a Grant-in-Aid. Of course, JSPS Research Fellowships for Young Scientists are highly competitive, so not everyone who applies will be accepted. This time, we sat down with Kaori Yamaguchi, a second-year doctoral student in the Graduate School of Science and Engineering, who earned a DC2 fellowship in 2025 after completing a RARA Student Fellowship.

Inspired by the beauty of how mathematics is tied to the natural world

―― As early as your first year in the master's program, you had already decided to pursue a doctoral degree. What was it that first sparked your interest in pure mathematics?

Yamaguchi: Looking back, I would say the starting point was the golden ratio that I learned about in elementary school. I though mathematics was something logical, but it is actually tied to the natural world, and you can use mathematical theories to explain natural phenomena. This was a surprising revelation, and I think this was the first time that I felt inspired by mathematics.

―― So, have you focused on nothing but mathematics since then?

Yamaguchi: That was not necessarily the case. I was not comfortable with the mathematics of examinations, where all you are supposed to do is get the answer right as soon as possible. Nevertheless, in my first year of high school, I was given the opportunity to join a seminar in which we studies university-level mathematics. That is where I first encountered Euler's formula, and I was enthralled. Even though trigonometric and exponential functions are taught as separate concepts in high school mathematics, this formula links the two functions using the imaginary unit “i.” I still vividly remember being moved; I wondered what this was all about.

* Euler's formula: e is the base of the natural logarithm (Napier's number) and i is the imaginary unit

―― Is that when you decided that wanted to focus solely on mathematics and pursue higher studies?

Yamaguchi: Yes. Although I made the decision that was right for me, I still could not get used to the mathematics of examinations. Still, I wanted to delve into mathematics at university, so I chose the Department of Mathematical Sciences in the College of Science and Engineering at Ritsumeikan University, which has a long tradition of excellence in mathematics. After joining Ritsumeikan, I immersed myself in mathematical research. I really enjoyed reading between the lines of my math textbooks and digging deeper into the ideas presented by my professors while listening to their lectures.

Making complex, high-dimensional data simpler and easier to understand

―― What kind of discipline is information geometry, which was the topic of your graduation research thesis?

Yamaguchi: To use an analogy, it is a field of mathematics in which information, specifically probability and statistics, is understood in the form of diagrams and other illustrations. It was founded by Professor Emeritus Shun’ichi Amari of the University of Tokyo, and it views things from the perspective of differential geometry, a sub-discipline of geometry. To give you a general description, coarse geometry rests on the idea that the set of real numbers and the set of integers are considered as one and the same. If you strictly interpret the number line, the real numbers are all the numbers on the line, and integers do not include things like decimals, fractions, and irrational numbers. So, this means real numbers are not the same as integers, but from a distance (say, on a larger scale), both appear to be straight lines. I am exploring how this idea can be applied to information geometry, by viewing information in coarse-grained manner.

―― Okay, this is a difficult topic. It is not easy to visualize...

Yamaguchi: Perhaps it will be easier to understand if we focus on what kind of information is needed. For example, let’s consider the case of sending information about space from a satellite in space back to Earth. If you try to send all the data, the amount of data will be so large that it will need to be compressed before sending. However, when data is compressed, some of the original information is lost. Therefore, you have to consider what the information that has been sent will be used for. If you are going to conduct some kind of analysis, even if some parts are left out in the process, as long as the essential information is there, it can still be useful enough. In this way, you can use this idea of “coarse-graining” from coarse geometry to simplify information, that is, probabilities and statistics, as needed.

―― We were told that you came up with and presented a new concept in the field of information geometry.

Yamaguchi: In the second year of my master's program, my advisor, Professor Hiraku Nozawa, and I came up with the new concept of the δ-almost sufficient statistic and presented it at a conference. The concept of a almost sufficient statistic, which is not a sufficient statistic in the strict sense but has properties similar to those of a sufficient statistic, had been around for some time, but it had not been fully applied. So, we applied additional geometric ideas to this concept and defined it quantitatively and rigorously as the δ-almost sufficient statistic. Thankfully, this presentation generated interest, and we have since been invited to Hokkaido University, Nagoya University, Waseda University, and other universities to give lectures on the δ-almost sufficient statistic.

Working in a field that is neither pure mathematics nor statistics

―― Had you already decided to advance to a doctoral program when you entered university?

Yamaguchi: No, not necessarily. However, when I was an undergraduate student, the COVID-19 pandemic struck, and I went through an emotionally difficult time. What saved me from suffering was mathematics. Being able to immerse myself in mathematical research helped me get through those tough times. So, I began to think that researching mathematics was my identity, and I wanted to continue to do even more research. As soon as I became a first-year master's student, I found my lectures and seminars so enjoyable that I did not want this joy to end after only two years. But to be honest, I thought it would be financially difficult for me to continue on to a doctoral program. That’s when I met a senior colleague from another laboratory who told me about the RARA Student Fellowship and JSPS. I decided that I had no choice but to get accepted and go on to a doctoral program.

―― What points did you pay attention to when writing the application forms for the RARA Student Fellowship and the JSPS Fellowship?

Yamaguchi: The content of my applications was quite difficult to understand, so I included conceptual diagrams and bolded the important parts. The jargon used in mathematics is quite specific, so I tried to keep the text structured so that the reader could follow the theory even without knowing the terminology. Another point to mention is that different people are involved in screening the RARA Student Fellowship versus the JSPS Fellowship. Therefore, assuming that the reviewers would have a certain level of understanding about mathematics and that my application would be read by a mathematics professor, I wrote the JSPS application in detail, mixing in some specialized terminology.

―― What do you feel are the benefits of being a RARA Student Fellow?

Yamaguchi: Unfortunately, I was not accepted for a DC1 fellowship, but I was selected as a RARA Student Fellow, so I entered the doctoral program, where I have had a very productive time. More than anything, it gave me a real sense of mental reassurance. The RARA Student Fellowship gave me the opportunity to think about career paths for women, and that is where I met people who would become my role models. There are very few women in mathematics, so this was a truly invaluable opportunity. Since you can basically delve into mathematical research on your own, you are expected to be your own mentor. That is why meeting so many different people as a RARA Student Fellow has been so stimulating.

―― You were selected for a DC2 fellowship after completing your RARA Student Fellowship. What kind of research do you plan on pursuing now?

Yamaguchi: I would like to contribute to both applied statistics and pure mathematics. This is because I think there is a little distance between these two fields and the strengths and interesting points of each are not fully shared with the other. Therefore, if I can make connections between these two fields, I should be able to create something new and meaningful. Furthermore, now that I have been recognized for presenting on the δ-almost sufficient statistic, a concept that did not exist previously, I would like to utilize it to contribute to society in some way.

Expressing yourself through mathematics and conducting research based on your sensibilities

―― Pursuing mathematics research on your own seems to take an emotional toll.

Yamaguchi: I am not an emotionally strong person, so I try to take care of both my mind and body. In the past, I was so determined to do my best that I sometimes pushed myself too hard, focusing more on how much time I put into my research than on sleep. However, I believe that research is not something you can do by pushing yourself to the limit; rather, it is something you have to pursue with more of a sense of excitement. Therefore, to ensure I can truly enjoy my research, I try to maintain my physical condition in the same way as an athlete, including watching my diet, exercising, and getting enough sleep. That being said, the only thing I can think of all day long is my research.

―― We were told that you had the opportunity to visit high schools and give a presentation on your research.

Yamaguchi: Yes. As a RARA Student Fellow, I’ve had opportunities to share my research with junior and senior high school students. The students asked very simple but essential questions, so it was a very stimulating experience. One of them asked me straight out, “Can mathematics research—especially a topic that seems incredibly difficult—really be useful in the real world?” While it is true that mathematics is not directly related to practical applications like machine learning, it can be a means of self-expression. It allows you to describe natural phenomena that you find beautiful from a scientific perspective. I think this is an important role of mathematics, and the more rigorously you can communicate your ideas, the more you can have discussions without prejudice. Perhaps I am exaggerating a bit, but I believe that humanity will progress by engaging in these kinds of in-depth discussions.

―― What message do you have for students who want to become researchers?

Yamaguchi: Be it mathematics or any other field, I think research has a certain aspect of self-expression. The famous mathematician Dr. Kiyoshi Oka one said that “mathematics is an emotion.” So, first of all, you should value your own feelings, your individuality, and those things that only you can do. After that, if you apply for a RARA Student Fellowship, you will be sure to expand your horizons. RARA Student Fellows also engage in cross-disciplinary activities, and I have received a lot of helpful advice by interacting with people in disciplines other than mathematics. I hope you can all expand your horizons by pursuing research.