![リガクル[RIGAKU-RU] Exploring Science](/ja/rigakuru/images/top/title_RIGAKURU.png)
Hiroyasu Miyazaki is a senior researcher at NTT Communication Science Laboratories. Inspired by a conversation with a high school friend, he ventured into the world of mathematics, pursued academic research, and now explores another new frontier: a corporate laboratory. What is the underlying philosophy that steered Miyazaki’s decisions at career crossroads?
Encountering mathematics, the language of numbers
Miyazaki knew he wanted to major in mathematics from the moment he entered university, thanks to an exchange with a friend in high school.
“I had a friend in high school who was incredibly gifted at math. He had a thorough grasp of linear algebra and calculus, was completely self-taught, and had read every math book in the library; that is how “wicked smart” he was.”
One day, this friend asked him what he thought an integral was. Miyazaki answered using his high-school-level knowledge acquired in class, but his friend explained it using university-level mathematical terms such as differential forms.
“I had no idea what he was talking about. I felt a bit bitter.”
Motivated to action, Miyazaki opened a university-level math textbook. There, he found a world completely different from the mathematics he had learned in high school.
“Linear algebra, sets, and topology… Of course, I could not understand everything at first. However, after reading it repeatedly, I somehow managed to comprehend the material. The content was different from the school math I had learned. It was about carefully constructing logic and concepts with words. At that moment, I realized this was the kind of math I liked and quietly decided to pursue it further.”
From complex analysis to arithmetic geometry, curiosity weaves together the path of exploration
Miyazaki was captured by the beauty of the theory of complex analysis. So much so that he planned to pursue a career in complex analysis at the time. However, a turning point during his senior year in college changed the shape of his future career.
“There was a reading class where a small group of students read a book together. In that class, we read the mathematician Jean-Pierre Serre’s renowned book Cours d'Arithmetique. In the latter half of the book, there was a section about applying complex analysis techniques to number theory, which I found fascinating.”
Miyazaki decided to give number theory a try, just for fun. Such a casual start led him into the vast and deep world of arithmetic geometry.
“Complex analysis is a theory that studies the properties of functions in the world of complex numbers. When you get immersed in this world, you end up studying geometric objects called Riemann surfaces*. The worlds of functions and geometry are connected. My current field of study, arithmetic geometry, was inspired by this and is based on a similar idea, trying to link number theory to the study of geometric objects called “schemes.” As I delved deeper into arithmetic geometry, I became completely captivated by its charm. Although there was a shift away from the complex analysis I had originally intended to pursue, to me it felt like a smooth transition.”
Functions, space, and integers. At first glance, these seem completely unrelated worlds, but they are intricately connected. At the core of this connection are “motives,” Miyazaki's research focus. It is the field that ambitiously attempts to find the universal structures underlying various discoveries across different mathematical fields. Miyazaki describes this as “an abstract painting made up of numbers, shapes, and categories that interweaves the common patterns hidden behind disparate mathematical discoveries.” Captivated by the depth of these relationships, Miyazaki's exploration began.
From academia to industry: blazing a new trail for mathematicians
After completing his doctoral program, Miyazaki continued his research as a postdoctoral fellow. With the encouragement of his advisor, he decided to pursue further research in France.
“My advisor, Professor Shuji Saito, encouraged me to go abroad. I went to the Mathematics Institute of Jussieu–Paris Rive Gauche (IMJ-PRG), which had several parent institutions including Paris VI at the time. There, I noticed that their approach to problem-solving, from framing a problem to choosing what to focus on while working, was completely different. Experiencing this difference left a strong impression.”
Moreover, in a community of Japanese mathematicians, it is easy to end up thinking and working in the same manner. By immersing himself in a different environment, Miyazaki also realized that the ways of thinking and techniques he had taken for granted were, in fact, unique strengths.
“When I, as someone who did their undergraduate and graduate studies in Japan, would find a certain problem interesting, people would often respond that they had never thought of it that way. This made me realize the strengths of the environment I grew up in and the situations in which these strengths could be leveraged.”
After returning to Japan, Miyazaki continued his research at RIKEN. Then, he came to another major turning point in his career. He was invited to join the newly established “Institute for Fundamental Mathematics” at NTT Communication Science Laboratories. It was an ambitious project, virtually unprecedented worldwide, to explore fundamental mathematics within a corporate setting.
“To be honest, I initially doubted whether it was possible to conduct pure mathematics research within a corporate setting. Moreover, I had just begun to put effort into expanding the community of mathematicians within RIKEN, so I was torn about the timing of the move.”
Ultimately, what pushed Miyazaki to accept the offer was a sense of duty to explore the possibilities of pure mathematics in a new environment.
“If I had turned down this opportunity, this intriguing endeavor might have disappeared. So, I decided to take the plunge, at least to lay the groundwork for a place in the corporate world where mathematicians can thrive.”
You should study things “irrelevant” to your research
Miyazaki finds joy in expanding the mathematics community and trying to fulfill its potential. At the core of this is his belief that communication across disciplinary boundaries brings new value not only to himself but also to the world of mathematics.
When people think of mathematical research, they perhaps imagine a solitary researcher sitting at a desk in silence. However, according to Miyazaki, this is far from reality.
“Mathematical research is actually a very social activity. During my student days, my friends and I would organize seminars and engage in hours-long debates over a single paper. Trying to explain things to others helped me notice areas where my understanding was shallow, ultimately leading to deeper comprehension. Dialogue with others is indispensable for exploration.”
This experience has become the foundation of Miyazaki's philosophy.
“The ways of thinking that mathematicians use effortlessly are not necessarily commonplace in society, but they can be extremely powerful tools. When engaging in dialogue with people from different fields, reinterpreting their unique intuitions in mathematical terms can lead to unexpected solutions to problems.”
Reflecting on his own experiences, Miyazaki offers warm encouragement to students aspiring to become future researchers.
“Do not be constrained by others' judgment or conventional wisdom. Follow the path you truly find interesting and make choices you will not regret. Do not decide on a fixed career path, but instead carefully build upon choices that excite you at each stage. I encourage you to proactively learn even things that seem irrelevant to your specific field of expertise. The knowledge you will truly need in the future may lie within what you now consider irrelevant.”
*Riemann surface: A structure created by pasting together the complex plane according to certain rules, making multivalued functions appear to behave like single-valued functions.
Year of interview: 2025
Text by HORIBE Naoto
Photos by KAIZUKA Junichi
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