Why did you become interested in mathematics?

I started seriously thinking about mathematics in high school. At the time, I was interested in a wide variety of things. After hearing about Eisenstein’s theory of relativity, I wished I could study Physics; after learning about mathematical models of the ecosystem, I wished I could apply this to make mathematical models of human society; I wished I could create a good Artificial Intelligence program and become friends; I thought about creating a language more accurate and descriptive than any natural language; I wished I could propose a perfect social system to achieve world peace; I wanted to write scripts for movies and novels – I really wanted to do everything. I felt that I did not want to restrict my options, and was looking for some feasible solution. Then, something happened which made me think that mathematics may be good.

It happened during a class in chemistry; I came across a differential equation describing the change in concentration of a substance during a chemical reaction. It was an equation I had just learned during a class in mathematics, but at first, I did not think much of it. Then immediately after, during a university biology class that I attended, when calculating the growth of a population of an animal in a certain ecosystem, I again encountered the exact same differential equation. “Wow!” I thought. Furthermore, I saw the same equation being used in an economics class. In other words, I found the exact same abstract mathematical equation used with a specific meaning in a wide range of fields. I was convinced that mathematics would be useful in doing anything.

This conviction was further enhanced by Hermann Hesse’s novel “The Glass Bead Game”(※). This novel is a story about the future and is written as a biography of a master of the “Glass Bead Game” – an intellectual artistic “game” created by integrating mathematics, laws of physics and chemistry, music, poetry and other forms of art. I felt that through mathematics, I would be able to understand not only phenomenon in chemistry, biology and economics, but also music, literature and other forms of art!

You said you noticed that mathematics was being used in many fields. What do you think now that you are an active mathematician?

Mathematics has the capacity to abstract and draw out the important essence of things and events. I believe that in this increasingly complex modern society, mathematics can play a major role by using its power of abstraction. For example, there are situations where people have so many different opinions that it may seem impossible to come to an agreement. However, if we think deeply about what each person wants to achieve, we may realize that in fact, the goals are actually very similar. Even in cases where specific methods or situations are so different that negotiation seems impossible, if we capture the problem in a sufficiently abstract way, we could achieve a common ground and begin to discuss how to solve the problem in a calm and rational manner.

Although mathematics itself mainly deals with such objects as equations and geometric figures, I am beginning to realize that the mathematical approach to problem solving, including the method of abstraction, is potentially a powerful instrument in solving real world problems.

To realize the full potential of mathematical thinking, I want to introduce to society many more people who have acquired through mathematics various methods of problem solving. Through this effort, I am hoping for example that an organization incapacitated by becoming too large and fractured may find a leader capable of abstracting the needs of the various branches of the organization and finding a unified goal to propel itself forward.

Therefore I would like for my students to learn not only techniques for solving specific problems at hand, but to properly learn very abstract mathematics. A specific solution to a concrete problem in many cases is harder to apply to other situations, and often the problem itself is difficult to solve because there may be many factors hiding the true problem. Abstract mathematics may at first appear difficult to understand, but its clarity and its applicability is spectacular!

(※) “The Glass Bead Game” is a novel by Hermann Hesse, a German writer.