Masato Kurihara, Professor, Faculty of Science and Technology, Department of Mathematics

Number theory is a study to explore the world of numbers, and has a history of over 4000 years. Integers may seem like a simple object for research, but new concepts and theories have been developed one after another, and today number theory has become a highly advanced and abstract theory. About 20 years ago when Fermat’s Last Theorem was solved, it became big news. Looking back, I loved numbers since childhood. When I was a junior high school pupil, I read several advanced books on number theory, and got to know various ideas, quite different from “mathematics” at school. I enjoyed these ideas as I felt they seemed close to the arithmetic of elementary school. However, I never thought I would become a researcher of number theory. After entering university, there was a moment when I realized that “mathematics" is a natural science. Certainly, mathematics is a science in which we explore “mathematical nature”. I saw this aspect at that time for the first time, and decided to explore the world of mathematical nature. Finally I became attracted to number theory and majored in it.

Recently, among number theory I am specifically researching Iwasawa theory, which is a theory created by Professor Kenkichi Iwasawa of Princeton University since the 1950s. Iwasawa theory has been studied around the world, including the U.S. and Europe. Unfortunately, the mathematical language that explains the world of mathematical nature is not easy to understand for usual people, so I cannot explain it well here. In short, Iwasawa theory clarifies the relationship of the number-theoretic objects such as the rational solutions of equations with the values of zeta functions, which are important analytical functions. In my recent research, I found out more refined and deeper relationship between number-theoretic objects with zeta values than before, and we furthermore make new conjectures, so our research is exciting as ever.

My laboratory is relatively large compared to other labs in the department of Mathematics. Mathematical research is international, so the students attend international summer schools and winter schools together, for example, held at Cambridge (United Kingdom) and Boston (U.S.A.). We also participate in conferences held at various places around the world. Some students have spent a few months studying at universities in London and Munich. We are all trying to make new discoveries with a global perspective.

Student’s Voices
Hibiki Tokio
First-year master’s program student, Graduate School of Science and Technology

Studying at Professor Kurihara’s laboratory

Under the guidance of Professor Kurihara, we study number theory, which is also called the “queen of mathematics”. When our professor provides us explanation in relation to knowledge we have already acquired, and when we can finally understand it, we all gain a sense of achievement beyond description. Lab members all get along very well, and other than going to the So-kei sen baseball games together, we also have a lab summer school. This year we gave presentations of what we studied. Except mathematics, we jogged around the lake at 6 a.m. and went climb Mt. Tateshina (2530meters high), despite the hangover from partying the previous night. It was a tough climb for me because normally, I hardly exercise, but the view looking down from the top of the mountain was exceptional. The process and joy of climbing the mountain seemed similar to mathematics, as we get to see the whole picture of a theory after struggling step by step to understand each proof.