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Campus Now

Autumn Issue (Nov.)

My study,My career

Introducing female researchers active at Waseda University.

Waseda 150 Vision defines the ideal form of our university as we move toward our 150th anniversary in 2032.
One aspect of the vision is "Waseda research which contributes to world peace and the happiness of mankind." As we work to achieve this goal, we expect new perspectives and ideas to be introduced through the activities of female researchers. In this 3rd installment, we spoke with Professor Yumiko Hironaka.

Conveying to students the appeal of ever-developing mathematics

Professor Yumiko Hironaka
Faculty of Education and Integrated Arts and Sciences

The appeal of number theory: Expanding the range of thought through accumulation of theory

I have always been surrounded by researchers. My father specialized in law and my grandfather conducted research in minerals. It was only natural for me to pursue research of my own. Although I was interested in a variety of fields, one reason for my selection of mathematics was that I wanted to do something different from my parents. Even so, law and mathematics are quite similar in regards to the need for logical thinking.

Although mathematics is often regarded as an abstract discipline, there are actually many models in nature. I logically explore how to express natural phenomena through a mathematical formula, as well as how to calculate answers to those formulas. The field of number theory can be described as interpretation of problems which originate in integers. For example, consider a linear equation such as 2X + 3 = 15. The only possible answer to this equation is 6. However, in the case of an equation such as 2X + 3Y + 5Z = 15, the increase in unknown numbers creates a large degree of freedom in the answer. Numerous variations can be created by heightening the degree or increasing the number of variables. Amidst such conditions, the appeal of number theory lies in expanding the range of thought by estimating results and accumulating theory.

Foreign study in Germany: Broadening my perspective through advanced research

I experienced many difficulties in forming a career as a researcher. However, I don't find much meaning or enjoyment in dwelling on such difficulties. Rather, it is better to spend life reflecting on positive experiences. When I was in my 30s and 40s, I conducted research at universities and research institutions in Germany and France. The experience was very surprising and instilled me with a variety of new knowledge. Compared to Japan, there are many female researchers in France. Women accounted for about 30% of all researchers at the mathematical research center where I was stationed. The presence of female researcher was completely normal. Also, normal French people seem to have less of an aversion to mathematics when compared with Japanese people. People in France were not at all taken aback when I talked about my research in mathematics.

The first time that I gave a research presentation overseas was in 1990 at the Mathematical Research Institute of Oberwolfach in Germany. The institute contains lodging facilities, so researchers gather from throughout the world for a research conference which spans several days. The friendship between researchers increases as a result of eating and lodging together. Seating for breakfast and dinner was shuffled every day. I remember trying my hardest to speak in poor English with researchers seated at the same table. I was sometimes seated next to directors of famous research institutes. The greatest merit of going overseas is the opportunity to come into direct contact with advanced research. Thanks to connections which I made by attending the research conference, I was invited to work as a visiting researcher at the University of Gottingen in Germany for 1 year. The University of Gottingen has a long history in the field of mathematics. It was an honor to have the chance to conduct research and give lectures at such a venerable institution. At the same time, it helped me to expand my academic perspectives. I still keep in touch with personal connections that I made through my affiliation with the university. I conduct joint research through email and meet about once per year for direct discussion with other researchers. We also invite each other to give lectures at our respective institutions. Recently, it has become easier to go overseas, so I hope that young people will travel abroad as much as possible. There are some things which can only be acquired outside of Japan.

Cultivating outstanding researchers by conveying the appeal of mathematics

The majority of students seem to believe that mathematics is already a finished field. Therefore, when teaching class, I try to give easy examples to show how mathematics continues to grow and how many things are still not understood. For example, there are still many unsolved problems regarding prime numbers. Consider alternate numbers such as 3 and 5 or 11 and 13. Do such numbers continue on infinitely? Is an end reached somewhere? The answer to such questions is still unknown. Also, even if we understanding that infinitely large prime numbers exist, it is a completely different matter to actual comprehend such numbers. Even today, many computers are working to find new and larger prime numbers. Every year, I check the largest prime number which is currently known and discuss it with students. Right now, the largest prime number requires approximately 13 million decimal places to be fully written. Through such examples, I hope that students will recognize the mysteries and appeal of mathematics. When student become working professionals some day in the future, I hope that they will tell others around them about how mathematics is an interesting field that continues to grow. If the number of people who enjoy mathematics increases, then the level of mathematical research in Japan will also rise and we will be able to cultivate outstanding researchers.

Finally, another hope of mine is for a society in which people are sympathetic towards someone who is working intently towards a goal. I hope for a society in which we can all recognize and accept our differences with others. I would like to see more people who possess conviction in their own action, even if it differs from the action of others.

Mountain climbing is a great way to relieve stress! (Swiss Alps)

With Professor Klingen, director of the academic conference (Germany, 1990)

Professor Yumiko Hironaka
Faculty of Education and Integrated Arts and Sciences

Graduated from the School of Science, Tokyo University of Education. Completed the Master's Program at the Ochanomizu University Graduate School. Completed the Doctoral Program at the University of Tsukuba Graduate School. In 1982, employed in the Faculty of Science, Shinshu University. In 1998, assumed her current position of Professor at Waseda University. Has conducted mathematical research at overseas institutions including 1 year at the University of Gottingen in 1992 (Visiting Researcher), 6 months at the University of Mannheim and the University of Heidelberg in 1996 (researcher deployed by MEXT), and Strasbourg University and the University of Mannheim in 2005 (research leave from Waseda University).