Iwanami Science Library 327 Sugakushano Shian (A mathematician’s thought)

I am a mathematician. As someone who has been involved in research and education in Japan, I have a deep and profound interest in the environment surrounding Japanese universities, particularly national universities, in recent years. While there are many analyses, opinions, and proposals regarding the issues of scientific research in Japan and their potential solutions, I often feel that they differ significantly from the views I hold as a mathematician. Furthermore, since I received my Ph.D. nearly 40 years ago at a graduate school in the United States, I am also interested in international comparisons of educational and research environments between Japanese and foreign universities. However, my experiences and impressions often do not align with the widely held views in Japan regarding this topic.
 
Mathematics is the foundation of science and technology, yet contemporary mathematical research is rarely featured in mass media. Moreover, when mathematics is discussed in the context of promoting scientific research, it is often in connection with fields such as AI and data science. The way pure mathematicians conduct research remains largely unknown, even among scientists from other disciplines. Mathematics does not involve experiments, require large research budgets or necessitate extensive research teams, and it is common even for graduate students to independently plan and carry out their own research. In this sense, mathematics shares some similarities with the research styles found in the humanities rather than natural sciences.
 
Mathematics has attracted significant attention as a core educational subject in examinations. Many people hold strong negative views toward mathematics education and testing, and debates, particularly regarding the types of exams, are abundant. As someone involved in socially significant exams, such as the University of Tokyo entrance exam, I have many thoughts on these matters.
 
This book is written from these standpoints, and it shares my thoughts on mathematics, its research, and its education in today’s Japan. It does not discuss the content of mathematics itself. I generally enjoy reading and writing, and my website includes a wide range of works, from technical research papers in English to casual essays. This book was commissioned by an editor at Iwanami Shoten after viewing my work on the website and is based on a series of 23 articles I wrote for their monthly magazine Kagaku (Science). Judging from the online reviews and direct feedback, The book seems to have reached a broader audience than anticipated, which is gratifying. The views expressed are my personal opinions and do not represent the consensus of the University of Tokyo or the mathematical community. I hope that the book will provide readers a rare glimpse into the thoughts of a mathematician.
 

(Written by KAWAHIGASHI Yasuyuki, Professor, Graduate School of Mathematical Sciences / 2024)