## Message from the Director

## Greetings

**Kenji Kajiwara, Director, Institute of Mathematics for Industry, Kyushu University**

October 1, 2022

The Institute of Mathematics for Industry (IMI), Kyushu University was established in April 2011 and celebrated its 10th anniversary in April 2021. During this period, IMI has grown into a unique institute in the world that combines and integrates deep and advanced mathematical research with the development of mathematics that responds to the needs of industry and society. In particular, I am proud to say that IMI is the best in Japan at conducting industry-academia and interdisciplinary collaborative research in mathematics. I succeeded as the fourth director of IMI in October 2022, and I am determined to further strengthen the IMI’s activities and accelerate its development. The IMI will further promote mathematical research, respond to the high needs of mathematics in industry, society, and academia, support the research activities of the mathematics community and related fields in Japan and abroad, foster young researchers who can contribute to solving social problems through mathematics research, and enhance international research activities with an emphasis on the Asia-Pacific area. Through these efforts, we intend to further develop the IMI as an international research center and contribute to the creation of a prosperous and sustainable society through the use of mathematics.

As is well known from the example of mechanics, which was developed in parallel with calculus by Newton, mathematics has historically developed with a high affinity to physics. Even today, for example, theoretical particle physics is developing while sharing its cutting edge with mathematics. In the field of engineering, one of the basic styles is to analyze the physical laws governing phenomena using theoretical or numerical methods after modeling them with differential equations, and then to proceed with understanding by comparing the results with experimental and measurement results. The mathematics used in this field has traditionally been called “applied mathematics” or “industrial mathematics.” Their importance has not changed, but the situation has changed dramatically since the beginning of this century, especially with the spread and utilization of big data and the development of AI-related technologies such as machine learning, which has led to a major development of the field called “data science”. In addition to statistics and probability theory, mathematics such as algebra, geometry, discrete mathematics, and foundations of mathematics, which have not been used much in the past, are now directly utilized in this field without going through physics. Through such efforts, it has become increasingly understood that abstract pure mathematics is useful not only in data science but also in formulating and solving various problems due to its universality, and is indispensable for the future development of society and science and technology. In fact, the Sixth Basic Plan for Science, Technology and Innovation, the basic document of the government’s science and technology policy approved by the Cabinet in March 2021, repeatedly mentions the importance of mathematics and the development of human resources to support it. In terms of research funding, the MEXT’s Grants-in-Aid for Scientific Research, which is strongly geared toward the promotion of basic science, as well as the Japan Science and Technology Agency’s application-oriented “Strategic Basic Research Programs” and “JST-Mirai Program,” and large-scale research projects such as the “Moonshot R&D Program,” which attracted public attention some time ago for its scale, have adopted mathematics-based projects. This is something that has never happened before, and it is a sign that expectations for mathematics are rising.

Mathematics for Industry (MfI), which is the name of the institute, is a new research area in mathematics that will serve as a foundation for the creation of future technologies, and is created by integrating and reorganizing pure and applied mathematics into a fluid and versatile form while responding to the demands of industry. Based on the idea of MfI, the most important mission of IMI is to contribute to society by identifying research problems from real-world problems and constructing new mathematics that is useful for solving those problems, and to promote mathematics that is attractive enough for mathematics researchers to want to work on. To this end, the first priority is to promote deep mathematical research that is both fundamental and advanced. In addition, we promote the active involvement of mathematics researchers with a variety of interests, both pure and applied, in joint research in different fields and in industry and academia. In this context, we will enhance the activities of the Division of Industrial and Mathematical Statistics, which was newly established in April 2022, and strengthen research in fields related to statistics and data science, which are in high demand from society.

IMI aims to further promote organized collaborative research by strengthening its support functions for tasks that mathematics researchers have difficulty with, such as matching research projects between industry, academia, and different fields, joint research contracts, and intellectual property management, in order to expand mathematics research into society, industry, and various scientific fields. In addition, we will expand the IMI technical consultation service and the network of 12 cooperative research centers established through the “Advanced Innovation Platform for Mathematics” (AIMaP, FY 2017 – FY 2021), a project commissioned by the Ministry of Education, Culture, Sports, Science and Technology, and link them to the functions of the Joint Usage and Research Centers described below, to We will establish an all-Japan system to collaborate with industry, society, and various scientific fields.

IMI has been recognized as an ” Joint Research Center for Advanced and Fundamental Mathematics-for-Industry” by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) since 2013, and has supported the research community through the joint research programs such as conferences, short-term joint research and short-term visiting research. The center will continue to establish a system that can more actively incorporate the opinions and needs of the research community and industry in mathematics and other scientific fields and reflect them appropriately in its programs, and to operate flexibly. In addition, we will further strengthen the activities of the Joint Usage/Research Center by incorporating Joint Usage research participants into the above network.

Human resource development is also one of IMI’s most important missions, and since its foundation, IMI has collaborated with the Faculty of Mathematics to provide education in the Department of Mathematics in the Faculty of Science and the Graduate School of Mathematics, as well as in specialized undergraduate mathematics courses in the Faculty of Engineering. The IMI has been conducting long-term doctoral internships in cooperation with the Faculty of Mathematics since before the IMI was founded, and Kyushu University was the first in Japan to do so. The Study Group Workshop, a short-term intensive problem-solving camp for problems arising in indutries and various scientific fields, is a well-established first step in industry-academia and interdisciplinary collaboration, and provides a valuable opportunity for young researchers such as graduate students to experience collaborative research. In addition, the Joint Graduate School of Mathematics-for-Innovation, jointly operated with the Graduate School of Economics and the Graduate School of Information Science and Electrical Engineering, has been selected by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) as a WISE Program, and aims to foster human resources who can create innovation in various fields of science and industry by utilizing mathematics. The program also offers unique educational programs, such as joint research at laboratories in different fields, and internships that are mandatory. In addition, IMI contributes to undergraduate education through the Kyushu University Center for Education and Research in Mathematical and Data Sciences, and is also considering offering tutorials on data science and statistics for young researchers inside and outside the university and in companies. In this way, IMI promotes human resource development in various forms.

As a basis for international collaborative activities, IMI established the Asia Pacific Consortium of Mathematics for Industry (APCMfI) with the support and cooperation of mathematics research institutes in the Asia-Pacific area, aiming to establish a third pole of industrial mathematics in the area along with Europe and the United States. As one of its core institutions, IMI has established the IMI Australia Branch at La Trobe University (Melbourne, Australia), which is staffed by a full-time faculty member. Taking advantage of this framework, IMI has already held more than 60 online joint seminars with La Trobe University on a regular basis. It has also sent the graduate students and academic staffs to the Forum “Math-for-Industry”, an international annual conference sponsored by APCMfI and hosted on a rotating basis by member institutions, and the annual conferences of the Australia New Zealand Industrial and Applied Mathematics (ANZIAM). In particular, graduate students from the Graduate School of Mathematics have received the Young Scientist Outstanding Lecture Award at ANZIAM. An IMI member also participates in the Japanese delegation to the International Council for Industrial and Applied Mathematics (ICIAM), which oversees the world’s applied and industrial mathematics societies. Through these activities, IMI strives to enhance its presence and expand its international research activities.

Since its establishment, the IMI has been the first research center for industrial mathematics in Japan, thanks to the leadership of its three directors, Masato Wakayama (April 2011 – September 2014), Yasuhide Fukumoto (October 2014 – September 2018), and Osamu Saeki (October 2018 – September 2022), and the efforts of the members. We would like to express our deepest gratitude to Kyushu University, academic research institutes in mathematics and related fields in Japan and abroad, companies, local governments, and government agencies such as the Ministry of Education, Culture, Sports, Science and Technology, which have shared the idea of MfI and made it possible. We sincerely hope that all concerned will continue to support us.