# Message from the former Dean of the Graduate School of Mathematical Sciences

The former Dean of the Graduate School of Mathematical Sciences

**Takashi Tsuboi**

In mathematics, education and research are very closely related processes. On the one hand they aim at continuing the mathematical culture which we humans have been developing since more than 2000 years, in order to pass it on to the next generation. On the other hand, they also aim at working on the various new objects that appear incessantly from problems in real life, in order to create new mathematical approaches to these problems. These days, because of the marvelous advances in computer science, it has become possible to carry out a wide variety of numerical experiments. However, the actual way of doing mathematics is nevertheless still rather primitive, as it seeks to ensure the basic and fundamental facts of a theory, while verifying its logic step by step.

The Graduate School of Mathematical Sciences was established 20 years ago, by regrouping the departments of mathematics of the Faculty of Science and of the College of Arts and Sciences. Since the days of the former departments of mathematics, the Graduate School of Mathematical Sciences has trained talented people to acquire a firm basis in mathematics.

It is important to keep this traditional way of education and research in mathematics. However, it is also becoming increasingly important to have a good understanding of the relationship of mathematics to the other sciences or to industry. In the development that it experienced during the 20th century, mathematics has become increasingly formal and abstract. However, at the same time, this development in fact enabled mathematics to spread its area of application enormously. With the development of information technology in this century, theoretical computations have become reality and mathematics is being applied ever more frequently. This again supports a growing demand for active applications of mathematics to other sciences and industry. There is increasing demand, not only for applications of the present mathematical theories, but also for the creation of new applicable mathematical theories.

The Leading Graduate Course for Frontiers of Mathematical Sciences and Physics (FMSP), which has been chosen as a "Program for Leading Graduate Schools, Japan Society for the Promotion of Science and Ministry of Education, Culture, Sports, Science and Technology", is run by the Graduate School of Mathematical Sciences in close collaboration with the School of Science and the Kavli Institute for the Physics and Mathematics of the Universe. FMSP aims to foster global leaders who will be able to develop the mathematical sciences as well as to apply them to other sciences or industry and thus to contribute to society as a whole.

In the history of research in mathematics, demands from other sciences or industry often motivated the creation of new mathematics. Conversely, originally purely mathematical development also often found applications in other sciences or in industry. This important exchange continues to happen in various forms and continues to contribute to the development of mathematics, as well as to that of the other sciences and of novel applications in industry. We designed our FMSP program so that this exchange can be carried out naturally and such that the students will have a good understanding of the deep connections beween mathematics and physics, as well as of the far reaching interrelations beween mathematics and industry.

We very much hope that the students who understand the aim of this FMSP program will grasp the opportunities the various course works in this the program have to offer, and that this will enable them to establish a firm basis of mathematical knowledge, as well as to build experience in the deep connections between mathematics and physics or industry, such that they will be able to play an essential role in the future of our society.

January 2013

**Takashi Tsuboi**