The establishment of a "Base for New development of Mathematics to Science and Technology" proposed by the Graduate School of Mathematical Sciences, was adopted as part of the "21st Century COE" program in fiscal year 2003, for a 5 year period.
 The aim of this proposal is to establish an international stronghold for research and education in mathematics and its applications and thereby to strengthen our existing international research activities. Also, from a long term perspective and in line with the general philosophy of the Graduate School in Mathematical Sciences since its inception, an important goal is to educate researchers in mathematics such that they possess a broad and diverse outlook over the mathematical sciences.

 The contributions of mathematics to society have long been indirect, be it as the basic science or infrastructure that supports science in general or, as a means for solving problems that arise in a scientific context. However, since the advent of computing, new techniques derived from mathematical theories have become directly applicable to real-life technologies and high level mathematics has become an important tool in for example modelling. As we have now arrived at a point where patents can even be awarded on purely mathematical content, the demand for mathematical applications that fit tightly with needs arising in society has increased even more.

　However, it is quite common for the time span between construction of a mathematical theory and its eventual application to reach fifty or even a hundred years. It also often happens that applicable mathematics arises from purely intellectual and theoretical pursuits, in which actual applications were never really considered. It is therefore crucial that research in mathematics be conducted in a free-reining atmosphere, without being captive to a specific field or to a need for immediate applicability. On the other hand, if one disregards applications completely, it becomes impossible to respond to any particular needs that might arise in society.  In view of the considerable expertise in research and education in mathematics we built up over the years, we therefore chose to emphasize more applied aspects in the realization of our proposal.

 Our project is intended to act as an interface between research in applied mathematics and mathematical research in itself. At its centre one finds the strategic board, presided by the project leader, where all plans and proposals for the COE project are drawn up and decided. Subjugate to the strategic board we have 3 research divisions (‘structure’, ‘nonlinear’ and ‘global’) and the applied mathematics research groups which comprise all research in fields that are not yet well-established as mathematical science in Japan. At present there are 3 such research groups : in Finance & Actuary, in Nonlinear Phenomena and in Statistical Analysis and Computing.

 The project aims not only at increasing the likelihood of finding applications of mathematics in society,  but also at generating new mathematical disciplines (from an applied perspective) while systematically assuming the role of a junction between mathematics and its applications.

 So far we have employed 3 invited professors, more than 100 postdoctoral fellows and research assistants and we have invited an important number of foreign researchers. This allowed us to organize numerous COE related lectures, lecture series and student seminars. Each year we also organize public lectures as well as large scale international conferences. For example, during fiscal year 2005 we organized the 3rd COE international conference “Groups, Homotopy and Configuration Spaces” (5~11 July 2005) as well as a colloquium on “Analysis in Society and the Natural Sciences” (5 November 2005) aimed at the general public. We also employed a video technician, which will enable us to offer (live or recorded) video feeds of seminars, lectures or conferences over the internet.

 The Graduate School of Mathematical Sciences already bears the responsibility for all basic education in mathematics that takes place at the University of Tokyo. In the future we wish to play a major role in research and education in applied mathematics as well and we shall try to establish ourselves as an internationally recognized research centre in this field.