Mathematics is a key player in the contemporary society. Apparently we are now confronted with a number of global and complex problems that we have never experienced before. Environmental issues, highly contagious diseases, global climate change, population explosion, information explosion, energy consumption, natural disasters, disparity,... They share a common feature that they extend over several different fields of science that have been so far established separately in the tradition. This is why interdisciplinary approaches are emphasized. However, conversation between different research fields is not straightforward in practice. Mathematics, as a universal language of science, is expected to more actively play a key role in the interdisciplinary fields. Indeed, mathematics has been a basic tool for logical concluding in every field of science. But we now expect slightly more in mathematics. Since the beginning of the 20th century the development of mathematics has changed qualitatively. The roots are axiomatization and abstraction, sometimes being criticized as mathematics only for itself. However, the accumulation of abstract concepts and results should be like a gold mine. Making a slightly patient effort of conversation, we are sure of a large profit to both sides. It is most noticeable that mathematics formulates analogy at various levels, which is certainly a strong tool not only for theoretical analysis but also for modeling. Stefan Banach said: a mathematician finds analogy between theorems, a better finds analogy between proofs, a further better finds analogy between theories, the best finds analogy between analogies.

The program "Interdisciplinary Mathematics Toward Smart Innovations," aiming at concretizing the above idea, launched out in 2011 with the five-year special support by Tohoku University. The major research disciplines are:

- 1) mathematical approach to material science
- 2) mathematical biology and life science
- 3) information communication technology
- 4) mathematical approach to social and environmental science

It is our hope that this program will bring us not only creative products but also active networks of researchers with different backgrounds, contributing to the global society. We thank all who encouraged us to plan this interfaculty program and sincerely hope further collaboration in all aspects.

Program Leader Prof. Nobuaki Obata