Because of its universal nature, mathematics has been viewed as a field that supports many areas of science. One obvious example is the role played by mathematics in thermodynamics theories that brought about the Industrial Revolution. But mathematical research has also given rise to a number of other new fields, including computers, mathematical finance, and complex system. These examples show that mathematics research has the potential of changing the entire face of our society.

While Japan takes pride in its world-leading research quality of mathematics, mathematics itself tends to be seen in other disciplines merely as a practical tool for computation or a technique for applying formulas; in other words, its sophisticated logical thinking is less appreciated in other fields. This mind-set, we suspect, has led to the relative lack of public attention to the importance of mathematics in Japanese society, as opposed to the social significance attached to mathematics in other countries.

To address this problem, our program commits itself to laying the
mathematical foundation for *nonlinear structure*, a notion that
plays a crucial role in various fields of study, and thereby aims to
deepen ties with other academic disciplines. New mathematical problems
that emerge from this initiative will be systematically tackled in
dynamic research contexts ranging from basic to applied studies. This
framework will enable us not only to **deepen mathematical
research itself** but to **promote fundamental progress in
other fields**.