### "Search for Breakthrough by Mathematical / Mathematical Sciences Researches toward the Resolution of Issues with High Social Needs (Focusing on Collaboration with Wide Research Fields in Science and Technology)" (Set in FY2007)

#### 1. Title of the Strategic Sector

Search for Breakthrough by Mathematical / Mathematical Sciences Researches toward the Resolution of Issues with High Social Needs (Focusing on Collaboration with Wide Research Fields in Science and Technology)

#### 2. Relationship with the relevant strategic priority for science and technology

In relation to this Strategic Sector, it is referred to in the information and communication field of the promotional strategy by field as follows: "It is clear that any information and communication technology utilizes mathematical achievements. Strengthening the fostering of mathematical researchers is an essential policy for the progress of information and communication technology as well as science and technology in other fields for the next 30 years." In addition, in other fields including life sciences as well, the needs for mathematics are shown in the form of simulation or system researches.

Furthermore, the 3rd Basic Plan for Science and Technology says that "it is necessary to create an environment to encourage intellectual inspiration and integration among different fields by, for example, promoting R & D in which the wisdom of researchers required for problem solving can freely be brought together beyond the existing field classification in order to create new wisdom."

#### 3. Reasons, urgency, and needs from specialists and the industries for the priority over other strategic priorities for science and technology, etc

Considering the present situation of mathematical researches in Japan, the following characteristics can be found:

(1) Though Japan maintains a certain level of mathematical researches, there is no quantitative increase as seen from the number of papers. It is equivalent to the number in Europe, but far less compared with that in the United States (4-5 times than that in Japan).

(2) Promotion of mathematics hardly gets into the political limelight, and investment in mathematics in Japan is quite small compared with that in major countries in Europe and in the U.S. (The U.S.: approx. 40 billion yen, France: approx. 19 billion yen, Japan: several billion yen)

(3) More emphasis is placed on pure mathematical researches, and fewer researches on application are carried out in Japan.

(4) There are barriers among different cultures, including the difference in technical terms among fields, leading to difficulty in having contact points with researches in different fields.

Meanwhile, mathematics is a study that serves as a basis for various sciences and provides a breakthrough in R & D of many areas through collaborative researches with other fields. In the 3rd Basic Plan for Science and Technology as well, it is mentioned as follows: "When developing eight promotional strategies by field, they should be proceeded while paying careful attention to flexibly responding to these emerging / multidisciplinary areas and appropriately linking to innovations."

In fact, according to the questionnaire survey of industry-academic-government researchers of eight priority fields in Japan at National Institute of Science and Technology Policy, the answer that there are issues for which mathematics' contribution is expected accounted for 81%, showing high needs for mathematics.

Therefore, it is necessary not only to promote mathematics itself but also to immediately launch activities that can contribute to further development in different fields by utilizing the achievements in mathematics.

#### 4. Image of innovative achievements expected to be achieved under this goal (expected innovative outcome with specific examples), background, and social and economical imperatives.

With regard to the issues raised at present, truly innovative solutions (innovations) should be obtained through the processes of logical discussion, organizing issues and selecting approaches which lead to concrete solutions. This "logical discussion" had conventionally been made only with the knowledge within the field, and sufficient in-depth discussions were limited. By introducing mathematical approaches here, a breakthrough in organizing issues and in getting concrete solutions can be expected.

To this end, as seen from various technological innovation cases utilizing mathematical theories in the past (application of the fuzzy set theory into home electric appliances, etc. announced in 1965, application of the wavelet analysis into data compression, etc. in image processing announced in the early 1980s, etc.), the breakthrough should be realized, the innovations be created and improvement in economic and social values be planned by applying mathematical approaches into issues with high social needs including the development of new products.

#### 5. Research and development goal to be achieved during this strategic project (creation of knowledge as the source of innovation, technology seeds, technology concepts to be demonstrated etc.)

In order to build deeper cooperation between mathematics and different fields, it is desirable to flexibly combine activities to promote individual researches with theme setting based on the mathematical researchers' intentions first under certain conditions and those to cultivate collaborative researches seeking the possibility of cooperation with other fields, developing them into collaborative researches with other fields. In addition, in order to judge if the intended Research Subjects can effectively be solved by utilizing mathematics, it is necessary to make the best use of personnel also with a broad view of other fields on the side of mathematical researchers. To this end, the system as shown below should be established for collaborative researches between mathematics and other fields:

(1) To appoint mathematical researchers also with a view of different fields (Research Area) as research supervisors.

(2) To collect mathematical subjects in which development to other fields can be expected from mathematical researchers and advance the researches after selection by research supervisors.

(3) To hold workshops, etc. as places of exchange between researchers of mathematics and other fields, developing an atmosphere conductive to collaborative researches between mathematics and other fields.

(4) To make arrangements so that the research forms (individual researches / team researches) can flexibly be settled according to collaborative phases with other fields at the time of application by the research proposers.

#### 6. Scientific justification for research and development goal to be achieved during this strategic project (progress status of related research, potential for development of this field in the future and prospect that many outstanding research plans are proposed)

At the Department of Mathematics in Hokkaido University, they are working on the project "Mathematics Center for Advanced Researches" to invite mathematical questions from researchers who are carrying out advanced researches in various fields in the university as part of "the 21st century COE Program." This is an experimental project to try to search for clues for problem solving by brainstorming with mathematical researchers after obtaining information about the present situation of researches relating to questions from questioners. Fourteen questions have been provided so far. In the process of this project, not only direct solutions are found, but also the following results are obtained:

· Logical structures of the questions become clear following discussions with mathematicians

· Discovery of new mathematical issues and young human resources development with it (development into research themes for students)

· Development into collaborative researches

· Better understanding of the characteristics of each other's fields leading to gaining in breadth as researchers

As mentioned above, the advanced efforts in a university are achieving results, and the accumulation of successful cases for the development into collaborative researches of mathematical researchers with other fields can be expected with experiences of such projects as a beginning.

#### 7. Specific issues to be overcome in achieving this research and development goal, points to be cared , and any overlapping with existing policies, projects, etc.

With respect to collaborative researches between mathematics and different fields proceeded under this Strategic Sector, consideration should also be given to cooperation with the existing policies and projects by handing them over to R & D projects with the existing competitive research funds , etc. depending on the development phases.