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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
Performing large-scale computations on complex systems and visualizing and analyzing the results pose new mathematical problems. The solutions to these problems will require new engineering science developments in computer architectures and communications and visualization systems. Future generations of computers will challenge mathematics even more.1
The need for research linkages is well described in Science, Technology, and the Federal Government: National Goals for a New Era (NAS, NAE, and IOM, 1993):
Traditionally, science has been organized into specific disciplines. However, science, by its nature, is in continual flux. New disciplines emerge at the edges or intersections of existing ones. Old disciplines are transformed by new knowledge and new techniques, while new disciplines draw knowledge and techniques from the old.
Furthermore, many of the problems that scientists are now trying to solve require contributions from more than one discipline. For this interdisciplinary research to succeed, scientists must be able to extend their knowledge to new areas and work effectively as members of teams.
The performers and funders of research must allow these dynamics of science to drive its organization. They must remove barriers to emerging areas of research and encourage permeable institutional structures that allow for the flow of interdisciplinary opportunities.
To encourage new linkages between mathematics and other fields and to sustain old ones, the NRC appointed the committee and gave it the following charge:
. . . to examine mechanisms for strengthening interdisciplinary research between the sciences and mathematical sciences, with the principal efforts of the committee being to suggest what are likely to be the most effective mechanisms for collaboration, and to implement them through the Internet, widely circulated reports, and other dissemination activities, such as campus workshops convened by committee members [and to] examine implications for education in the sciences and mathematics and suggest changes in graduate training intended to reinforce efforts to strengthen the dialogue among the sciences.
The committee represents a cross-section of scientists and mathematicians from academia, national laboratories, and industry. The members' backgrounds encompass disciplines from the biomedical, life, physical, engineering, and social sciences, and from different mathematical sciences, including statistics and theoretical computer sciences. The methods used by the committee to arrive at the recommendations in this report include the following:
Examination of case studies documenting the value of cross-disciplinary work involving mathematical sciences;
Personal experience and interviews with peers, administrators, representatives of industry, federal agencies, and private foundations;
For a few specific examples of research areas ripe for advancement through cross-disciplinary efforts, see the National Science Foundation (NSF) white paper “Mathematics and Science,” by A. Chorin and M. Wright, available from the NSF Division of Mathematical Sciences.