Mathematics and the sciences^{1} have grown up together, repeatedly interacting. Discoveries in science open up new advances in statistics, computer science, operations research, and pure and applied mathematics. These, in turn, enable new practical technologies and advance entirely new frontiers of science. Frequently, however, cooperation and collaboration between mathematical scientists and scientists have come as a result of chance encounters. Often a scientific or technological problem exists for years before a mathematical scientist discovers it and recognizes it as interesting and mathematically tractable. Similarly, scientists have frequently expended energy “inventing” mathematical solutions that existed for decades but were not familiar to them from their training.

To encourage new linkages between the mathematical sciences and other fields and to sustain old linkages, the National Research Council (NRC) constituted a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. Its task was to “examine the mechanisms for strengthening interdisciplinary research between the sciences and mathematical sciences, with the principal efforts being to suggest what are likely to be the most effective mechanisms for collaboration. . . . ”

The committee believes that the benefits to be derived from cross-disciplinary^{2} activities linking the mathematical sciences with science and engineering are indeed huge and far reaching. Its recommendations can be found in Chapter 4. The main elements of these recommendations are summarized here.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
Executive Summary
Mathematics and the sciences1 have grown up together, repeatedly interacting. Discoveries in science open up new advances in statistics, computer science, operations research, and pure and applied mathematics. These, in turn, enable new practical technologies and advance entirely new frontiers of science. Frequently, however, cooperation and collaboration between mathematical scientists and scientists have come as a result of chance encounters. Often a scientific or technological problem exists for years before a mathematical scientist discovers it and recognizes it as interesting and mathematically tractable. Similarly, scientists have frequently expended energy “inventing” mathematical solutions that existed for decades but were not familiar to them from their training.
To encourage new linkages between the mathematical sciences and other fields and to sustain old linkages, the National Research Council (NRC) constituted a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. Its task was to “examine the mechanisms for strengthening interdisciplinary research between the sciences and mathematical sciences, with the principal efforts being to suggest what are likely to be the most effective mechanisms for collaboration. . . . ”
The committee believes that the benefits to be derived from cross-disciplinary2 activities linking the mathematical sciences with science and engineering are indeed huge and far reaching. Its recommendations can be found in Chapter 4. The main elements of these recommendations are summarized here.
1
The terms “mathematics” and “science” are used in their broadest sense: for the purposes of this report, “mathematics” means the mathematical sciences, which include pure mathematics, applied mathematics, statistics and probability, operations research, and scientific computing; “science” includes the biomedical sciences, engineering sciences, computer science, life sciences, physical sciences, and social and behavioral sciences.
2
For the purposes of this report, “cross-disciplinary” denotes interactions between the sciences and the mathematical sciences.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
FUNDING DIRECTIONS
The committee recommends that additional funding be allocated to initiatives that will strengthen existing linkages between the mathematical sciences and other sciences and that will build new linkages.
New resources are required if the nation is to realize the enormous potential of cross-disciplinary fertilization. However, a key premise of the committee's report is that the basic sciences and the mathematical sciences must remain healthy if cross-disciplinary research is to advance. Some disciplines will, accordingly, need additional funds to be capable of developing cross-disciplinary ties. Funding for cross-disciplinary research must not compromise support for basic disciplinary research or for individual investigators.
Chapter 4 contains detailed recommendations to funding agencies that will enhance multidisciplinary activities: support for summer institutes, workshops at existing research centers, and new science and technology centers. The committee also recommends fellowship programs of various types to sustain research scientists in their pursuit of compelling multidisciplinary ideas.
Case studies of math-science research linkages provide compelling evidence for the synergism between science and mathematics. They also elucidate the factors that made these cross-disciplinary efforts possible, as well as the barriers that inhibited them. Appendix A presents the 10 case studies and Chapter 2 discusses the lessons learned from them, with an emphasis on the obstacles to cross-disciplinary collaborations. Some obstacles are resource-related, and it is these obstacles the committee hopes to overcome with its recommendation on funding. Other obstacles are cultural: different disciplines have different goals, philosophies, and languages.
The committee found that many institutions have overcome barriers to cross-disciplinary research despite the obstacles and have flourished. Examples of such programs can also be found in Chapter 2. Moreover we can anticipate even more activity at the interface of mathematics and other fields in the future. Universities with vision are developing, at an increasing pace, new interdisciplinary programs that cut across traditional departmental and college boundaries; such programs are vital to the strategic planning of a university's educational and research mission. Mathematics can, because of its uniquely central role in science and engineering, play an important part in these plans for interdisciplinary growth.
CROSS-DISCIPLINARY INTERACTIONS
The committee recommends that academic institutions take responsibility for implementing vigorous cooperative programs between the sciences and the mathematical sciences.
As the examples show, departments and their faculty can actively pursue cross-disciplinary research opportunities and make changes in the curriculum that will give students cross-disciplinary skills. It is particularly important to develop effective criteria for the

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
evaluation of cross-disciplinary research to ensure that promotion, tenure, and reward mechanisms fully recognize the importance of quality cross-disciplinary research.
OVERSIGHT
The committee recommends that a new standing committee be established with a long-term focus on improving the linkages between the mathematical sciences and other sciences in both academia and industry.
A standing committee would have as its special mission the fostering and nurturing of such linkages by monitoring and evaluating successful initiatives and by communicating its findings to the community. The committee could advise funding agencies on how they might better evaluate cross-disciplinary research, advise private foundations on effective methods for supporting such research, and inform professional societies about multidisciplinary research opportunities and related educational opportunities. Some specific responsibilities for such a committee are suggested in Chapter 4.

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