The committee is not the first to consider the need for cross-disciplinary linkages and how to forge them. Many other efforts have focused on or considered the contributions that math-science linkages can make to the development and timely advance of frontier areas of research (Appendix C). It is difficult, however, to demonstrate quantitatively the need for further cross-disciplinary research links. Data on graduation rates, research funding, and other quantitative measures are routinely collected for the various individual disciplines but would be difficult to collect for cross-disciplinary research, as even the definition of “cross-disciplinary” is a topic of debate among the various research communities. Even if such data were available, they could not be used to project how many more cross-disciplinary researchers are needed and should be trained every year. While this exercise has been done for disciplines with well-defined and agreed-upon goals (see, for example, NRC, 1984), no such consensus exists on scientific cross-disciplinary research. Accordingly, the evidence suggesting cross-disciplinary linkages should be strengthened is qualitative rather than quantitative: a growing body of organizations, individuals, committees, and other entities have indeed recognized the importance of cross-disciplinary research to advancing the frontiers of their fields, and a number of programs have been set up to begin to address this need (Appendix D).

National interest in cross-disciplinary research peaked sharply after World War II and began rising again in the mid-1980s. In 1986, the Chairman of the House Committee on Science and Technology emphasized that interdisciplinary solutions would be required for the major scientific and technological problems of the world, claiming that the “mega-problems [are those] that cannot be neatly pigeonholed into any one of the traditional academic disciplines” (U.S. Congress, House, 1986). This new interest was presumably in response to the increasing amount of data being generated and stored by scientists, the richness of the systems they investigate, and a perceived disconnection between scientists and mathematicians (Sigma Xi, 1988).

This growing interest in linking mathematics and science is most easily observed in reports generated by the mathematical community. The so-called David I report (NRC, 1984) identified a significant decline in funding for mathematics despite its increasing relevance to science, technology, and society. It gave many examples of important applications of mathematics. Six years later, the “David II” report identified significant opportunities for

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3
Previous Efforts and Studies Relevant to Math/Science Linkages
The committee is not the first to consider the need for cross-disciplinary linkages and how to forge them. Many other efforts have focused on or considered the contributions that math-science linkages can make to the development and timely advance of frontier areas of research (Appendix C). It is difficult, however, to demonstrate quantitatively the need for further cross-disciplinary research links. Data on graduation rates, research funding, and other quantitative measures are routinely collected for the various individual disciplines but would be difficult to collect for cross-disciplinary research, as even the definition of “cross-disciplinary” is a topic of debate among the various research communities. Even if such data were available, they could not be used to project how many more cross-disciplinary researchers are needed and should be trained every year. While this exercise has been done for disciplines with well-defined and agreed-upon goals (see, for example, NRC, 1984), no such consensus exists on scientific cross-disciplinary research. Accordingly, the evidence suggesting cross-disciplinary linkages should be strengthened is qualitative rather than quantitative: a growing body of organizations, individuals, committees, and other entities have indeed recognized the importance of cross-disciplinary research to advancing the frontiers of their fields, and a number of programs have been set up to begin to address this need (Appendix D).
National interest in cross-disciplinary research peaked sharply after World War II and began rising again in the mid-1980s. In 1986, the Chairman of the House Committee on Science and Technology emphasized that interdisciplinary solutions would be required for the major scientific and technological problems of the world, claiming that the “mega-problems [are those] that cannot be neatly pigeonholed into any one of the traditional academic disciplines” (U.S. Congress, House, 1986). This new interest was presumably in response to the increasing amount of data being generated and stored by scientists, the richness of the systems they investigate, and a perceived disconnection between scientists and mathematicians (Sigma Xi, 1988).
This growing interest in linking mathematics and science is most easily observed in reports generated by the mathematical community. The so-called David I report (NRC, 1984) identified a significant decline in funding for mathematics despite its increasing relevance to science, technology, and society. It gave many examples of important applications of mathematics. Six years later, the “David II” report identified significant opportunities for

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mathematics research, including cross-disciplinary collaborations (NRC, 1990). The David II report also recommended that academic mathematical science departments give more recognition to faculty engaging in cross-disciplinary collaborations. In 1994, the Joint Policy Board for Mathematics encouraged the mathematical sciences community to develop a rewards system that does not distinguish between core and applied mathematics and that values a number of activities, including teaching, outreach activities, and cross-disciplinary pursuits (AMS, 1994). Other recent reports have warned that U.S. mathematics should pay serious attention to its interactions with other disciplines in order to remain preeminent in the field (NRC, 1997; AMS, 1999). The Report of the Senior Assessment Panel of the International Assessment of the U.S. Mathematical Sciences (NSF, 1998) bases its evaluations in part on the rate at which new mathematics is utilized by other disciplines. The report argues that by retreating from multidisciplinary involvement, mathematics misses opportunities to be enriched by the ideas and challenges of other disciplines. The other disciplines suffer from a loss of expertise and easy access to the vast knowledge base being developed by the mathematical sciences and from the overly specialized mathematical languages and tools that inhibit communication with other disciplines. According to this report, “strengthening the connections between the creators and the users of mathematics, while maintaining historical proficiency in pure mathematics, is the most important opportunity now open for the National Science Foundation in support of that field.”
Reports from the scientific community likewise acknowledge the benefits of research at the interface between science and mathematical sciences and of providing students, postdoctoral fellows, and other researchers with more training in the mathematical sciences. For example, a growing interest in math-related research and training is evident from reports and program initiatives coming from the life sciences and biomedical research community. The David II report, mentioned above (NRC, 1990), suggested ways of better reviewing and otherwise promoting collaborations between life and medical scientists, on the one hand, and physical scientists (including mathematical sciences) and engineers, on the other. In 1992 and 1996, the National Science Foundation published reports detailing the historical relationship between mathematical sciences and biology and suggesting areas of emerging opportunity at the math-biology interface (NSF, 1992 and 1996). More recently, four foundations supportive of biomedical research convened a workshop to discuss the impact of market forces on health care research in the United States and the ways in which private foundations could best “meet the challenging needs of research and advance in the field” (American Cancer Society, Burroughs Wellcome Fund, Howard Hughes Medical Institute, and the Pew Charitable Trusts, 1998). The resulting report lists seven emerging themes identified at the workshop. One of these acknowledges the potentially high payoff associated with crosscutting research in biology and the mathematical sciences. Expressing concern about the financial crises faced by academic health centers (AHCs), the report claims that general support of multidisciplinary research can be critical to the long-term success of an AHC program because it facilitates breakthrough research; maximizes the attractiveness of an institution to graduate students, postdoctoral trainees, and outstanding faculty; brings the research community together; and increases the likelihood of facilitating linkages with the commercial sector. Other disciplines have similarly expressed the need to promote research linkages with the mathematical sciences community.
Appendix C briefly describes these and other studies that considered how to establish better research linkages as well as some actions taken to remedy the situation. The chronology

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demonstrates a growing recognition of the importance of interdisciplinary research to the health and advancement of U.S. science and technology generally and the necessity of cross-disciplinary linkages in maintaining and increasing the health of the mathematical sciences in particular. Several studies recognize the special role mathematics has to play in the advancement of the research infrastructure as sciences that were traditionally descriptive become more and more quantitative.
The studies repeatedly identify certain factors that must be addressed to foster research linkages. Many recommend increased interdisciplinary training at all levels and the integration of interdisciplinary problems and experiences into disciplinary curriculums, and many discuss cultural issues such as the need for open communications and collegiality between disciplines. The need to reform current institutional structures or build new ones is noted again and again. These structures include incentives such as promotion and tenure criteria, which generally need modification if they are to fully value cross-disciplinary research, and disciplinary departments that can introduce new structures and means to promote interaction with colleagues from other departments. Funding agency structures, which work well for disciplinary research proposals but often lack mechanisms for adequately reviewing cross-disciplinary work, also need reform. Finally, the need for greater resources, both to strengthen the health of mathematics and to increase the number of cross-disciplinary research linkages, is repeatedly noted.
This body of work represents the continuing effort of a number of research communities to encourage, evaluate, and prioritize efforts to promote cross-disciplinary research linkages. As a whole it arrives at the same conclusion—that cross-disciplinary research linkages are crucial to many important advances in science and technology and to health of the research enterprise itself. And yet, no action plan for moving the U.S. research infrastructure forward has emerged. The committee was left to ask itself what more it could say in the face of such a large body of earlier work. It concluded that it could offer some detailed, specific recommendations for programs that would enhance interactions at the math-science interface. In addition, it felt that limited efforts, such as those represented by its own work and that of the committees that had preceded it, would not be sufficient to move the research community and funding organizations forward or to ensure that math-science interfaces were enhanced. Instead, the committee felt a more continuous effort and oversight was required. Chapter 4 discusses some steps the committee feels can be taken to strengthen cross-disciplinary research in the United States.
REFERENCES
American Cancer Society, Burroughs Wellcome Fund, Howard Hughes Medical Institute, and the Pew Charitable Trusts. 1998. Strengthening Health Research in America: Philanthropy's Role. Available at <http://www.pewtrusts.com/pubs/publications.cfm>.
American Mathematical Society (AMS). 1994. Recognition and Rewards in the Mathematical Sciences. Washington, D.C.: AMS.

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American Mathematical Society (AMS), Task Force on Excellence. 1999. Towards Excellence: Leading a Mathematics Department into the 21st Century. Available at <http://www.ams.org/towardsexcellence>.
National Research Council (NRC). 1984. Renewing U.S. Mathematics: Critical Resource for the Future. Washington, D.C.: National Academy Press.
National Research Council (NRC). 1990. Renewing U.S. Mathematics: A Plan for the 1990s. Washington, D.C.: National Academy Press.
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National Science Foundation (NSF). 1998. Report of the Senior Assessment Panel of the International Assessment of the U.S. Mathematical Sciences. NSF9895. Arlington, Va.: National Science Foundation.
Sigma Xi. 1988. Removing the Boundaries: Perspectives on Cross-Disciplinary Research. Research Triangle Park, N.C.: Sigma Xi Publications.
U.S. Congress, House of Representatives. 1986. American Science and Science Policy Issues: Chairman's Report to the Committee on Science and Technology, U.S. House of Representatives. Washington, D.C.: Government Printing Office.