The first three chapters identified some of the enabling factors as well as some of the obstacles to successful interactions between mathematics and the sciences. The committee hopes the recommendations in this chapter will enhance existing linkages, stimulate new interactions, and help to overcome some of the obstacles. It expects that the implementation of these recommendations will increase the flow of interesting and challenging ideas between the sciences and mathematics and improve communication between the two groups.

**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 benefits of cross-fertilization. The committee believes the responsibility lies equally with the practitioners of mathematical sciences and the sciences. Some disciplines can benefit from a shift in some of their resources from strictly disciplinary to cross-disciplinary activities. Others are too close to the critical mass of necessary resources to benefit from such shifts. Since productive cross-disciplinary research cannot be built on a base of foundering disciplines, some disciplines will need additional monies to be capable of developing effective cross-disciplinary ties. The health of the basic sciences is a prerequisite for the advance of cross-disciplinary research, so funding for cross-disciplinary research must not compromise support for basic disciplinary research or individual investigators. The committee expects that successful linkages will expand the horizons of disciplinary research in many directions in both the mathematical sciences and other sciences. It offers here specific recommendations for programs that would foster cross-disciplinary research, along with an estimate of the cost based on the committee members' experience in running similar programs.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
4
Recommendations
The first three chapters identified some of the enabling factors as well as some of the obstacles to successful interactions between mathematics and the sciences. The committee hopes the recommendations in this chapter will enhance existing linkages, stimulate new interactions, and help to overcome some of the obstacles. It expects that the implementation of these recommendations will increase the flow of interesting and challenging ideas between the sciences and mathematics and improve communication between the two groups.
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 benefits of cross-fertilization. The committee believes the responsibility lies equally with the practitioners of mathematical sciences and the sciences. Some disciplines can benefit from a shift in some of their resources from strictly disciplinary to cross-disciplinary activities. Others are too close to the critical mass of necessary resources to benefit from such shifts. Since productive cross-disciplinary research cannot be built on a base of foundering disciplines, some disciplines will need additional monies to be capable of developing effective cross-disciplinary ties. The health of the basic sciences is a prerequisite for the advance of cross-disciplinary research, so funding for cross-disciplinary research must not compromise support for basic disciplinary research or individual investigators. The committee expects that successful linkages will expand the horizons of disciplinary research in many directions in both the mathematical sciences and other sciences. It offers here specific recommendations for programs that would foster cross-disciplinary research, along with an estimate of the cost based on the committee members' experience in running similar programs.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
Enhancing Multidisciplinary Activities
Increase the number of specialized summer institutes, each sustained for at least 5 years, organized around a core of committed senior scientists and mathematical scientists, and aimed at fostering linkages between the sciences and mathematical sciences.
The Geophysical Fluid Dynamics Program at Woods Hole, described in Chapter 2, could serve as a model for introducing senior scientists, graduate students, and postdoctoral fellows to cross-disciplinary research and for sustaining their interest in and commitment to such research. The success of that program lies in the long-term continuity assured by a core group of senior faculty, combined with its educational aspect—the training of graduate students during an intense, summer-long program. The committee recommends that other such institutes be created that are devoted to bridging the mathematical sciences and other sciences and having the same elements of long-term continuity in funding and education. Such institutes would foster the prolonged interactions necessary to establish meaningful cross-disciplinary collaborations, provide researchers opportunities to network with colleagues from other disciplines, and help a core group of researchers establish a sufficient understanding of each other's disciplines to recognize promising research opportunities at the disciplines' interface.
Proposals for such institutes should be subject to vigorous competition and peer review. Based on the committee's experience, an institute could be established and continued for a cost of about $2 million per year. As these institutes mature, costs may decrease—the cost of the well-established Geophysical Fluid Dynamics Program, for example, is currently about $150,000 per year.
Encourage existing large-scale programs (such as research institutes, NSF science and technology centers (STCs)) or Department of Defense-University Research Initiatives (multidisciplinary university research initiatives) to develop targeted initiatives when promising ideas need new linkages between science and the mathematical sciences.
Existing large-scale programs provide an infrastructure that can be leveraged to build new math-science linkages. Agencies can encourage centers to explore new research topics at little additional cost, as the centers already have the framework in place to run workshops and pursue novel directions. For example, the NSF-STC for Discrete Mathematics and Theoretical Computer Science (DIMACS) sponsored workshops on mathematical support for molecular biology from 1994 to 1996. These workshops attracted many biologists, chemists, computer scientists, and mathematical scientists. Also, the Aspen Center for Physics, the Institute for Advanced Study, the Institute for Theoretical Physics, and the Mathematical Sciences Research Institute all sponsored workshops and programs that supported the exciting connections between high energy physics and modern mathematics. These activities provide unique opportunities for networking between disciplines and for educating researchers about problems outside their own disciplines.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
Fellowship Programs to Sustain Research Scientists Pursuing Promising Multidisciplinary Ideas
Support long-term crossover visitor and sabbatical programs by which mathematical scientists could visit science departments and laboratories and scientists could visit mathematical science departments.
Sabbatical programs would provide opportunities for researchers to be colocated with colleagues from other disciplines for long enough times to establish meaningful collaborations. The programs could last for 6 months or a year or they could involve participation in specific courses targeted at math-science collaboration for shorter periods. These cross-disciplinary sabbaticals should be highly competitive and endowed with particular prestige, both to encourage researchers to participate and to make them a plus in participants' promotion files. It would be useful to distinguish such sabbatical awards with an appealing title, such as the von Neumann, Wiener, or Fisher sabbatical visitor. The committee estimates the cost for each exchange at $70,000.
Establish cross-disciplinary research grants with sustained funding for at least 5 years to allow young investigators to collaborate across the mathematical sciences and the sciences.
Such sustained support would help talented young researchers with vision pursue cross-disciplinary research, which by its nature poses greater career risks than traditional disciplinary research and often takes longer to show substantial results. The committee estimates a reasonable level of support to be $250,000 per investigator for the 5 years.
Establish cross-disciplinary, postdoctoral-plus fellowships, highly competitive grants for postdoctoral research that would provide continuing research support once the recipient obtains a tenure-track academic position.
Similar to the two programs described above, these fellowships would consist of a postdoctoral fellowship followed by a research grant for the first 2 tenure-track years. The exceptional young researcher could then begin an academic career with full momentum and move ahead on whatever ideas come from the postdoctoral years. These grants would address the difficulty faced in securing funding for research that falls between traditional disciplines and would provide an additional year of research time to offset the additional time often required to establish good cross-disciplinary research. Such funding should not preclude the possibility of teaching, as is the common practice among postdoctoral fellows in mathematical sciences. Cross-disciplinary teaching might even be encouraged. Such a proposal might be funded at a level of $325,000 per investigator for a 4-year period.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
CROSS-DISCIPLINARY INTERACTIONS
The committee recommends that academic institutions take responsibility for implementing vigorous cooperative programs between the sciences and the mathematical sciences.
Universities with vision are developing new programs that cut across traditional departmental and college boundaries. Such programs are being recognized as a significant component of a university's research and educational missions. The mathematical sciences, because their role is central to all the sciences, are well placed to participate fully in the dramatic changes taking place. Indeed, a recent AMS report (AMS, 1999) suggests that forming good ties to the university's mission and to other academic departments is key to the success of a mathematics department and discusses in depth several departments that have used this approach to strengthen their programs. Astute mathematical science departments and cooperating, sympathetic senior administrators can create a hospitable environment that encourages research scientists to pursue exciting cross-disciplinary activities and can develop the curricula needed to give students cross-disciplinary skills. Academic programs in sciences such as engineering and biology can encourage cross-disciplinary educational programs as departments modify curricula to meet the evolving needs of their disciplines. Leadership at the university and departmental levels can do much to build and sustain cross-disciplinary programs and, in so doing, to enhance the U.S. research enterprise.
No cross-disciplinary program will succeed unless the institution demonstrates that it values and is committed to such efforts. In the end, no other attempts to convey that message will succeed unless the reward structure for researchers is consistent with the message.
Departments and colleges should develop effective criteria for the evaluation of cross-disciplinary research, ensuring that the university's promotion, tenure, and reward mechanisms fully recognize quality cross-disciplinary research.
It is imperative to improve evaluation criteria for investigators pursuing cross-disciplinary research in order to demonstrate its value to the university. Particularly helpful would be protocols for the inclusion of extra disciplinary expert testimonial in departmental and college promotion and tenure committees. There are institutions in which interdisciplinary work is naturally accepted and effectively handled in promotion and tenure. One example is medical schools, where the basic science and clinical science departments follow procedures of faculty vote and approval similar to those of the basic science departments at universities and where the tenure committees include faculty from other disciplines. Universities with vision must recognize that the implementation of such criteria is critical for the health of cross-disciplinary endeavors. This is one of the most important steps that can be taken to change attitudes and cultures that view cross-disciplinary research as second-rate or less important than disciplinary work.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
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.
In reviewing earlier studies of the linkages between the mathematical sciences and other sciences, the committee was struck by the number of reports that had had relatively little impact, despite their good ideas. The committee felt one reason for this was the lack of an effective follow-through mechanism. An ongoing group with special responsibility for advocating cross-disciplinary projects between the mathematical sciences and other sciences could nurture linkages. The group could monitor and evaluate the various initiatives to foster linkages and communicate their evaluations to the community. The committee would be a source of information on opportunities for research linkages.
A standing committee devoted to maintaining the health of linkages between science and mathematical sciences would be asked to do the following:
Take a proactive role in alerting funding agencies and policy makers to promising new cross-disciplinary directions;
Promote, compile, and publicize opportunities for cross-disciplinary work;
Advise administrators setting up cross-disciplinary programs and curricula involving the mathematical sciences and acquaint them with successful models;
Increase the visibility of cross-disciplinary mathematical research to the scientific community by disseminating the results of such research through workshops, conferences, and publications;
Monitor and identify effective mechanisms by which academic institutions and funding agencies can assess cross-disciplinary research proposals; and
Report regularly on the status of linkages between the mathematical sciences and other sciences.
The standing committee should be distinct from current disciplinary bodies so it can maintain a focus on cross-disciplinary education and research. It should be distinct from existing groups representing specific disciplines to avoid diluting the missions of those bodies and also to avoid the perception that it is advocating one discipline over another. Nonetheless it would be critical for the new committee to have representation from existing bodies in order to have a strong link to the communities that would carry out its suggestions.
The committee could be established on a 5-year trial basis, with an evaluation of its effectiveness at 2 years to allow adjusting its efforts. An evaluation after 5 years would determine whether it should be continued. The committee's activities could be funded by agencies and foundations interested in fostering math-science research linkages.
The standing committee would advise funding agencies on how they might better evaluate cross-disciplinary research.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
The committee recognizes and applauds the efforts already under way by federal agencies to increase math-science linkages. For example, NSF's Office of Multidisciplinary Activities (OMA) supports particularly novel, challenging, or complex multidisciplinary research projects that do not fit well into the existing program structure or whose realization might otherwise be hampered by existing institutional and procedural barriers. Its new Integrative Graduate Education and Research Training (IGERT) program is evidence of NSF's commitment to multidisciplinary approaches to graduate education. NIH is actively involved in new funding and research at the interface of mathematical sciences and science. Its recently announced Fellowships in Quantitative Biology program, for example, encourages highly qualified individuals with doctoral training in the traditional quantitative disciplines to obtain training in biological areas congruent to the mission of the National Institute of General Medical Sciences (NIGMS). DOE is currently advancing a major initiative in the application of computational science to science and engineering problems. DARPA, DOE, and ONR have a long history of funding cross-disciplinary projects related to their missions. (Some current efforts to increase the linkages between the mathematical sciences and other sciences are described in Appendix C.)
However, because the funding agencies were established when scientific disciplines were strictly separate, their organizational structure can discourage promising multidisciplinary research. As an example, cross-disciplinary proposals are sent to different panels with different goals and cultures and so are evaluated differently, making it seem as if it is more difficult to get them funded. Some mechanism needs to be devised so agencies can get an objective scientific evaluation of cross-disciplinary proposals. As another example, the application of mathematics to the biomedical sciences is a frontier research area vital to the NIH mission. Organizing a permanent study section composed of scientists from different disciplines, including the mathematical sciences, might be one inexpensive way for NIH to ensure the proper consideration of highly mathematical proposals. In any event, a committee could advise federal agencies on how to evaluate cross-disciplinary proposals by describing the methods of organizations that have successfully done so.
The new committee could advise private foundations and philanthropies on effective methods for supporting promising cross-disciplinary research.
Private foundations such as the Pew Charitable Trust, the Keck Foundation, Burroughs-Wellcome, Howard Hughes, and others foster collaborative research through their support for training programs and for faculty research, training, and in some cases, new hires. Since research at the interface of the mathematical sciences and other sciences is playing an increasingly important role in all areas of research, especially biomedical research, considerable leveraging can be anticipated for investments that foster such research. Private foundations can design and fund the sort of innovative institutes, fellowships, and research positions that the committee believes will effectively strengthen and increase collaborative research efforts.
The new committee could help identify curriculum changes that would enable more and better linkages.
Many scientific disciplines are recognizing the increasing importance of mathematics to the success of their fields and are adjusting their educational programs accordingly.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences
Mathematical science departments are also increasingly recognizing the importance of exposing their students to applications in the sciences and are changing their programs accordingly. A standing committee could convene and facilitate dialogue on curricular modifications at both the undergraduate and graduate level, enabling an ongoing examination of efforts undertaken throughout the country and disseminating information on successful reforms.
The new committee could inform professional societies about multidisciplinary research opportunities and related educational opportunities.
Professional societies can promote good cross-disciplinary research. By combining forces, societies representing different disciplines can disseminate information about cross-disciplinary research and funding opportunities through mechanisms such as special sessions at their annual meetings, articles in membership journals, symposia, and newsletters. A committee concerned specifically with cross-disciplinary research would help the many professional societies to collaborate in the pursuit of these goals. It could also help these societies discuss and disseminate ideas and recommendations for curriculum changes and professional development pertinent to cross-disciplinary research. It would cite examples of departments that have successfully forged substantial cross-disciplinary linkages and would highlight the mechanisms used to achieve that success.
There are several ways to organize and administer such a committee, but certain criteria for its composition are critical. It must contain members who would be perceived as respected representatives of relevant disciplines in mathematical and other sciences. It is important for the membership to have the capacity to relate the committee's deliberations and findings to other standing committees of the various professional societies, federal agencies, and the National Academies; to that end it would be ideal to draw a portion of the membership from such standing bodies. Because of the important influence educational programs can have on building the math-science interface, the membership must also include individuals viewed as influential educators in their disciplines. Founding such a group would improve the likelihood of follow-up to the findings of this committee.
REFERENCE
American Mathematical Society (AMS), Task Force on Excellence. 1999. Towards Excellence: Leading a Mathematics Department in the 21st Century. Available at <http://www.ams.org/towardsexcellence>.

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