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5 Recommendations The 1984 Report described serious deficiencies in the situation of the mathematical sciences (see Appendix A). These shortcomings were reflected in the inability of the mathematical sciences research com- munity to renew itself by attracting a suitably large and talented cohort of students, and they suggested the prospect of declining pro- cluctivity in research activities. The 1984 Report recommended a plan for renewal, the National Plan for Graduate and Postdoctoral Educa- tion in the Mathematical Sciences, which called for mathematical sci- ences funding to balance that in the principal disciplines it supports, namely, the physical and life sciences and engineering. That 1984 National Plan has been only partially carried out: funding has risen to some $130 million per year, a figure that is about $100 million per year short of the 1984 plan's goal for 1989. PRIMARY RECOMMENI)ATIONS The committee believes it is imperative to meet the goals set out in the 1984 National Plan, but the funding to meet those goals should be increased to $250 million per year, $225 million to cover the present cost of the 1984 National Plan, plus $25 million to support coherent programs that can effectively address the career path problems. In the committee's judgment this funding level, if achieved within three to five years beginning in FY 1991, will result in a reasonably balanced situation, one that will allow the mathematical sciences community to replace retiring members and also supply the growing needs of indus- try and government. Note that the recent report by W.G. Bowen and J.A. Sonar estimates that the supply to demand ratio for mathematics 69

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RENEWING U.S. MATHEMATICS and physical sciences faculty in the 1990s will be only 0.8. This projec- tion is doubly worrisome for the mathematical sciences with their existing renewal difficulties. Increased research funding alone will not be adequate to assure the renewal of the mathematical sciences. Other serious deficiencies in the mathematical sciences career path make it less attractive to stu- dents than the paths in the other sciences and in engineering. These deficiencies include markedly less opportunity for faculty research, fewer graduate research positions with stipends, and fewer postdoc- toral research positions. Then, too, students seem to perceive a sink- or-swim attitude among many mathematical sciences faculty mem- bers.2 These deficiencies exist despite efforts to increase graduate student funding and postdoctoral opportunities over the past five years. The drop-out rate from the mathematics career pipeline (begin- ning at the undergraduate level and terminating at the doctoral level) averages 50% per year, which is markedly higher than the correspond- ing rates in the other sciences and engineering. A significant part of any increased funding over the coming five years should be used for coherent programs operated by departments, fac- ulty groups, or even individual faculty members to (1) improve re- cruiting of qualified students, particularly women and minority stu- dents, (2) keep students within the field by providing mentors at every educational level, (3) provide research opportunities at all stages of students' careers, and (4) provide improved research opportunities for junior faculty and better access to research facilities and collabora- tors for senior faculty. The reward structure for mathematicians should be modified to credit involvement in such activities. Comprehensive, integrated programs should be encouraged and even solicited by funding agencies as part of their mathematical sciences activities. The National Science Foundation has already taken steps in this direction. Thus this committee's three primary recommendations are as follows: I. Implement the 1984 National Plan, but increase the level of federal funding for the mathematical sciences to $250 million per year. (The 1984 plan's goal of $180 million per year has risen due to inflation to $225 million, to which this committee has added $25 million per year for implementing Recommen- dation II.) 70

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RECOMMENDATIONS II. Improve the career path in the mathematical sciences to continue to attract sufficient numbers of talented people and to use the entire human resource base more effectively. Im- plementation of the 1984 National Plan by itself would accom- plish much toward this goal. The committee estimates that $25 million per year of the federal funds called for in Recommen- dation I will significantly augment the 1984 National Plan through the funding of coherent programs aimed at directly encouraging young people, especially women and minorities, to enter and remain in mathematical sciences careers. Mathe- matical sciences departments should give increased recogni- tion to faculty who act as mentors, who contribute to educa- tion, and who interact with collaborators from other disciplines, while universities should do more to help their mathematical sciences departments meet their multifaceted missions; these actions would improve the career path and thereby indirectly encourage young people to enter and remain in mathematical sciences careers. Cooperation between university mathemati- cal sciences departments and their administrations is critical for successful implementation of this recommendation. III. Because a wealth of striking research problems many with potential applications to modern science and technol- ogy currently challenges mathematical scientists, and be- cause added intellectual stimulation will contribute to the renewal of the field, increase to 2600 (the level recommended in the 1984 National Plan) the number of senior investigators supported annually. This goal is implicit in Recommenda- tions I and II, but it demands clear emphasis. Mathematical sciences research has been highly productive over the past five years. Furthermore, mathematicians have become increas- ingly interested in transferring new mathematics into applied fields and in working with users of mathematics. These trends are bringing core and applied mathematics closer together as well as integrating formerly distinct fields of mathematics. The resulting vigor has been augmented by the rise of computation as a too! in research. Indeed, the pace of research in the mathematical sciences is accelerating. Thus the increase in productivity from additional funding is likely to be disproportionately large. In the United States there are some 1900 federally supported senior investigators. The committee estimates 71

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RENEWING U.s. MATHEMATICS that an additional 700 highly productive mathematical sciences re- searchers are not supported. These people, who represent an opportu- nity to sustain the vigor and productivity of the field, should be given adequate funding. Finally, the committee emphasizes that a vigorous mathematical sci- ences enterprise in the United States is essential to addressing the educational shortfalls so widely perceived by the public and their representatives. Too few primary and secondary school teachers are qualified to teach mathematics. Yet it is at this level that students often decide that they can or cannot undertake careers in science or engineering. Mathematics is perceived as a barrier to students who might otherwise make ambitious career choices: this is esneciallv true for women and minorities. Mathematics faculties in colleges and universities directly and incli- rectly affect the quality of primary and secondary school mathematics teaching. Preparation and continuing education for these mathemat- ics professors must be improved if the United States is to remain competitive in science and technology. Mathematics education is crucial to achieving international competitiveness in all the sciences. Major initiatives, as suggested above, are critical to any serious attempt to address the educational problems so often lamented publicly. The health and vigor of the mathematical sciences is a vital index in judg- ing the prospects for national attempts to solve the science-based problems of U.S. society. DIRECTED RECOMMENDATIONS Federal Agencies Agencies Collectively Continue to encourage the internal unification of the mathematical sciences and their outreach to other fields. Support efforts toward community-wide implementation of the career path improvements called for in Recommendation II. Continue to push for adequate funding for the mathematical sciences and especially for the support of signifi- cantly more senior investigators. 72

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RECOMMENDATIONS National Science Foundation Begin to increase the number of supported senior investigators in the mathematical sciences. Continue to increase the number of supported graduate student researchers and postdoctoral researchers. Work with national groups to address issues involving human resources. Department of Defense Push for real growth in the mathematics budgets of the Air Force Office of Scientific Research, the Army Research Office, and the Office of Naval Research. Continue the progress of the DARPA and NSA programs. Persuade the leaders of Department of Defense agencies to appreciate the importance of the mathematical sciences for national defense and to understand that the long-range prospects for the de- fense of the country must rest on a strong, continuing research base. Department of Energy, National Institutes of Health, and National Aeronautics and Space Administration Reevaluate programs to take advantage of the role the mathematical sciences can and do play. Increase support for the mathematical sci- ences, which currently is concentrated too much in the NSF and DOD. This can have an adverse impact on the nation's total science, engi- neering, and technology research and education, especially if DOD funding of mathematics does not increase. Recognize that the future quality of technology bases affecting agency missions is dependent on the mathematics being done now. Office of Science and Technology Policy Send a clear message to the federal agencies that reversing past de- clines in the mathematical sciences is a continuing national priority. Universities Recognize the central importance of healthy mathematical sciences departments to any university. Conduct in-depth reviews of the cir- cumstances of mathematical sciences departments and work with department chairs to develop and emphasize plans for departmental 73

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RENEWING U.S. MATHEMATICS improvement. Discuss and clarify the department's mission and goals and the administration's expectations of faculty members. Plan coor- dinated action to address career-path and reward-structure issues and undergraduate and graduate education standards. In acldition, work as intermediaries between mathematical sciences departments and local government and industry. Apprise state tech- nology offices of the importance of mathematics to the quality of education and to the local economy. Make industry aware of the contributions that mathematical scientists can make as both research- ers and teachers. Department Chairs and University Administrators Make special efforts to recruit women and minorities. Reassess and broaden reward structures so that they reflect the broad missions of mathematical sciences departments: research, service teaching, un- clergraduate and graduate education, and contributions to the national precollege mathematics education effort. Reevaluate the use of gradu- ate teaching assistantships, being mindful of the twin goals of high- quality undergraduate instruction and well-balanced Ph.D. training. Mathematical Sciences Community Maintain the tradition of first-class research. Focus more attention on career-path problems (Recommendation II). Offer better training, including a commitment to a system of mentors for graduate students and postdoctorals. Create programs that provide the breadth neces- sary for today's mathematics research and applications. Establish guidelines for evaluating and improving mathematical sciences Ph.D. programs. Recognize the breadth of the mathematical sciences aca- ~e . . aemlc mlsslon. NOTES ~Bowen, W.G., and Sosa, J.A., Prospects for Faculty in the Arts ~ Sciences (Princeton University Press, Princeton, N.J., 1989). This observation has been made about faculty members in all of the sciences; see, for instance, Kenneth C. Green, "A Profile of Undergraduates in the Sciences," American Scientist, Vol. 77, No. 5 (Sept.-Oct. 1989), p. 478. 74