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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
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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.)
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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
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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.
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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
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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-
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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
Representative terms from entire chapter:
national plan
