The first strategic examination of the mathematical sciences, *Renewing U.S. Mathematics: Critical Resource for the Future* (known as the “David report”),^{1} found worrisome trends. Although the mathematical sciences were producing excellent and valuable research, the number of young people entering the profession had declined, threatening a contraction in the size of the mathematical science research enterprise. The report documented an erosion in federal support for mathematical sciences research that had taken place over more than a decade. The result was an imbalance between research in the mathematical sciences and research in the physical sciences and engineering, which depend on mathematical and statistical tools. For example, the report cited 1980 figures on the number of faculty members in chemistry, physics, and mathematical sciences (three fields with very similar numbers of faculty members) who received federal research funding. Approximately 3,300 chemists and 3,300 physicists received federal research funding in 1980, compared with just 2,300 mathematical scientists.^{2} The study estimated the number of graduate student research associateships and postdoctoral research positions that would be needed for a healthy pipeline of new researchers and, from that, argued for a doubling of federal funding for mathematical sciences research.

The David report (named after its chair, former Presidential Science Advisor Edward David) led to striking increases in federal funding for mathematical

______________________

^{1} National Research Council (NRC), 1984, *Renewing Mathematics: Critical Resource for the Future*. The National Academies Press, Washington, D.C.

^{2} Ibid., p. 5.

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Appendix A
Past Strategic Studies
The first strategic examination of the mathematical sciences, Renewing
U.S. Mathematics: Critical Resource for the Future (known as the “David
report”),1 found worrisome trends. Although the mathematical sciences
were producing excellent and valuable research, the number of young
people entering the profession had declined, threatening a contraction in the
size of the mathematical science research enterprise. The report documented
an erosion in federal support for mathematical sciences research that had
taken place over more than a decade. The result was an imbalance between
research in the mathematical sciences and research in the physical sciences
and engineering, which depend on mathematical and statistical tools. For
example, the report cited 1980 figures on the number of faculty members in
chemistry, physics, and mathematical sciences (three fields with very similar
numbers of faculty members) who received federal research funding. Ap-
proximately 3,300 chemists and 3,300 physicists received federal research
funding in 1980, compared with just 2,300 mathematical scientists.2 The
study estimated the number of graduate student research associateships and
postdoctoral research positions that would be needed for a healthy pipeline
of new researchers and, from that, argued for a doubling of federal funding
for mathematical sciences research.
The David report (named after its chair, former Presidential Science
A
dvisor Edward David) led to striking increases in federal funding for math-
1 National Research Council (NRC), 1984, Renewing Mathematics: Critical Resource for
the Future. The National Academies Press, Washington, D.C.
2 Ibid., p. 5.
155

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156 APPENDIX A
ematical sciences for a few years, partially restoring balance, though the
increases shrank later in the 1980s before the doubling goal was reached.
The report also stirred a good deal of discussion within the community and
led to greater involvement of mathematical sciences in discussions about
federal science policy. According to the subsequent “David II report,”3
members of the mathematical sciences community had “shown a growing
awareness of the problems confronting their discipline and increased inter-
est in dealing with the problems, particularly in regard to communication
with the public and government agencies and involvement in education.”
Because the imbalance in federal funding was only partially remedied
as a result of the David report—federal funding for mathematical sciences
research increased by 34 percent, not 100 percent—the funding agencies
that support the mathematical sciences decided in 1989 to commission
the David II report to assess progress and recommend further steps to
strengthen the enterprise. That report found that federal support for gradu-
ate and postdoctoral students had increased substantially between 1984
and 1989—by 61 percent and 42 percent, respectively—and some aspects
of infrastructure, such as computing facilities and research institutes, had
been upgraded. But overall, the David II report found that the foundations
of the research enterprise continued to be “as shaky now as in 1984.”4 It
reiterated the calls of the first David report and recommended continued
work toward doubling of federal support. It also recommended improve-
ments to the career path in the mathematical sciences, through increases in
the number of researchers, postdoctoral research positions, and graduate
research associateships, all of which indeed did grow during the 1990s. It is
not clear, though, that those steps reduced the degree to which U.S. students
from high school onward leave the mathematical sciences pipeline. The
David II report also asserted specifically that “recruitment of women and
minorities into the mathematical sciences is a high priority,” but it did not
propose concrete steps to improve this. In general, the early 1990s was
not a favorable time for a renewed push for federal funding, and it is not
clear whether the David II report had much impact in that area.
In 1997, the National Science Foundation (NSF’s) Division of Math-
ematical Sciences (DMS) organized the Senior Assessment Panel for the
International Assessment of the U.S. Mathematical Sciences. The study
was meant to evaluate how well DMS was supporting NSF’s strategic goals
with respect to the mathematical sciences—which included “enabl[ing] the
United States to uphold a position of world leadership in all aspects of . . .
mathematics . . . promot[ing] the discovery, integration, dissemination, and
3 NRC, 1990, Renewing U.S. Mathematics: A Plan for the 1990s. National Academy Press,
Washington, D.C., p. 3.
4 Ibid.

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APPENDIX A 157
employment of new knowledge in the service of society; and achiev[ing] ex-
cellence in U.S. science, mathematics, engineering and technology education
at all levels.5 The panel was chaired by Lt. Gen. William E. Odom, former
head of the National Security Agency.
The Executive Summary of the Odom report reaches conclusions and
makes recommendations:
The modern world increasingly depends on the mathematical sciences
in areas ranging from national security and medical technology to com-
puter software, telecommunications, and investment policy. More and
more American workers, from the boardroom to the assembly line, cannot
do their jobs without mathematical skills. Without strong resources in the
mathematical sciences, America will not retain its pre-eminence in industry
and commerce.
At this moment, the U.S. enjoys a position of world leadership in the
mathematical sciences. But this position is fragile. It depends very substan-
tially on immigrants who had their mathematical training elsewhere and
in particular on the massive flow of experts from the former Communist
bloc. . . . Young Americans do not see careers in the mathematical sci-
ences as attractive. Funding for graduate study is scarce and ungenerous,
especially when compared to funding for other sciences and with what
happens in Western Europe. Further, it takes too long to obtain a doctorate
because of the distractions of excessive teaching. Students wrongly believe
that jobs that call for mathematical training are scarce and poorly paid.
Weaknesses in K-12 mathematics education undermine the capabilities of
the U.S. workforce.
Based on present trends, it is unlikely that the U.S. will be able to
maintain its world leadership in the mathematical sciences. It is, however,
essential for the U.S. to remain the world leader in critical subfields, and
to maintain enough strength in all subfields to be able to take full advan-
tage of mathematics developed elsewhere. Without remedial action by the
universities and [the NSF], the U.S. will not remain strong in mathematics:
there will not be enough excellent U.S.-trained mathematicians, nor will it
be practicable to import enough experts from elsewhere, to fill the Nation’s
needs. . . .
We recommend that [the NSF] encourage programs that:
• roaden graduate and undergraduate education in the mathematical
B
sciences. Provide support for full time graduate students in the math-
ematical sciences comparable with the other sciences.
• rovide increased opportunity for postdoctoral study for those who
P
wish to become academic researchers as a means to broaden and
strengthen their training as professional mathematicians.
5 NationalScience Foundation, 1998, Report of the Senior Assessment Panel for the Inter-
national Assessment of the U.S. Mathematical Sciences. NSF, Arlington, Va., p. ii.

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158 APPENDIX A
• ncourage and foster interactions between university-based mathemati-
E
cal scientists and users of mathematics in industry, government, and
other disciplines in universities.
• aintain and enhance the historical strength of the mathematical sci-
M
ences in its academic setting as an intellectual endeavor and as a foun-
dation for applications, sustaining the United States position of world
leadership.6
The release of the Odom report was followed by strong increases in
funding for NSF/DMS, with the division’s budget nearly doubling from
FY2000 to FY2004, when it reached $200 million per year. The NSF
d
irector at that time, Rita Colwell, was very supportive of the mathematical
sciences and encouraged a number of new initiatives, including partnerships
between DMS and other NSF units. In addition, DMS began programs
aimed at improving career preparation for the future mathematical sciences
workforce and substantially broadened the portfolio of mathematical sci-
ences research institutes.
6 Op. cit., pp. 1-2.