**Suggested Citation:**"Appendix A: Past Strategic Studies." National Research Council. 2013.

*The Mathematical Sciences in 2025*. Washington, DC: The National Academies Press. doi: 10.17226/15269.

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

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

^{2} Ibid., p. 5.

**Suggested Citation:**"Appendix A: Past Strategic Studies." National Research Council. 2013.

*The Mathematical Sciences in 2025*. Washington, DC: The National Academies Press. doi: 10.17226/15269.

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 interest 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 graduate 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 improvements 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 Mathematical 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

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^{3} NRC, 1990, *Renewing U.S. Mathematics: A Plan for the 1990s*. National Academy Press, Washington, D.C., p. 3.

^{4} Ibid.

**Suggested Citation:**"Appendix A: Past Strategic Studies." National Research Council. 2013.

*The Mathematical Sciences in 2025*. Washington, DC: The National Academies Press. doi: 10.17226/15269.

employment of new knowledge in the service of society; and achiev[ing] excellence 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 computer 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 substantially 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 sciences 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 advantage 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:

• Broaden graduate and undergraduate education in the mathematical sciences. Provide support for full time graduate students in the mathematical sciences comparable with the other sciences.

• Provide increased opportunity for postdoctoral study for those who wish to become academic researchers as a means to broaden and strengthen their training as professional mathematicians.

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^{5} National Science Foundation, 1998, *Report of the Senior Assessment Panel for the International Assessment of the U.S. Mathematical Sciences*. NSF, Arlington, Va., p. ii.

**Suggested Citation:**"Appendix A: Past Strategic Studies." National Research Council. 2013.

*The Mathematical Sciences in 2025*. Washington, DC: The National Academies Press. doi: 10.17226/15269.

• Encourage and foster interactions between university-based mathematical scientists and users of mathematics in industry, government, and other disciplines in universities.

• Maintain and enhance the historical strength of the mathematical sciences in its academic setting as an intellectual endeavor and as a foundation 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 director 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 sciences research institutes.

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^{6} Op. cit., pp. 1-2.