NSF Panel Calls for Stronger Linkages Between Creators and Users of Mathematics

June 15, 1998

James A. Crowley

"There is a danger that academic mathematics will be perceived as solely a scholarly endeavor rather than as a full participant in the explosion of scientific and technological advances that began five decades ago." So begins the summary of findings in the National Science Foundation's recently released Report of the Senior Assessment Panel for the International Assessment of the U.S. Mathematical Sciences. Similar in its overall findings to last year's report of the National Research Council [1], the NSF assessment differs from earlier reports by making strong recommendations (see below).

Among the recommendations is a call to the mathematical sciences community to strengthen its connections to users of mathematics in industry and in other disciplines. While recognizing the importance of maintaining strength in the basic areas within mathematics, including applied and computational mathematics, the report emphasizes the need for rapid transfer of information between the creators and users of mathematics. The report's recommendations, if followed, would represent a major shift for NSF.

In addition to the important theme of "missed opportunities"---connections with other sciences that need to be pursued---the report considers government support for the mathematical sciences, which is found to be lower in the U.S. than in other countries and, within the U.S., lower than that for other sciences, especially in the area of graduate education. Echoing the NRC report, this assessment notes that the U.S. "enjoys a position of world leadership" in the mathematical sciences. This position is viewed as fragile, however, in that it depends on the influx of talented people from other nations. The report includes assessments of subareas within the mathematical sciences (as an appendix), but its strength lies in the overall findings and recommendations.

The report was prepared in part as an experimental step toward meeting the requirements of the Government Performance and Results Act (GPRA) of 1993. It is not at all clear, says Donald Lewis, director of the Division of Mathematical Sciences at NSF, that such benchmarking efforts will meet the present thinking of the Office of Management and Budget as to what it wants to see as a GPRA report; the report, however, goes beyond a GPRA assessment in that it makes recommendations for keeping U.S. mathematics at the forefront.

Missed Opportunities
"A major finding of the report," according to Lewis, "is missed opportunities for mathematics to play a substantial role in exciting, increasingly numerous developments that have major impact on the general populace. Engineering, science, finance, manufacturing, and public policy all need mathematics to advance. The question is whether mathematicians will rise to the challenge, and whether they will recognize that all of mathematics can be useful."

One of the most important opportunities for NSF, according to the report, is the strengthening of connections between creators and users of mathematics, both in industry and in other disciplines. The report contains a clear call for multidisciplinary involvement: "Both industrial and academic mathematics must reach out to one another if the two are to interact effectively."

The assessment panel perceives a weakness in the linkages between academic mathematicians and users of the mathematical sciences. The report points to a growing trend, most apparent in England and the Netherlands, to foster interactions between academia and industry, citing as examples the Oxford Centre for Industrial and Applied Mathematics at Oxford University and the Isaac Newton Institute in Cambridge. While identifying the Institute for Mathematics and Its Applications as an example in the U.S., the panel finds U.S. departments that interact with industry to be very much in the minority. The ongoing DARPA-NSF initiative in thin films is given as one example of an attempt by DMS to foster multidisciplinary research with industrial connections.

DMS currently uses approximately 10% of its budget to co-fund projects with other NSF divisions, Donald Lewis points out, "so it already is moving in the directions suggested by the report." The KDI (Knowledge and Distributed Intelligence) initiative provides mathematicians with the opportunity to make greater strides in this direction, he says; work on thin films, in particular, would fit into the current emphasis on problems of scale in the NCC (New Computational Challenges) component of KDI.

The SIAM Report on Mathematics in Industry [2], undertaken to increase awareness of opportunities for interactions with industry, is heavily cited in the panel's report. SIAM is continuing its efforts in that direction through a series of regional workshops; the first took place in May, at Worcester Polytechnic Institute, and a second is scheduled for the fall, at the University of Illinois Chicago (both to be reported in SIAM News or on the Web).

"Fundamental changes" taking place in many areas of science and technology, according to the report, are increasing the need for new mathematics and introducing new problems and "deep challenges." These emerging areas, in biology and communications, for example, offer new opportunities for mathematics.

The need for connections has been a theme of several recent studies, including that of the National Research Council's Committee on Strengthening the Linkages between the Sciences and Mathematical Sciences.

The Health of the Discipline---Students
The report discusses ways to maintain a flow of high-quality students into the discipline, focusing on the retention of graduate students. "Careers in mathematics," the report states, "have become less attractive to U.S. students." Reasons cited include the length and narrowness of training, the limited opportunities for postdoctoral training, and the focus on academic careers.

Especially compelling are data comparing support for graduate students in the mathematical sciences and those in other disciplines. The ratio of institutional support (primarily teaching assistantships) to federal support (research assistantships) is about 7:1 in the mathematical sciences, as compared with 1.25:1 in the biological sciences and 1.43:1 in the physical sciences.

The panel believes that the preponderance of teaching assistantships, by significantly increasing the time required to complete a degree in mathematics, is contributing to the departure of graduate students from the discipline before completing their degrees. (A secondary effect, not mentioned in the report, is that the reliance on teaching assistantships may also discourage graduate students from seeking industrial positions on completion of their degrees---the system reinforces the notion that an academic career is what mathematics is all about while masking opportunities outside academia for those with mathematical training.)

Antidotes for this trend include increased funding for graduate training and broadening of the curriculum. The panel points out that undergraduate students motivated by a desire to apply mathematics often find that they must study in departments outside mathematics but then do not acquire a strong foundation in mathematics. "Academic mathematical science must strike a better balance between theory and applications," the report states.

The recent emergence of graduate programs in computational science may bring opportunities for the mathematical sciences. Without increased openness to these opportunities on the part of mathematicians, however, there is a risk that a valuable component of the mathematical sciences will be lost.

The Health of the Discipline---Funding
The report documents the low level of funding in the mathematical sciences in the U.S., relative both to other nations and to other disciplines. Among active academic researchers in the U.S., for example, only 35% in the mathematical sciences, as compared with 69% in the biological and 67% in the physical sciences, receive federal support.

The panel highlights the responsibility of NSF as "the principal federal funder of US mathematical sciences." SIAM members, however, must also recognize the important role of agencies in the Departments of Energy and Defense for certain subareas of the discipline. As documented in the report, declining funding at these agencies would impose serious risks and would adversely affect parts of the discipline, which would in turn have serious effects on NSF's programs.

Panel Composition
The senior assessment panel was composed of 13 researchers, both from the mathematical sciences and from other disciplines, with seven from the U.S. and the remainder from outside the U.S. (All the members of the NRC panel, by contrast, were from the mathematical sciences community, with only a quarter from outside the U.S.) Lt. General William Odom, USA (Ret.), served as the panel chair, and Ettore Infante of Vanderbilt University convened the panel. To be a panel member, an individual could not have received funding from NSF in the previous eight years.

References
[1] International Benchmarking of US Mathematics Research, Peter Lax, ed., National Research Council, Washington, DC, 1997.

[2] SIAM Report on Mathematics in Industry, SIAM, Philadelphia, 1995.

James M. Crowley is the executive director of SIAM.

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