Close Scrutiny for National Research Investments in the U.K., U.S.

January 8, 1998

James Crowley

A spate of recent reports has documented efforts in several countries--Australia, Canada, the U.K., and the U.S., among others--to benchmark national research results. The most recent of the reports, International Benchmarking of US Mathematics Research (Fall 1997), is the first in a projected series of disciplinary studies from the Committee on Science, Engineering, and Public Policy (COSEPUP) of the U.S. National Research Council. It was produced by a 12-member panel chaired by Peter Lax.*

The various studies have been conducted to survey the health of research in each of the nations, with the introspection most likely driven by the need to assess the national investment in research. In the U.S., for example, the 1995 NRC report Allocating Federal Funds for Science and Technology recommended that the U.S. "strive for clear leadership in the most promising areas of science and technology and those deemed most important to our national goals." A 1993 NRC report had recommended that the U.S. be among world leaders in all major fields of science and technology.

Different Assessment Strategies, Similar Conclusions
The Quality of the UK Science Base was issued in March 1997 by the Office of Science and Technology of the Department of Trade and Industry. The study based its assessment of the quality of scientific research in the U.K. on the Science Citation Index produced by the Institute of Scientific Information in Philadelphia. The report compares bibliometric data for many nations and most major fields of scientific research, including mathematics. The recent NRC report relies in large part on assessments obtained by the 12 panel members (three from outside the U.S.), who conducted informal surveys of experts in 19 subfields. In addition, the panel considered the distribution of international honors, including major prizes and invitations to speak at major international meetings, such as the International Congress of Mathematicians and the International Congress on Industrial and Applied Mathematics.

The reports analyze a country's contributions to world science in terms of the output of individuals from institutions in that country, not with regard to the individuals' citizenship or countries of origin. The NRC report makes it clear that the strength of U.S. research stems from the openness on the part of U.S. institutions to distinguished scientists from around the world. The two reports come to rather similar conclusions. Both argue that the health of the discipline is strong, overall and within the U.K. and the U.S. The U.S. report indicates that roughly 40% of major honors in mathematics go to U.S. mathematicians. According to the U.K. report, the U.S. has the largest shares of world papers (34.6%) and world citations (49.0%); the U.K., with 8.0% and 9.1%, respectively, is second.

Information at a subdisciplinary level is sparse in these reports. The U.K. report discusses the breadth of the science base, providing little information about any single discipline at a finer level. The NRC report does not convey any information about variations within the mathematical sciences; no assessments of subfields are reported, except for the observation that, in all but two of the 19 subfields, at least half of the current leading researchers are from the U.S.

Mathematics in the U.K.
Of greatest interest to readers of SIAM News are the report's assessments of mathematics and computer science. In terms of relative citation impact (number of citations for a country divided by its share of world publications in the field), the U.K. report ranks the U.K. in the top six nations in the world, "with clear strengths in . . . mathematics" and a weaker showing in computer science. One subarea in which the report finds the U.K. relatively weak is mathematical analysis. The report claims "world class strengths" in algebra and geometry, and also in software engineering.

In numbers of citations in mathematics, the top-ranking U.S. and U.K. are followed by France, Germany, and Canada. Denmark and Norway are the leaders for relative citations, followed by the U.K., the U.S., and the Netherlands. In computer science, the report shows the U.S. first in total number of citations, followed by the U.K., Canada, Germany, and France. Israel leads the field in relative citations, followed by the U.S., Switzerland, Canada, and Denmark.

Mathematics in the U.S.
The bottom line of International Benchmarking of US Mathematics Research is that "US mathematical research is thriving in both quality and opportunities." One of those opportunities, interdisciplinary research, is highlighted in the report. The report describes successful applications of mathematics, often through computing, to important problems spanning many disciplines. Successes include the strong connections that have been forged between research in the mathematical sciences and the physical and biological sciences and engineering. Among other examples, the report cites semiconductor modeling, thin films, signal transmission in optical fibers, materials modeling, and imaging (the theme of Mathematics Awareness Week for 1998). (These and other examples are described with references to a long list of NRC reports and to the 1995 joint Minerals, Metals, and Materials Society–SIAM workshop.)

Turning to industrial applications, the report points to the role of mathematics and computing in the design of the Boeing 777 and in animation (citing the SIAM News article "Mathematcis Meets Film Animation," September 1996). The rapid application of wavelets to various problems in imaging and in the storage and transmission of information is also cited. Without diminishing the important role of fundamental discoveries in all areas of the mathematical sciences, the report emphasizes both the need and the growing opportunities for interdisciplinary research and the application of mathematics to interdisciplinary problems through computing. Observing that U.S. mathematicians play an important role in interdisciplinary research, the report emphasizes emerging opportunities for mathematicians. Examples include the need for mathematical analysis and algorithms to make sense of large data sets, a possible major focus of the National Science Foundation's Knowledge and Distributed Intelligence (KDI) initiative. Other new opportunities for interdisciplinary research and industrial applications include analysis and control of communications traffic and transmission of signals in optical fibers.

An interesting graph from the NRC report compares the numbers of publications in the U.S. and in the European Community countries during the period from 1981 to 1996. (Worldwide, according to the U.K. report, the total number of scientific publications increased at a rate of 3.7% per year during the period from 1981 to 1994.) The graph depicts the substantial, steady growth in research in the EC relative to the U.S., with the EC countries surpassing the U.S. in number of papers produced in 1995.

A Warning Note
Why are all these reports appearing now? The obvious answer is the need to justify research funding in an environment of limited funds and, moreover, to make a case for further funding, especially for nonmilitary R&D. With its comparisons of scientific disciplines within the U.K., and its assessments of performance in those disciplines in the U.K. relative to other countries, the U.K. report comes closest to naming the areas that are doing well and those that are not.

The NRC report focuses on the mathematical sciences alone and makes clear the need for sustained funding for mathematical research. It is here that it strikes a troubled note. Because of differences in the ways in which research is supported in various countries, the panel points out, it is difficult to make comparisons between countries. Within the U.S., however, the mathematical sciences have not fared well in recent years when compared with other disciplines. In 1994–95, mathematics had the lowest rate of growth (1%) in federal funding and was the only science to grow more slowly than inflation. Much of the relative disfavor is attributed to a large decrease in military spending on the mathematical sciences. A second area of concern is "the potential erosion of the US research base because of a decrease in the number of graduate students at leading universities." This is related to two phenomena: employment opportunities and the growth in the number and proportion of PhDs received in the U.S. by non-U.S. students.

Employment trends cited include an oversupply of new PhDs relative to available tenure-track positions (a 33% decrease in the number of academic positions open to new PhDs from 1989 to 1994), with no distinction among the subfields within the mathematical sciences; an increase in the number of nonpermanent positions (with these positions accounting for 50% of the openings for new PhDs in doctorate-granting departments in 1994–95); and an increase in industrial employment of mathematicians, from less than 10% of PhD mathematicians in 1973 to more than 20% in 1995, with most of the increase occurring from 1973 to 1987. The U.K. report, considering employment in far more general terms, cites an unemployment rate among recent science and engineering graduates of only 2–3%.

Worrisome funding trends described in the NRC report bear close scrutiny, as do the decline in the number of graduate students in U.S. institutions and the related problem of jobs for new graduates. The various reports conclude, however, that research in the mathematical sciences, measured in terms of scholarly output and connections with other sciences and applications to technology, is extremely healthy and productive.

James Crowley is the executive director of SIAM.

*In addition to Peter Lax of New York University, the members of the panel are Michael Atiyah, Trinity College, Cambridge, England; Spencer Bloch, University of Chicago; Joseph Keller, Stanford University; Jacques-Louis Lions, Collège de France, Paris; Yuri Manin, Max Planck Institut für Mathematik, Bonn, Germany; Rudolph Marcus, California Institute of Technology; Gary McDonald, GM Research and Development Company; Cathleen Morawetz, New York University; Peter Sarnak, Princeton University; I. M. Singer, Massachusetts Institute of Technology; Margaret Wright, Bell Laboratories, Lucent Technologies.

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