U.S. Research Institutes in the Mathematical Sciences: Assessment and Perspectives (1999)

The Committee on U.S. Mathematical Sciences Research Institutes circulated a call for comments (Box A.1) to all PhD-granting department chairs, to officers and board or council members of the major mathematical sciences research professional societies, and to approximately 35 managers or heads of business or industry mathematical sciences research groups. Although, due to the pressure of time, the committee was unable to obtain input from a large number of individuals, there were a fair number of responses (82) to the committee's request for comments. The caveat that these results are most likely not robust should be kept in mind.

Due to the fast-track nature of the committee's study, the request was circulated internationally by electronic mail and through an Internet home page. Although this was not a formal survey, it is the committee's view that electronic circulation of the call for comments resulted in contact with a reasonably wide cross section of mathematical scientists, perhaps a more diverse class than might have been reached in a more traditional circulation of printed queries.

Respondents to the request included individuals in academia, industry, and government, as well as mathematical sciences professional society leaders, with the bulk of the respondents being academics. The majority of respondents (77) were U.S.-based mathematical scientists; a few comments were also received from European scientists.

The research backgrounds of respondents represented a broad spectrum of the mathematical sciences, including what is traditionally considered pure mathematics (32), classical applied mathematics (13), theoretical and applied statistics (12), computational modeling and simulation (11), and several closely connected other disciplines (9). For academic respondents, the institutions represented ranged from Group I through Group III universities (as defined in AMS, 1996, pp. 1501–1502).

The general community that responded was extremely well disposed toward the concept of research institutes in the mathematical sciences.

The prevailing opinion of respondents was that a collection of mathematical institutes, properly constituted, would be well positioned to help the mathematical sciences meet new

challenges and take better advantage of the opportunities now facing the community. A number of those who responded noted that the U.S. mathematical sciences community has an outstanding record of research advances based in academic departments, and some of those achievements can be traced directly to the existence and influence of mathematical sciences research institutes. Such comments were received from both junior and senior academic researchers, as well as from individuals in industry and government.

Many respondents provided extensive commentary on their highly positive professional interactions with existing mathematical sciences research institutes inside and outside the United States. Several junior researchers noted that a dramatic improvement in their early research career could be traced directly to a critical involvement with an institute. A number of senior researchers reported on the highly positive effect that a sabbatical period spent at a research institute had on their careers, or on the careers of mathematical scientists known to them.

Some respondents commented on the personal growth they experienced as the direct consequence of contact with one or more mathematical sciences research institutes. They noted that they had benefited greatly from the opportunity to meet other mathematical scientists with dissimilar backgrounds; sometimes there was the added effect of a broadening and, in some cases, a rejuvenation of the respondent's research interests.

A small group of respondents commented that the list of questions circulated seemed to be somewhat narrowly drawn, focusing mainly on the needs and health of the mathematical sciences community rather than on the progress of U.S. science as a whole. This group was of the opinion that an application for substantial additional funding for existing or new institutes would be most strongly supported if a clear benefit for science and the wider society were demonstrated. Nevertheless, this group also expressed strong support for research institutes dedicated to advancing the mathematical sciences.

There was overwhelming agreement among respondents that neither the continued funding of existing institutes, nor the creation of new institutes, should take place at the expense of research grants for individual investigators. Moreover, nearly all considered that there was no "optimal number" of institutes. These views were a dominant theme among reactions to the committee's questions.

Industry respondents pointed out that institutes that make a strong effort to interact with the physical sciences, engineering, and computer science communities have a superb opportunity to increase awareness of the importance of the mathematical sciences to the nation's economic activities. These institutes can display instances of the mathematical sciences at work and demonstrate the usefulness of the field to a public that often does not understand or appreciate the roles that the mathematical sciences play in everyday life.

There is great need for a variety of interdisciplinary programs to communicate cutting-edge mathematical sciences research to the broader physical and social sciences and engineering communities.

Because of tightening budgets and escalating competition from foreign-based corporations, U.S. businesses are under great pressure to improve their efficiency. Mathematical scientists and institutes willing to interact with corporate scientists in a way that helps the latter's efficiency are in a position to benefit both scientifically and economically.

Government respondents commented that the high visibility of institutes provides the mathematical sciences community with an opportunity to capture the attention of policymakers. Institutes should make it a priority to facilitate cross-disciplinary interactions that expose academic mathematical scientists to non-academic problems. Institutes can also serve as a training ground for young researchers to broaden their horizons.

Institutes can be a highly effective vehicle for the mathematical sciences community to respond to federal or state educational initiatives. They can also help in publicizing mathematical sciences' contributions and in conducting outreach to the general public.

All of the academic respondents said that funding from individual research investigator grants should not be redirected to institutes, and the overwhelming majority of academics felt that the number of mathematical sciences institutes should not be increased at the expense of individual investigator grants.

Overwhelmingly favorable comments were received from academics who had attended an institute. These comments were positive about virtually all aspects of the visit, ranging from interactions between researchers with differing expertise, to rejuvenation of slowing research careers, to the physical surroundings of the institute.

Academic respondents felt strongly that institutes help to fill the need for greater interaction within the broader mathematical community. Given the importance of interdisciplinary research both within disparate branches of the mathematical sciences and between the mathematical sciences and other fields, the view was expressed that institutes help fill a gap that universities may find more difficult to bridge.

There was no enthusiasm among academic respondents for the United States to establish an Oberwolfach-type conference-oriented institute, one concern being the cost, and another being that Oberwolfach was seen as an operation better suited to intradisciplinary, rather than interdisciplinary, research.

The prevailing sentiment among the group of respondents identifying themselves as applied and core mathematicians was that there has been a continual and dramatic decrease in funding for basic research in the mathematical sciences, with one consequence being the virtual disappearance of fully funded sabbatical periods. Both applied and core mathematicians who responded noted the need for increased financial support for senior mathematical scientists to spend sabbatical periods at an institute.

Some of the applied mathematicians who responded expressed the opinion that institutes would be well placed to foster new and significant advances in mathematical modeling for experimental sciences. Some also indicated that now is an appropriate time to consider a new type of institute devoted in large part to the dramatically increased role of computers in computation, large-scale modeling and simulation, industrial engineering and manufacturing, and so on.

Both core academic and industry-based respondents pointed to the resurgence of the strong interaction between core mathematics and theoretical physics.

Respondents felt that new institutes would alleviate the continual and dramatic decrease in funding for basic research in the mathematical sciences, at all levels (from postdoctoral programs to research opportunities for senior researchers). They also felt that new institutes would help counter the great dispersion of research mathematicians from PhD-granting institutions.

Statisticians who responded expressed the view that significant advances in mathematical modeling for the experimental sciences should be a priority for institutes.

It was pointed out that statistics (and probability) play major roles in significant problems involving interdisciplinary research. Statistics is notable in its contact with the empirical side of science. As a discipline, it has undergone a culture shift, returning to its roots in data analysis and scientific inference. Statisticians would benefit from institutes that could facilitate interdisciplinary work between statisticians and, for instance, neuroscientists, geophysicists, and molecular geneticists, as well as social scientists, financial modelers, and engineers.

Among the statisticians who responded, extremely strong support was expressed for institutes modeled after the existing National Institute for Statistical Sciences (NISS). Significant advantages to the mathematical sciences from NISS-type institutes were noted in that they are generically very well suited for outreach to the public, making linkages to industry, and influencing public policy decisions.