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Executive Summary The Committee on U.S. Mathematical Sciences Research Institutes was charged with characterizing the role that such institutes currently play in furthering research in the mathematical sciences1 and with evaluating the advisability of changing or expanding that role. The committee was favorably impressed by the breadth and depth of the contributions of research institutes in the mathematical sciences that have appeared throughout the world. These institutions have catalyzed the development of important new results, nurtured continued growth of the mathematical enterprise, and initiated exciting new applications of mathematics. Existing broadly based mathematical research institutes in the United States have served the scientific community well and will continue to do so by contributing in the following important ways to the vitality of the mathematical sciences: 1. Decisively advancing mathematical research, and ensuring that its progress is robust; 2. Catalyzing group and team interactions focused on topics of noteworthy potential; 3. Supplying high-quality outreach to and interaction with industry and the scientific community; 4. Providing first-class postdoctoral programs in both core and interdisciplinary mathematics; 5. Enabling renowned senior researchers to direct, influence, and mentor younger scientists at crucially beneficial points in those younger researchers' careers; 6. Sharpening, both in core and applied areas, mathematical research's focus via quick-response workshops on key, cutting-edge issues and fast-breaking "hot topics"; 7. Enriching and invigorating mathematical education at every level; and 8. Being a hub for mathematical resources, archives, and tools. Of course some university departments also can and do address at least some of these needs. In spite of the accomplishments and positive attributes of existing institutes, the committee identified fundamental needs and challenges unlikely to be met by broadly based institutes. A primary reason for considering new types of institutes is the growing U.S. dependence on scientific and technological advances, an increasing number of which rely on progress in mathematical sciences research. New research in the mathematical sciences is essential to address theoretical and practical questions, often radically new and increasingly difficult, that underlie progress in many fields of science and technology. Therefore, the nation will benefit from rapid expansion and robust development of mathematical sciences research, as well as from increases in the level of interaction between core mathematicians, other mathematical sciences researchers, and researchers in areas of science, engineering, medicine, and technology that are ripe for investigation via mathematical techniques. Institutes are a significant mechanism for enabling these sorts of interactions. Another driver for new types of institutes is that advances in computer technology and software development have changed dramatically the ways in which mathematical scientists interact and do research and have also made possible the creation of completely new mechanisms for experimental research that are playing a rapidly increasing role in the mathematical sciences. Inadequate access to existing research resources and software tools developed by mathematical scientists working in different areas points to an opportunity to make better use of modern technology. Specifically, a systematic effort is needed to make all such information and computer resources visible and accessible to researchers in the mathematical sciences, especially in view of the fact that mathematical researchers are increasingly more geographically dispersed in the 1 The mathematical sciences include mathematics and its applications, statistics, operations research, and scientific computing (COSEPUP, 1997; NRC, 1992).
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United States. Such an effort would promote the development of new tools capable of addressing important open questions that cannot be pursued today. To address these critical needs, the committee makes two recommendations: The committee recommends that the National Science Foundation's Division of Mathematical Sciences embark on a process of cooperation with other funding units or agencies to establish a well-chosen and critically focused research institute for mathematical sciences devoted to intensive research in a field whose emerging interface with the mathematical sciences shows great potential for the incorporation of mathematical ideas to achieve important societal advances. The committee recommends that the National Science Foundation's Division of Mathematical Sciences establish a research institute for experimental mathematics and electronic tools in the mathematical sciences. Its mission would be to promote the experimental component of mathematical sciences research, to facilitate the development of new computer-based tools, and to provide visibility and accessibility to existing tools and to existing research resources that are scattered throughout the world. In making these recommendations, the committee emphasizes that mathematical research institutes must be based on a strong and vigorous mathematical community. With this in mind, the committee strongly believes that it would not be in the best interest of either the mathematical sciences community or society as a whole to transfer funding from existing NSF mathematical sciences individual (principal investigator) research grant programs to funding for existing or additional mathematical sciences institutes. The strategic and increasingly important role played by mathematical sciences research in every segment of society constitutes a strong justification for new federal funding for the proposed new ventures.
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