• mathematical sciences research from the other sciences, engineering, medicine, and technology.

An e-MSI would emphasize providing tools for individual mathematical sciences researchers through the most effective use of electronic resources. Its structure could take any of several possible forms. For example, it might have one director, a technical staff with several members, and visiting research mathematicians. Or it might be a virtual entity, cooperatively overseen by a consortium of institutions with its directorship periodically rotating among designated representatives from the institutions. A competition for proposals would undoubtedly elicit a wide variety of innovative alternatives.

Research at an e-MSI would focus on the role of experimentation in the development of new mathematical sciences results and on the use of mathematical experiments to construct and test conjectures and to generate counter-examples. Such an institute should serve as a forum where experiments can be described, conjectures posed, techniques debated, and standards set. Many of the researchers involved with an e-MSI would be individuals who already pursue some of these goals but seek opportunities to share others' tools and pool their experience. The e-MSI is envisioned as being an entity whose establishment would support and facilitate curiosity-driven mathematical sciences research.

An outgrowth of these activities would be software tools, numerical and non-numerical algorithms, and visualization software that would both support this type of mathematical sciences research and be made available to the mathematical sciences research community at large. A primary mission of an e-MSI would be to collect and maintain a mathematical software library of tools for mathematical experimentation and to produce new software in support of research in the mathematical sciences.

Currently, there exist various electronic research resources that are not easily accessible. It is increasingly difficult for researchers to keep track of this information or to even know where to look for it. No concerted effort has been made to coordinate it and make all of it readily available to all members of the mathematical research community. Anticipated advances in network communications would enable an e-MSI to provide additional access to such resources to aid in the development of mathematical researchers' capabilities and stimulate new mathematical sciences research. The institute would solicit and accumulate cutting-edge resources developed in various fields in the mathematical sciences.

The committee envisions that an e-MSI would be initiated by the National Science Foundation for a minimum operating period of 5 years. Whatever its ultimate form, an e-MSI's design should reflect careful attention to the experiences (including successes, difficulties, and any failures) of previous or continuing institutes or centers that could be viewed as being similar in some way. Examples might include the Geometry Center and the center for Discrete -Mathematics and Theoretical Computer Science, among others.

Recommendation: Establish a Research Institute for Experimental Mathematics and Electronic Tools in the Mathematical Sciences

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.

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