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INVITED WORKSHOP PAPERS

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Introductory Comments
Avner Friedman
Chair, Board on Mathematical Sciences, National Research Council
In August 1993 at Chantilly, Virginia, the Commission on Physical Sciences, Mathematics, and Applications of the National Research Council held a workshop entitled ''Beginning a Dialogue on the Changing Environment for the Physical and Mathematical Sciences." The workshop was attended by participants from academia, government, and industry. It was followed in June 1994 by two other regional dialogues, held in San Francisco, California, and Vail, Colorado. The following main themes emerged from these three workshops:
The need to effect significant changes in both the educational and research missions of the universities;
A recognition that the traditional training of scientists may be too narrow from the perspective of society, industry, and, in particular, the scientific community itself; and
A desire to move from analysis to action.
Ron Douglas and I participated in the Vail meeting. On the two-hour ride back to the Denver Airport, we discussed the need for the mathematics community to take the lead in a process that will articulate the challenges our community faces within the changed environment, and develop a process needed to position our community so that it can thrive in the new environment.
I subsequently discussed the idea of addressing this need in a workshop; I talked with Shmuel Winograd, Lou Auslander, William Browder, Mary Ellen Bock, and members of the Board on Mathematical Sciences. The Sloan Foundation, the National Science Foundation, and the Intel Foundation agreed to fund this workshop. John Tucker, director of the Board of Mathematical Sciences (BMS), has been instrumental in working out the details.
This workshop is organized as follows.
Today, Friday, from 1:30 p.m. to 5:30 p.m., we shall hear from speakers who will provide information and perspectives on (1) how the public views science and mathematics, (2) how scientists view the role of mathematicians, (3) the challenges for NSF, (4) challenges in the education arena, and (5) areas of new opportunities for the mathematical sciences.
The next phase of the workshop will begin tonight after dinner, with an initial meeting of the four break-out groups as described in the program. Each group will be given a general theme and a set of questions. In the initial meeting the groups may discuss any and all of the themes. Saturday morning each break-out team will make a brief report in a general session. This will set the stage for the third phase, which begins tomorrow at 10:00 a.m., when each break-out group will concentrate on its own theme. Tomorrow at 4:30 p.m. each team will make its final report in a general session. The break-out group leaders, together with John Tucker and myself, will then generate a draft summary document. We shall present this document to all of you Sunday morning, in a general session, for discussion, modifications, and adjustments.
The break-out groups, in addressing their individual themes, are asked to respond in a way that addresses the following general questions:

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What are the national needs for the mathematical sciences?
How can the mathematical sciences community respond to these needs?
What resources do we require to do that?
Let me briefly go over the assigned topics.
The first topic deals with communication within and outside the discipline. Several items have been suggested for discussion. The most important are the following:
How to establish mechanisms by which the mathematical sciences community can communicate its contributions and values, and
How to develop a network of mathematical scientists to maintain regular contact with legislators and the public at large.
Your ideas are needed on how to help mathematics departments maintain and enhance their programs and their standing within the university. You are asked to provide more than general advice. You are asked for mechanisms that will be useful and that can be implemented. One possible suggestion is to set up a regular series of workshops for chairs of departments to address issues concerning the impact of university restructuring and reorganization on mathematics departments: how to anticipate, avoid, and react to such changes.
To increase public appreciation of the contribution that mathematicians make to the nation, our community needs to cultivate leadership. Perhaps a series of tutorial workshops that will deal with science policy and public awareness issues could be run in Washington for young tenured professors.
The second topic is education. Many students receiving a Ph.D. in research universities cannot find jobs for which they were trained. Around the country, graduate programs in mathematics are shrinking and some may close down. The report of an NSF workshop held June 5-6, 1995, Graduate Education and Postdoctoral Training in the Mathematical and Physical Sciences, recommended that departments broaden their educational program by introducing more multidisciplinary courses and off-campus experience. If a mathematics department wishes to introduce such a program, how can it be facilitated? This group could, for example, recommend that the professional societies develop a database or a sequence of workshops that feature case studies on how some departments made the transition, what the obstacles were, and where they succeeded.
Going to the third topic, funding for research and education, here are two items you may want to think about:
In a recent meeting, mathematical sciences program directors of the Air Force Office of Scientific Research, the Office of Naval Research, and the Army Research Office told the Board on Mathematical Sciences Executive Committee that "more and more money goes to multidisciplinary research," and that "many attractive topics of mathematical content are being 'hijacked' by nonmathematicians" since mathematicians do not pay enough attention to upcoming new programs. How can the mathematical sciences community better take advantage of new funding opportunities?
What is the best strategy for apportioning the budget of the NSF Division of Mathematical Sciences? By "best," I mean so that the mathematical sciences community can best

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respond to national needs. I am not suggesting that we resolve this question today. But you may want to consider a recommendation to set up a committee that for a period of, say, 6 months solicits views from all members of the community, and then comes up with strategic guidelines on priorities.
Finally I come to the topic of evaluating performance. The Joint Policy Board of Mathematical Sciences published in 1994 a report titled Recognition and Reward in the Mathematical Sciences. The next step is to examine whether departments are doing a good job or can do a better job in evaluating programs in (1) education (K-12, multidisciplinary) and (2) interdisciplinary research. For example, might a national rating be developed that will help mathematics departments?
I do not wish to give the impression that what is needed is an ever increasing number of committees. Our community has new challenges that it must respond to, and your ideas are needed on how to go about it.
Finally, I want to emphasize the importance of this workshop to reach a consensus. It will not serve the mathematical sciences well if we are divided in our recommendations. At this time of stress from so many directions, this workshop can succeed only if the community moves forward in unity.