INTRODUCTION

The mathematical sciences hold a special position in science: They are the intellectual disciplines for the study of abstract structures as well as the language of modeling, analysis, and computation. The mathematical sciences provide the other scientific and engineering fields with the concepts and computational tools so necessary for their advances.

Mathematical sciences research has many recent achievements to which it can point with pride. The proof of Fermat's Last Theorem not only resolved a 350-year-old problem, but also deepened the understanding of important mathematical structures. The mathematical development of wavelets provided new computational tools for important engineering problems, such as data compression and imaging, whose full potential is still being explored and expanded. The recent outpouring of support for the mathematical sciences by leaders in various scientific and engineering disciplines, in response to a (subsequently rescinded) decision to eliminate the graduate mathematics program at the University of Rochester, illustrates how widespread is the recognition of the importance of mathematical sciences research for advances in science and technology. Moreover, it is internationally recognized that U.S. universities are world leaders in graduate-level mathematics education.

A workshop titled "Actions for the Mathematical Sciences in the Changed Environment" was planned as a follow-on to a 1993-1994 project initiated by the National Research Council's (NRC's) Commission on Physical Sciences, Mathematics, and Applications (CPSMA) and reported on in Dialogues on the Changing Environment for the Physical and Mathematical Sciences (National Academy Press, Washington, D.C., 1994), and in Regional Dialogues on the Changing Environment for the Physical and Mathematical Sciences: Report of Two Conferences (National Academy Press, Washington, D.C., 1995). The purpose of the BMS workshop was to advance those CPSMA dialogues by focusing on and exploring specific issues now facing the mathematical sciences community. The workshop's goal was to lead the mathematical sciences community in productive directions that reflect and respond to the new imperatives facing the scientific community at large and all of society as a result of recent changes in the national and international economic and political arenas.

Nominations for possible workshop participants were obtained from numerous mathematical sciences professional organizations, including the American Mathematical Society, Mathematical Association of America, Society for Industrial and Applied Mathematics, Association for Women in Mathematics, National Association of Mathematicians, Institute of Mathematical Statistics, American Statistical Association, National Council of Teachers of Mathematics, American Mathematical Association of Two-Year Colleges, and Institute for Operations Research and the Management Sciences, as well as from the Mathematical Sciences Education Board. A BMS-designated steering committee, consisting of BMS chair Avner Friedman, BMS Executive Committee member Mary Ellen Bock, CPSMA member (and former BMS chair) Shmuel Winograd, and William Browder of Princeton University, developed a draft agenda and tentative workshop plan and prepared extensive lists of background issues and motivating questions for each of four areas on which workshop break-out groups would focus (see Appendix A). The steering committee also suggested names of people to be invited to lead the break-out groups, and to be invited as workshop speakers.



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INTRODUCTION The mathematical sciences hold a special position in science: They are the intellectual disciplines for the study of abstract structures as well as the language of modeling, analysis, and computation. The mathematical sciences provide the other scientific and engineering fields with the concepts and computational tools so necessary for their advances. Mathematical sciences research has many recent achievements to which it can point with pride. The proof of Fermat's Last Theorem not only resolved a 350-year-old problem, but also deepened the understanding of important mathematical structures. The mathematical development of wavelets provided new computational tools for important engineering problems, such as data compression and imaging, whose full potential is still being explored and expanded. The recent outpouring of support for the mathematical sciences by leaders in various scientific and engineering disciplines, in response to a (subsequently rescinded) decision to eliminate the graduate mathematics program at the University of Rochester, illustrates how widespread is the recognition of the importance of mathematical sciences research for advances in science and technology. Moreover, it is internationally recognized that U.S. universities are world leaders in graduate-level mathematics education. A workshop titled "Actions for the Mathematical Sciences in the Changed Environment" was planned as a follow-on to a 1993-1994 project initiated by the National Research Council's (NRC's) Commission on Physical Sciences, Mathematics, and Applications (CPSMA) and reported on in Dialogues on the Changing Environment for the Physical and Mathematical Sciences (National Academy Press, Washington, D.C., 1994), and in Regional Dialogues on the Changing Environment for the Physical and Mathematical Sciences: Report of Two Conferences (National Academy Press, Washington, D.C., 1995). The purpose of the BMS workshop was to advance those CPSMA dialogues by focusing on and exploring specific issues now facing the mathematical sciences community. The workshop's goal was to lead the mathematical sciences community in productive directions that reflect and respond to the new imperatives facing the scientific community at large and all of society as a result of recent changes in the national and international economic and political arenas. Nominations for possible workshop participants were obtained from numerous mathematical sciences professional organizations, including the American Mathematical Society, Mathematical Association of America, Society for Industrial and Applied Mathematics, Association for Women in Mathematics, National Association of Mathematicians, Institute of Mathematical Statistics, American Statistical Association, National Council of Teachers of Mathematics, American Mathematical Association of Two-Year Colleges, and Institute for Operations Research and the Management Sciences, as well as from the Mathematical Sciences Education Board. A BMS-designated steering committee, consisting of BMS chair Avner Friedman, BMS Executive Committee member Mary Ellen Bock, CPSMA member (and former BMS chair) Shmuel Winograd, and William Browder of Princeton University, developed a draft agenda and tentative workshop plan and prepared extensive lists of background issues and motivating questions for each of four areas on which workshop break-out groups would focus (see Appendix A). The steering committee also suggested names of people to be invited to lead the break-out groups, and to be invited as workshop speakers.

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This workshop summary indicates what issues were discussed as possible actions and reflects the workshop discussions as refined by further consultation with workshop attendees and subsequent NRC review. They are presented as observations of themes raised at the workshop and are for the mathematical sciences community to use as it wishes. They do not constitute the recommendations of an NRC-appointed committee.