U.S. Research Institutes in the Mathematical Sciences

Assessment and Perspectives

Committee on U.S. Mathematical Sciences Research Institutes

Board on Mathematical Sciences

Commission on Physical Sciences, Mathematics, and Applications

National Research Council

National Academy Press
Washington, D.C.



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U.S. Research Institutes in the Mathematical Sciences Assessment and Perspectives Committee on U.S. Mathematical Sciences Research Institutes Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council National Academy Press Washington, D.C.

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NOTICE: The project that is the subject of this report was approved by the Governing Board of the National Research Council, whose members are drawn from the councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences and with regard for appropriate balance. The National Academy of Sciences is a private, nonprofit, self-perpetuating society of distinguished scholars engaged in scientific and engineering research, dedicated to the furtherance of science and technology and to their use for the general welfare. Upon the authority of the charter granted to it by the Congress in 1863, the Academy has a mandate that requires it to advise the federal government on scientific and technical matters. Dr. Bruce Alberts is president of the National Academy of Sciences. The National Academy of Engineering was established in 1964, under the charter of the National Academy of Sciences, as a parallel organization of outstanding engineers. It is autonomous in its administration and in the selection of its members, sharing with the National Academy of Sciences the responsibility for advising the federal government. The National Academy of Engineering also sponsors engineering programs aimed at meeting national needs, encourages education and research, and recognizes the superior achievements of engineers. Dr. William A. Wulf is president of the National Academy of Engineering. The Institute of Medicine was established in 1970 by the National Academy of Sciences to secure the services of eminent members of appropriate professions in the examination of policy matters pertaining to the health of the public. The Institute acts under the responsibility given to the National Academy of Sciences by its congressional charter to be an adviser to the federal government and, upon its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of the Institute of Medicine. The National Research Council was organized by the National Academy of Sciences in 1916 to associate the broad community of science and technology with the Academy's purposes of furthering knowledge and advising the federal government. Functioning in accordance with general policies determined by the Academy, the Council has become the principal operating agency of both the National Academy of Sciences and the National Academy of Engineering in providing services to the government, the public, and the scientific and engineering communities. The Council is administered jointly by both Academies and the Institute of Medicine. Dr. Bruce Alberts and Dr. William A. Wulf are chairman and vice-chairman, respectively, of the National Research Council. This material is based on work supported by the National Science Foundation under Grant No. DMS-9812000. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Copyright 1999 by the National Academy of Sciences. All rights reserved. International Standard Book Number 0-309-06492-9 Additional copies of this report are available from: Board on Mathematical Sciences National Research Council 2101 Constitution Avenue, N.W. Washington, D.C. 20418 Printed in the United States of America

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COMMITTEE ON U.S. MATHEMATICAL SCIENCES RESEARCH INSTITUTES JEAN-PIERRE BOURGUIGNON, Institut des Hautes Études Scientifiques, Chair JANE K. CULLUM, IBM T.J. Watson Research Center DONALD A. DAWSON, The Fields Institute YAKOV ELIASHBERG, Stanford University ERIC FRIEDLANDER, Northwestern University AVNER FRIEDMAN, University of Minnesota SHANTI GUPTA, Purdue University DONALD St. P. RICHARDS, University of Virginia NOLAN WALLACH, University of California at San Diego Staff JOHN R. TUCKER, Study Director

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BOARD ON MATHEMATICAL SCIENCES ROBERT D. MACPHERSON, Institute for Advanced Study, Chair LYNNE BILLARD, University of Georgia GEORGE CASELLA, Cornell University JENNIFER CHAYES, Microsoft Research FAN R.K. CHUNG GRAHAM, University of Pennsylvania RONALD R. COIFMAN, Yale University ROBERT FEFFERMAN, University of Chicago C. WILLIAM GEAR, NEC Research Institute DIANNE O'LEARY, University of Maryland ALAN S. PERELSON, Los Alamos National Laboratory WILLIAM R. PULLEYBLANK, IBM Corporation DONALD ST. P. RICHARDS, University of Virginia KAREN E. SMITH, University of Michigan DANIEL W. STROOCK, Massachusetts Institute of Technology DEWITT L. SUMNERS, Florida State University Ex Officio Member PETER J. BICKEL, University of California at Berkeley Chair, Committee on Applied and Theoretical Statistics Staff SCOTT T. WEIDMAN, Director RUTH E. O'BRIEN, Staff Associate BARBARA W. WRIGHT, Administrative Assistant

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COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS PETER M. BANKS, ERIM International, Inc., Co-chair W. CARL LINEBERGER, University of Colorado, Co-chair WILLIAM BROWDER, Princeton University LAWRENCE D. BROWN, University of Pennsylvania MARSHALL H. COHEN, California Institute of Technology RONALD G. DOUGLAS, Texas A&M University JOHN E. ESTES, University of California at Santa Barbara JERRY P. GOLLUB, Haverford College MARTHA P. HAYNES, Cornell University JOHN HENNESSY, Stanford University CAROL M. JANTZEN, Westinghouse Savannah River Company PAUL G. KAMINSKI, Technovation, Inc. KENNETH H. KELLER, University of Minnesota MARGARET G. KIVELSON, University of California at Los Angeles DANIEL KLEPPNER, Massachusetts Institute of Technology JOHN KREICK, Sanders, a Lockheed Martin Company (retired) MARSHA I. LESTER, University of Pennsylvania M. ELISABETH PATÉ-CORNELL, Stanford University NICHOLAS P. SAMIOS, Brookhaven National Laboratory CHANG-LIN TIEN, University of California at Berkeley NORMAN METZGER, Executive Director

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Preface This report is the result of a fast-track study of U.S. mathematical sciences research institutes done in response to a request from the National Science Foundation (NSF). The task of the Committee on U.S. Mathematical Sciences Research Institutes was to address the following three questions: 1.   What are the characteristic features of effective mathematical sciences research institutes in the ways that they further mathematical research in the United States, and are there ways that the current configuration can be improved? 2.   What kinds of institutes should there be in the United States, and how many does the nation need? 3.   How should U.S. mathematical sciences research institutes be configured (with regard to, for example, diversity of operating formats, distribution of mathematical fields, and interinstitute cooperation or coordination) in order to have the nation's mathematical research enterprise continue to be most productive and successful?     To address these questions, data that could be assembled and input that could be received from the community in the available time were obtained. In mid-May of 1998, the committee circulated a call for comments (see the appendix) to all PhD-granting department chairs, to officers and board or council members of the major professional societies devoted to mathematical sciences research, and to approximately 35 managers or heads of business or industry mathematical sciences research groups. The committee also held an open information-gathering session in which, at the committee's invitation, the director of the NSF's Division of Mathematical Sciences and executive officers of the Mathematical Sciences Research Institute, the Institute for Mathematics and Its Applications, and the National Institute of Statistical Sciences provided background information and responded to committee members' questions. The committee then held a three-day meeting, had two extended teleconferences, and exchanged electronic mail in which it deliberated extensively on the assigned topics, framed its conclusions and recommendations, and drafted and revised its report. Chapter 1 of this report gives a brief historical view of mathematical research institutes and summarizes community input to the committee, Chapter 2 reviews the impact of current U.S. mathematical research institutes and offers views on continuing value, and Chapter 3 outlines new challenges and a recommended approach for addressing them. Chapter 4 provides closing comments. The committee is grateful for the comments of the following individuals who reviewed this report: John Ball, University of Oxford; Spencer Bloch, University of Chicago; William Browder, Princeton University; Jill Mesirov, Whitehead Institute for Biomedical Research; Harrison Shull, U.S. Naval Postgraduate School (retired); I.M. Singer, Massachusetts Institute of Technology; and Frank Stillinger, Lucent Technologies. Responsibility for the report's final content rests solely with the authoring committee and the National Research Council.

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Contents     Executive Summary   1 1.   Perspective on and Approach to Characterizing Institutes' Roles in the Mathematical Sciences   3     A Brief Historical View of Mathematical Sciences Institutes   3     Initial Mathematical Research Institutes   3     Institutes Based on the IAS Model   3     Mathematical Sciences in Other Institutes and Research Centers   4     Conference Centers   4     Worldwide Growth After Mid-Century   4     Recent Trends   5     A Rough Classification of Existing Mathematical Sciences Institutes   6     Brief Summary of Input to the Committee   7 2.   Current U.S. Research Institutes in the Mathematical Sciences—Impact and Continuing Need   9     Impact of Existing U.S. Research Institutes in the Mathematical Sciences   9     Impact on Research   9     Impact on Mathematical Quality and Culture   9     Vitality of the U.S. Mathematical Enterprise   11     Benefits to Mathematical Education and Other Areas   11     The Continuing Value of Broadly Based Research Institutes in the Mathematical Sciences   13 3.   New Challenges and Two New Types of Research Institutes in the Mathematical Sciences   15     Evolution in the Mathematical Sciences   15     Evolution of Science and Technology: Increasing Need for Mathematical Applications   15     Effects of Technology Development on Research in the Mathematical Sciences   16     Growth and Change in the U.S. Mathematical Sciences Research Community   16     How to Address New Challenges   17     New Requirements   17     Need for Focused Exploration of Topics That Are Becoming Mathematical   17     Need for an Infrastructure for Mathematical Sciences Experimentation and for Sharing of Tools   18     A Proposal for Two New Types of Institutes   18     Research Institute for Mathematical Sciences in Emerging Fields   19     Envisioning an Emerging-Field Mathematical Research Institute   19     Illustration of a Potential Emerging-Field Mathematical Institute   20     Recommendation: Start a Process to Establish Emerging-Field Institutes   21

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    Research Institute for Experimental Mathematics and Electronic Tools in the Mathematical Sciences   21     Envisioning an Institute for Experimental Mathematics and Electronic Tools in the Mathematical Sciences   21     Recommendation: Establish a Research Institute for Experimental Mathematics and Electronic Tools in the Mathematical Sciences   22 4.   Recap and Closing Comments   23     References   25     Appendix Description of Input from the Mathematical Sciences Community   27