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International Benchmarking of US Mathematics Research (1997)
National Academy of Sciences, National Academy of Engineering, Institute of Medicine (SEM)

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH

PREPUBLICATION COPY

INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH

Panel on International Benchmarking of US Mathematics Research

Committee on Science, Engineering, and Public Policy

NATIONAL ACADEMY OF SCIENCES

NATIONAL ACADEMY OF ENGINEERING

INSTITUTE OF MEDICINE

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1

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH PREPUBLICATION COPY INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH Panel on International Benchmarking of US Mathematics Research Committee on Science, Engineering, and Public Policy NATIONAL ACADEMY OF SCIENCES NATIONAL ACADEMY OF ENGINEERING INSTITUTE OF MEDICINE

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH This page in the original is blank.

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH NATIONAL ACADEMY OF SCIENCES NATIONAL ACADEMY OF ENGINEERING INSTITUTE OF MEDICINE COMMITTEE ON SCIENCE, ENGINEERING, AND PUBLIC POLICY 2101 Constitution Avenue Washington, D. C. 20418 202/334-2424 John Gibbons Director, Office of Science and Technology Policy White House Executive Office of the President Washington, DC 20502 RE: Mathematics Research Benchmarking Report Dear Dr. Gibbons: In 1993, the Committee on Science, Engineering, and Public Policy (COSEPUP) of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine issued the report Science, Technology, and The Federal Government: National Goals For a New Era. In that report, COSEPUP suggested that the United States adopt the principle of being among the world leaders in all major fields of science so that it can quickly apply and extend advances in science wherever they occur. In addition, the report recommended that the United States maintain clear leadership in fields that are tied to national objectives, that capture the imagination of society, or that have multiplicative effect on other scientific advances. These recommendations were reiterated in another Academy report, Allocating Federal Funds for Science and Technology, by a committee chaired by Frank Press. To measure international leadership, the reports recommended the establishment of independent panels that would conduct comparative international assessments of scientific accomplishments of particular research fields. COSEPUP indicated that these panels should consist of researchers who work in the specific fields under review (both from the United States and abroad), people who work in closely related fields, and research users who follow the fields closely. To test the feasibility of that recommendation, COSEPUP is conducting experimental evaluations of three fields: mathematics, materials science and engineering, and immunology. The panel for each field has been asked to address the following questions: What is the position of the United States in research in the field relative to that in other regions or countries? What key factors influence relative US performance in the field? On the basis of current trends in the United States and abroad, what will be the relative US position in the near term and the longer term? Panels were asked to develop findings and conclusions, but not recommendations.

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH Attached to this letter is the first of these assessments--that of the field of mathematics. The panel found that today US mathematical research is thriving and preeminent in the world, as demonstrated by the numerous achievements of US mathematicians in mathematics itself and in scientific, engineering, medical, and industrial applications. Key factors that have brought US mathematics to this leadership position are the strength of the research universities, the funding of mathematical research by the US government, and the ability of the United States in the last 60 years to attract foreign talent. Increased employment of mathematicians in industry is a very positive trend. It is hard to predict the future, but the panel sees storm clouds on the horizon. Widespread financial pressures have forced research universities to reduce the size of their graduate programs and the number of permanent faculty. The number of full-time PhD students in mathematics has steadily decreased since a high in 1992. Furthermore, since 1989 the number of academic positions for which new PhDs could apply has fallen by one-third. Government funding for academic mathematics is one of the great uncertainties of the future. In addition, because of improving conditions for mathematicians abroad and restrictive US regulations, the United States might not be able to continue to rely on foreign talent. The other assessments will probably be released in the winter of 1998. Once all three studies are completed, COSEPUP will discuss the feasibility and utility of the benchmarking process and make whatever recommendations it deems necessary. I hope you will find the results useful. Sincerely, Phillip A. Griffiths Chair

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH Panel on International Benchmarking of US Mathematics Research Committee on Science, Engineering, and Public Policy NATIONAL ACADEMY OF SCIENCES NATIONAL ACADEMY OF ENGINEERING INSTITUTE OF MEDICINE PREPUBLICATION COPY NATIONAL ACADEMY PRESS Washington, D.C. 1997

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH NATIONAL ACADEMY PRESS 2101 Constitution Ave., N.W. Washington, D.C. 20418 NOTICE: This volume was produced as part of a project 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. It is a result of work done by the Committee on Science, Engineering, and Public Policy (COSEPUP) as augmented, which has authorized its release to the public. This report has been reviewed by a group other than the authors according to procedures approved by COSEPUP and the Report Review Committee. The National Academy of Sciences (NAS) 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. Under the authority of the charter granted to it by Congress in 1863, the Academy has a working mandate that calls on it to advise the federal government on scientific and technical matters. Dr. Bruce M. Alberts is president of NAS. The National Academy of Engineering (NAE) was established in 1964, under the charter of NAS, as a parallel organization of distinguished engineers. It is autonomous in its administration and in the selection of members, sharing with NAS its responsibilities 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 NAE. The Institute of Medicine (IOM) was established in 1970 by NAS 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 NAS in its congressional charter to be an adviser to the federal government and, on its own initiative, to identify issues of medical care, research, and education. Dr. Kenneth I. Shine is president of IOM. The Committee on Science, Engineering, and Public Policy (COSEPUP) is a joint committee of NAS, NAE, and IOM. It includes members of the councils of all 3 bodies. Financial Support: The development of this report was supported by the National Research Council and the Sloan Foundation. Internet Access: This report is available on COSEPUP's World Wide Web site at http://www2.nas.edu/cosepup. Order from: National Academy Press, 2101 Constitution Ave., NW, Washington, DC 20418. All orders must be prepaid with delivery to a single address. No additional discounts apply. Prices are subject to change without notice. To order by credit card, call 1-800-624-6242 or 202-334-3313 (in Washington metropolitan area) Copyright 1997 by the National Academy of Sciences. All rights reserved. This document may be reproduced solely for educational purposes without the written permission of the National Academy of Sciences. Printed in the United States of America

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH International Benchmarking of US Mathematics Research Panel Members PETER D. LAX (Chair), Professor of Mathematics and Director, Courant Mathematics and Computing Laboratory, New York University, New York, NY MICHAEL F. ATIYAH, Master, Trinity College, Cambridge, England SPENCER J. BLOCH, Professor, Department of Mathematics, University of Chicago, Chicago, IL JOSEPH B. KELLER, Professor, Departments of Mathematics and Mechanical Engineering, Stanford University, Stanford, CA JACQUES-LOUIS LIONS, President, French Academy of Sciences and Professor, College de France, Paris, France YURI I. MANIN, Director, Max Planck Institut fur Mathematik, Bonn, Germany RUDOLPH A. MARCUS, A.A. Noyes Professor of Chemistry, California Institute of Technology, Pasadena, CA GARY C. McDONALD, Head, Operations Research Department, GM Research and Development Center, Warren, MI CATHLEEN S. MORAWETZ, Professor Emeritus, Courant Institute of Mathematical Sciences, New York University, New York, NY PETER SARNAK, Chair, Department of Mathematics, Princeton University, Princeton, NJ I.M. SINGER, Institute Professor, Massachusetts Institute of Technology, Cambridge, MA MARGARET H. WRIGHT, Distinguished Member of Technical Staff, Bell Laboratories, Lucent Technologies, Murray Hill, NJ Project Staff: DEBORAH D. STINE, Study Director PATRICK P. SEVCIK, Research Associate JOHN R. TUCKER, Senior Program Officer NORMAN GROSSBLATT, Editor

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH COMMITTEE ON SCIENCE, ENGINEERING, AND PUBLIC POLICY PHILLIP A. GRIFFITHS (Chair), Director, Institute for Advanced Study, Princeton, NJ BRUCE M. ALBERTS, * President, National Academy of Sciences, Washington, DC WILLIAM F. BRINKMAN, Vice President, Physical Sciences Research, Lucent Technologies, Murray Hill, NJ PETER DIAMOND, Professor of Economics, Massachusetts Institute of Technology, Cambridge, MA GERALD P. DINNEEN, Retired Vice President, Science and Technology, Honeywell, Inc., Edina, MN MILDRED S. DRESSELHAUS, Institute Professor of Electrical Engineering and Physics, Massachusetts Institute of Technology, Cambridge, MA JAMES J. DUDERSTADT, President Emeritus and University Professor of Science and Engineering, Millennium Project, University of Michigan, Ann Arbor, MI MARYE ANNE FOX, Vice President for Research, University of Texas at Austin, Austin, TX RALPH E. GOMORY, President, Alfred P. Sloan Foundation, New York, NY RUBY P. HEARN, Vice President, The Robert Wood Johnson Foundation, Princeton, NJ MARIAN E. KOSHLAND, Professor of Immunology, Department of Molecular and Cell Biology, University of California, Berkeley, Berkeley, CA PHILIP W. MAJERUS, Professor of Medicine, Biochemistry and Molecular Biophysics and Director, Division of Hematology-Oncology, Washington University School of Medicine, St. Louis, MO KENNETH I. SHINE, * President, Institute of Medicine, Washington, DC MORRIS TANENBAUM, Vice President, National Academy of Engineering, Short Hills, NJ WILLIAM JULIUS WILSON, Malcolm Wiener Professor, Center for Social Policy, Harvard University, Cambridge, MA WILLIAM A. WULF, * President, National Academy of Engineering, Washington, DC LAWRENCE E. McCRAY, Executive Director DEBORAH D. STINE, Associate Director * Ex officio member.

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INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH COSEPUP GUIDANCE GROUP MARYE ANNE FOX (Chair), Vice President for Research, University of Texas at Austin, Austin, TX DAVID R. CHALLONER, Vice President for Health Affairs, University of Florida, Gainesville, FL ELLIS B. COWLING, University Distinguished Professor At-Large, North Carolina State University, Raleigh, NC MILDRED S. DRESSELHAUS, Institute Professor of Electrical Engineering and Physics, Massachusetts Institute of Technology, Cambridge, MA GERALD P. DINNEEN, Retired Vice President, Science and Technology, Honeywell, Inc., Edina, MN ALEXANDER H. FLAX, Consultant, Potomac, MD PHILLIP A. GRIFFITHS, Director, Institute for Advanced Study, Princeton, NJ MATHEMATICS BENCHMARKING GUIDANCE GROUP MARYE ANNE FOX (Chair), Vice President for Research, University of Texas at Austin, Austin TX PHILLIP A. GRIFFITHS, Director, Institute for Advanced Study, Princeton, NJ DANIEL KLEPPNER, Professor of Physics, Massachusetts Institute of Technology, Cambridge, MA AVNER FRIEDMAN, Director, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN SHMUEL WINOGRAD, IBM Fellow, International Business Machines Corporation, Thomas J. Watson Research Center, Yorktown Heights, NY ROBERT MacPHERSON, Professor, School of Mathematics, Institute for Advanced Study, Princeton, NJ Staff: LAWRENCE E. McCRAY, Executive Director, COSEPUP DEBORAH D. STINE, Associate Director, COSEPUP JOHN R. TUCKER, Director, Board on Mathematical Sciences NORMAN METZGER, Executive Director, Commission on Physical Sciences, Mathematics, and Applications

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Representative terms from entire chapter:

international benchmarking