MATHEMATICAL SCIENCES, TECHNOLOGY, AND ECONOMIC COMPETITIVENESS

EDITED BY JAMES G. GLIMM

Board on Mathematical Sciences

Commission on Physical Sciences, Mathematics, and Applications

National Research Council

National Academy Press
Washington, D.C. 1991



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Mathematical Sciences, Technology, and Economic Competitiveness MATHEMATICAL SCIENCES, TECHNOLOGY, AND ECONOMIC COMPETITIVENESS EDITED BY JAMES G. GLIMM Board on Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council National Academy Press Washington, D.C. 1991

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Mathematical Sciences, Technology, and Economic Competitiveness 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. This report has been reviewed by a group other than the authors according to procedures approved by a Report Review Committee consisting of members of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. 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. Frank Press 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. Robert M. White 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. Samuel O. Thier 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. Frank Press and Dr. Robert M. White are chairman and vice chairman, respectively, of the National Research Council. The National Research Council established the Board on Mathematical Sciences in 1984. The objectives of the board are to maintain awareness and active concern for the health of the mathematical sciences and to serve as the focal point in the National Research Council for issues connected with the mathematical sciences. In addition, the board is designed to conduct studies for federal agencies and maintain liaison with the mathematical sciences communities and academia, professional societies, and industry. Support for this project was provided by the Air Force Office of Scientific Research, the Army Research Office, the Department of Energy, the National Science Foundation, the National Security Agency, and the Office of Naval Research. Library of Congress Catalog Card No. 91-60253 International Standard Book Number 0-309-04483-9 Copies available for sale from National Academy Press 2101 Constitution Avenue, NW Washington, DC 20418 S 333 Printed in the United States of America

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Mathematical Sciences, Technology, and Economic Competitiveness BOARD ON MATHEMATICAL SCIENCES PHILLIP A. GRIFFITHS, Duke University, Chair LAWRENCE D. BROWN, Cornell University SUN-YUNG CHANG, University of California at Los Angeles RONALD DOUGLAS, State University of New York-Stony Brook AVNER FRIEDMAN, University of Minnesota FREDERICK W. GEHRING, University of Michigan JAMES GLIMM, State University of New York-Stony Brook JOSEPH KADANE, Carnegie-Mellon University DIANE LAMBERT, AT&T Bell Laboratories GERALD J. LIEBERMAN, Stanford University JEROME SACKS, University of Illinois SHMUEL WINOGRAD, IBM T. J. Watson Research Center Ex Officio Member WILLIAM EDDY, Carnegie-Mellon University Staff NORMAN METZGER, Interim Staff Director LAWRENCE H. COX, Principal Staff Officer CRAIG E. HICKS, Senior Editorial Assistant JO NEVILLE, Administrative Secretary RUTH E. O'BRIEN, Staff Associate HANS J. OSER, Staff Officer SEYMOUR M. SELIG, Senior Staff Officer JOHN TUCKER, Staff Officer JAMES A. VOYTUK, Senior Staff Officer SCOTT T. WEIDMAN, Senior Staff Officer BARBARA W. WRIGHT, Administrative Assistant

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Mathematical Sciences, Technology, and Economic Competitiveness COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS NORMAN HACKERMAN, Robert A. Welch Foundation, Chair PETER J. BICKEL, University of California at Berkeley GEORGE F. CARRIER, Harvard University HERBERT D. DOAN, The Dow Chemical Company (retired) DEAN E. EASTMAN, IBM T. J. Watson Research Center MARYE ANNE FOX, University of Texas PHILLIP A. GRIFFITHS, Duke University NEAL F. LANE, Rice University ROBERT W. LUCKY, AT&T Bell Laboratories CHRISTOPHER F. McKEE, University of California at Berkeley RICHARD S. NICHOLSON, American Association for the Advancement of Science JEREMIAH P. OSTRIKER, Princeton University Observatory ALAN SCHRIESHEIM, Argonne National Laboratory ROY F. SCHWITTERS, Superconducting Supercollider Laboratory KENNETH G. WILSON, Ohio State University NORMAN METZGER, Executive Director

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Mathematical Sciences, Technology, and Economic Competitiveness PREFACE The fundamental importance of mathematics to the U.S. technology base, to the ongoing development of advanced technology, and, indirectly, to U.S. competitiveness is well known in scientific circles. However, the declining number of U.S. high school students who decide to seek a career in science or engineering is an important indication that many people do not appreciate how central the mathematical sciences have become to our technological enterprise. The National Research Council's Board on Mathematical Sciences has prepared this report to underscore the importance of supporting mathematics instruction at all levels, from kindergarten through graduate school, to prepare our youth for successful careers in science and engineering. The report is addressed first to the members of the mathematics community, who must play an active role in effecting quite aggressively the technology transfer that stimulates innovation and puts U.S. industry in a competitive position with its trading partners. Corporate decision makers will also benefit from acquainting themselves with the conclusions drawn in this report: mathematics is useful across the entire product cycle, contributing to making better products, improving quality, and shortening the design cycle. Policy makers at the federal and state levels, college and university administrators, high school teachers, and nonscientists as well may also find instructive this report's discussion of how mathematical and quantitative reasoning have penetrated the real world around us. To trace the impact of mathematics on U.S. technology necessarily involves making choices. The examples in this report are intended to illustrate the widespread use of mathematical reasoning. The board has focused primarily on the use of such reasoning by mathematical

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Mathematical Sciences, Technology, and Economic Competitiveness scientists themselves, as defined by their professional training, departmental or professional affiliation, or funding sources. Also included in this discussion are examples of the cross-disciplinary impacts of mathematical scientists working with members of other disciplines. A few examples have been drawn from the mathematically oriented portions of related disciplines, such as engineering and computer science. A report such as this cannot be exhaustive, nor can it be free of repetition as the same ideas are considered from different viewpoints. Powerful mathematical concepts, once thought to be without practical relevance, affect thinking today in many unrelated fields and, more often than not, it is the mathematician who has discovered such connections. Mathematical models established by engineers for fluid flow turn up in transportation studies and in economics; ideas developed in linear algebra are basic to the large input-output models that describe the national economy. Differential equations describe weather forecasting models, semiconductor behavior, and crystallization of substances; even when the equations differ radically, common methods of solution have often been developed and are widely used not only by mathematicians but also by professionals in many other disciplines who could not function without the tools developed by mathematicians. While considering such examples of the impact of mathematics, the reader should keep in mind that the distinction between direct and indirect support and between short- and long-range connections cannot be drawn clearly. Neither does the board possess a formula that establishes a numerical relationship between increased support for mathematical research and an increase to the gross national product. Mathematical principles and ideas manifest themselves in several ways: sometimes the connection is obvious and direct; in other cases the influence is more subtle and long-range in nature. Chapter 2, "Key American Industries," illustrates the use of advanced technology in five major U.S. industries—aircraft, semiconductors and computers, petroleum, automobiles, and telecommunications—and examines how their competitive positions over the past decade have been affected by the industries' access to advanced technology. In chapter 3, "The Product Cycle," 11 technologies widely used in modern manufacturing are examined for the impact of mathematics in such applications as economic planning, simulation, quality control, inventory manage-

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Mathematical Sciences, Technology, and Economic Competitiveness ment, marketing, and maintenance and repair. "The Technology Base," chapter 4, describes some of the mathematical technologies that mathematicians employ in their interactions with industrial clients and also emphasizes the importance of technology transfer—the process of incorporating research results in the design of a commercial product or service. It concludes with some strong recommendations for addressing the training of mathematicians for industrial careers. The overall conclusions and recommendations of the report are summarized in chapter 5. Appendix A describes some noteworthy policy studies on advanced technology in recent years, and Appendix B lists the studies by the mathematical community itself since the appearance of the first David report in 1984 (Renewing U.S. Mathematics: Critical Resource for the Future, National Academy Press, Washington, D.C., 1984). Many people, most of them not associated with the Board on Mathematical Sciences, provided information that aided in the preparation of this report. They include S. Andreou, L. Baxter, S. Bisgaard, I. E. Block, H. Cohen, Y. Deng, B. Enquist, R. Ewing, A. Friedman, P. W. Glynn, B. Irwin, E. Johnson, T. Kailath, D. Kleitman, R. Lundegard, L. Mancini, G. McDonald, S. A. Orszag, A. Packer, G.-C. Rota, D. H. Sharp, M. Sobel, A. Tucker, S. Weidman, M. Wheeler, and M. Wright. One of the board members, James G. Glimm, served as editor of this report. Additional editorial assistance was provided by A. Glimm and H. J. Oser. Phillip A. Griffiths, Chairman Board on Mathematical Sciences

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Mathematical Sciences, Technology, and Economic Competitiveness CONTENTS     EXECUTIVE SUMMARY   1 1   INTRODUCTION   9 2   KEY AMERICAN INDUSTRIES   14     2.1 Aircraft   16     2.2 Semiconductors and Computers   21     2.3 Petroleum   23     2.4 Automobiles   27     2.5 Telecommunications   30 3   THE PRODUCT CYCLE   32     3.1 Economic Planning   32     3.2 Simulation and Design—Aircraft   34     3.3 Design and Control of Complex Systems   37     3.4 Machine Tools for Manufacturing   42     3.5 Simulation and Production—Petroleum   43     3.6 Statistical Quality Control and Improvement   45     3.7 Manufacturing Process Control   47     3.8 Sensor-Based Manufacturing   49     3.9 Manufacturing Standards   51     3.10 Production, Inventories, and Marketing   52     3.11 Maintenance and Repair   53 4   THE TECHNOLOGY BASE   55     4.1 Technology Transfer   57     4.2 Simulation and Computational Modeling   63     4.3 Statistical Quality Improvement   69

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Mathematical Sciences, Technology, and Economic Competitiveness     4.4 Differential Equations   71     4.5 Optimization, Discrete, and Combinatorial Mathematics   78     4.6 Statistical and Probabilistic Models   83     4.7 Manpower, Education, and Training   85 5   FINDINGS AND RECOMMENDATIONS   88     REFERENCES   96     APPENDICES   99     Appendix A: Studies of Advanced Technology   99     Appendix B: Studies by the Mathematical Sciences Community   113

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Mathematical Sciences, Technology, and Economic Competitiveness MATHEMATICAL SCIENCES, TECHNOLOGY, AND ECONOMIC COMPETITIVENESS

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