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.
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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
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
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
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-
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