Strengthening the Linkages Between the Sciences and the Mathematical Sciences

Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences

Commission on Physical Sciences, Mathematics, and Applications

National Research Council

NATIONAL ACADEMY PRESS
Washington, D.C.



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Strengthening the Linkages Between the Sciences and the Mathematical Sciences Strengthening the Linkages Between the Sciences and the Mathematical Sciences Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences Commission on Physical Sciences, Mathematics, and Applications National Research Council NATIONAL ACADEMY PRESS Washington, D.C.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences 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 material in this report is based on work supported by the National Science Foundation and the Defense Advanced Research Projects Agency under Grant No. DMS-9703610 and by DHHS Contract No. N01-OD-4-2139 between the National Academy of Sciences and the National Institutes of Health, an agency of the U.S. Department of Health and Human Services. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the organizations or agencies that provided support for the project. International Standard Book Number 0-309-06947-5 Additional copies of this report are available from: Commission on Physical Sciences, Mathematics, and Applications National Research Council, NAS 285 2101 Constitution Avenue, N.W. Washington, DC 20418 202-334-3061 Copyright 2000 by the National Academy of Sciences. All rights reserved. Printed in the United States of America

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences THE NATIONAL ACADEMIES National Academy of Sciences National Academy of Engineering Institute of Medicine National Research Council 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 M. 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 M. Alberts and Dr. William A. Wulf are chairman and vice chairman, respectively, of the National Research Council.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences COMMITTEE ON STRENGTHENING THE LINKAGES BETWEEN THE SCIENCES AND THE MATHEMATICAL SCIENCES THOMAS F. BUDINGER, E.O. Lawrence Berkeley National Laboratory, Chair R. STEPHEN BERRY, University of Chicago NICHOLAS R. COZZARELLI, University of California, Berkeley INGRID DAUBECHIES, Princeton University MARTIN FARACH-COLTON, Rutgers, The State University of New Jersey LARS PETER HANSEN, University of Chicago FRANK CHARLES HOPPENSTEADT, Arizona State University JOHN P. LEHOCZKY, Carnegie Mellon University GREGORY J. McRAE, Massachusetts Institute of Technology MERCEDES PASCUAL, Center of Marine Biotechnology, University of Maryland Biotechnology Institute JOSEPH PEDLOSKY, Woods Hole Oceanographic Institution JAMES L. PHILLIPS, The Boeing Company I.M. SINGER, Massachusetts Institute of Technology MICHAEL TABOR, University of Arizona SUZANNE DAVIES WITHERS, University of Washington ELLEN GOULD ZWEIBEL, University of Colorado, Boulder STACEY BURKHARDT, Project Assistant (through March 1998) HEIDI L. DAVIS, Senior Program Officer (through January 1999) NORMAN METZGER, Executive Director, CPSMA (through November 1999) LA VONE WELLMAN, Project Assistant (through March 1999) DOROTHY ZOLANDZ, Study Director

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences COMMISSION ON PHYSICAL SCIENCES, MATHEMATICS, AND APPLICATIONS PETER M. BANKS, Veridian ERIM International, Inc., Co-chair W. CARL LINEBERGER, University of Colorado, Co-chair WILLIAM F. BALLHAUS, JR., Lockheed Martin Corporation SHIRLEY CHIANG, University of California, Davis MARSHALL H. COHEN, California Institute of Technology RONALD G. DOUGLAS, Texas A&M University SAMUEL H. FULLER, Analog Devices, Inc. JERRY P. GOLLUB, Haverford College MICHAEL F. GOODCHILD, University of California, Santa Barbara MARTHA P. HAYNES, Cornell University WESLEY T. HUNTRESS, JR., Carnegie Institution CAROL M. JANTZEN, Westinghouse Savannah River Company PAUL G. KAMINSKI, Technovation, Inc. KENNETH H. KELLER, University of Minnesota JOHN R. KREICK, Sanders, a Lockheed Martin Company (retired) MARSHA I. LESTER, University of Pennsylvania DUSA M. McDUFF, State University of New York at Stony Brook JANET L. NORWOOD, Former Commissioner, U.S. Bureau of Labor Statistics M. ELISABETH PATÉ-CORNELL, Stanford University NICHOLAS P. SAMIOS, Brookhaven National Laboratory ROBERT SPINRAD, Xerox PARC (retired) NORMAN METZGER, Executive Director (through July 1999) MYRON F. UMAN, Acting Executive Director

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences Preface The relationship between the sciences and the mathematical sciences is a long and symbiotic one. The two have grown up together, repeatedly interacting, with discoveries in science opening up new problems in mathematical science and advances in mathematics, statistics, computer science, and operations research enabling new practical technologies and advancing entirely new frontiers of science. The cooperation and collaboration of mathematical scientists with engineers and scientists have occurred through chance encounters, and more often than not a scientific or technological problem exists for years before a mathematician or statistician recognizes or discovers the problem as interesting and mathematically tractable. Although a biologist, medical scientist, geophysicist, or economist might naturally seek out a mathematical scientist to embark on a joint research venture, collaborations are frequently impeded by hurdles ranging from a dissimilarity in scientific language and understanding to a lack of funding. On the one hand, cultural and institutional barriers can stand in the way of training mathematical scientists in interdisciplinary research, and on the other, educational priorities can limit the exposure of students in other sciences to mathematics curricula. Faculty interested in and encouraged to pursue cross-disciplinary research can face barriers associated with precedents and the attitudes of some of their colleagues. The success of many individual partnerships and that of the few organized institutes that encourage and fund interdisciplinary ventures give ample evidence that cross-disciplinary research and education can bring about great social benefits. In addition, several recently published analyses have recommended that the United States should strengthen its mathematical science resources or risk losing its preeminent position in international research. In response to these concerns, and at the request of several federal agencies, the National Research Council established the Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences. The charge to the committee was . . . to examine the mechanisms for strengthening interdisciplinary research between the sciences and mathematical sciences, with the principal efforts of the committee being to suggest what are likely to be the most effective mechanisms for collaboration, and to implement them through the Internet, widely circulated reports, and other dissemination activities, such as campus workshops convened by committee members. The committee will also examine implications for education in the sciences and mathematics and suggest changes in graduate training intended to reinforce efforts to strengthen the dialogue among the sciences.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences The committee was composed of researchers and educators from various disciplines who were themselves known for their interest in and pursuit of cross-disciplinary research at the math/science interface. The committee met five times over the course of a year, both to receive testimony from others engaged in conducting or supporting cross-disciplinary research and to discuss its members' own experiences and knowledge of cross-disciplinary pursuits. Previous studies and recommendations related to cross-disciplinary research and enhancement of the mathematical sciences were reviewed. The current cross-disciplinary activities of government bodies and university scientists were examined as models for successful collaboration. It is the committee's sincere hope that this report will motivate both young and established researchers and educators to pursue training and research in cross-disciplinary areas and that it will encourage academic institutions to create mechanisms that foster cross-disciplinary education and research and that reward faculty appropriately. The committee hopes the recommendations will serve as guidance for funding agencies, both government and private, to advance research in the cross-disciplinary areas relevant to their missions and that it will demonstrate to the general reader the importance of such interactions. Thomas F. Budinger, Chair Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences Acknowledgment of Reviewers This report has been reviewed by individuals chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the Report Review Committee of the National Research Council (NRC). The purpose of this independent review is to provide candid and critical comments that will assist the authors and the NRC in making the published report as sound as possible and to ensure that the report meets institutional standards for objectivity, evidence, and responsiveness to the study charge. The contents of the review comments and draft manuscript remain confidential to protect the integrity of the deliberative process. The committee wishes to thank the following individuals for their participation in the review of this report: Elwyn R. Berlekamp, University of California, Berkeley, Alexandre J. Chorin, University of California, Berkeley, Kenneth A. Dill, University of California, San Francisco, Ronald G. Douglas, Texas A&M University, Robert W. Dutton, Stanford University, L.B. Freund, Brown University, Ernest M. Henley, University of Washington, William G. Howard, Jr., independent consultant, Harry Kesten, Cornell University, Nancy J. Kopell, Boston University, and Shmuel Winograd, IBM T.J. Watson Research Center. Although the individuals listed above have provided many constructive comments and suggestions, responsibility for the final content of this report rests solely with the authoring committee and the NRC.

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences Contents     Executive Summary   1 1   Introduction   5     References   7 2   Examples of Linkages   9     Cross-Disciplinary Efforts by Researchers   9     Lessons Learned   14     Programs That Foster Cross-Disciplinary Research   17     Success Factors   27     References   28 3   Previous Efforts and Studies Relevant to Math/Science Linkages   31     References   33 4   Recommendations   35     Funding Directions   35     Cross-Disciplinary Interactions   38     Oversight   39     Reference   41     Appendixes   43     A Ten Case Studies of Math/Science Interactions   41     1 Modeling Weather Systems Using Weakly Nonlinear, Unstable Baroclinic Waves   45     2 Mixing in the Oceans and Chaos Theory   47     3 Wavelets: A Case Study of Interaction Between Mathematics and the Other Sciences   50     4 From Forest Dynamics to Interacting Particle Systems   54     5 Modeling the Dynamics of Infectious Diseases: Two Examples   57     6 Topology and Dynamics of Mutant Bacteria, and Applications to Materials Science   60

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences     7 Examples from Molecular Biology   63     8 Challenges, Barriers, and Rewards in the Transition from Computer Scientist to Computational Biologist   67     9 Crossbreeding Mathematics and Theoretical Chemistry: Two Tales with Different Endings   69     10 Martingale Theory   71     B Workshop Agenda and Presentations   75     C Partial Chronology of Previous Efforts to Strengthen Mathematics and Cross-Disciplinary Research   91     D Federal Agencies That Provide Funding Opportunities   101     E Acronyms and Abbreviations   121

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Strengthening the Linkages Between the Sciences and the Mathematical Sciences STRENGTHENING THE LINKAGES BETWEEN THE SCIENCES AND THE MATHEMATICAL SCIENCES

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