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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.
This project was supported by the National Science Foundation under grant number DMS-0911899. 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-13: 978-0-309-28457-8
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Suggested citation: National Research Council. 2013. The Mathematical Sciences in 2025. Washington, D.C.: The National Academies Press.
Copyright 2013 by the National Academy of Sciences. All rights reserved.
Printed in the United States of America
THE NATIONAL ACADEMIES
Advisers to the Nation on Science, Engineering, and 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. Ralph J. Cicerone 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. Charles M. Vest is president of the National Academy of Engineering.
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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. Ralph J. Cicerone and Dr. Charles M. Vest are chair and vice chair, respectively, of the National Research Council.
COMMITTEE ON THE MATHEMATICAL SCIENCES IN 2025
THOMAS E. EVERHART, California Institute of Technology, Chair
MARK L. GREEN, University of California, Los Angeles, Vice-chair
TANYA S. BEDER, SBCC Group, Inc.
JAMES O. BERGER, Duke University
LUIS A. CAFFARELLI, University of Texas at Austin
EMMANUEL J. CANDES, Stanford University
PHILLIP COLELLA, E.O. Lawrence Berkeley National Laboratory
DAVID EISENBUD, University of California, Berkeley
PETER W. JONES, Yale University
JU-LEE KIM, Massachusetts Institute of Technology
YANN LeCUN, New York University JUN LIU, Harvard University
JUAN MALDACENA, Institute for Advanced Study
JOHN W. MORGAN, Stony Brook University
YUVAL PERES, Microsoft Research
EVA TARDOS, Cornell University
MARGARET H. WRIGHT, New York University
JOE B. WYATT, Vanderbilt University
Staff
SCOTT WEIDMAN, Study Director
THOMAS ARRISON, Senior Program Officer
MICHELLE SCHWALBE, Program Officer
BARBARA WRIGHT, Administrative Assistant
BOARD ON MATHEMATICAL SCIENCES AND THEIR APPLICATIONS
DONALD G. SAARI, University of California, Irvine, Chair
GERALD G. BROWN, U.S. Naval Postgraduate School
LOUIS ANTHONY COX, JR., Cox Associates
BRENDA L. DIETRICH, IBM T.J. Watson Research Center
CONSTANTINE GATSONIS, Brown University
DARRYLL HENDRICKS, UBS Investment Bank
ANDREW LO, Massachusetts Institute of Technology
DAVID MAIER, Portland State University
JAMES C. McWILLIAMS, University of California, Los Angeles
JUAN MEZA, University of California, Merced
JOHN W. MORGAN, Stony Brook University
VIJAYAN N. NAIR, University of Michigan
CLAUDIA NEUHAUSER, University of Minnesota, Rochester
J. TINSLEY ODEN, University of Texas at Austin
FRED ROBERTS, Rutgers University
J.B. SILVERS, Case Western Reserve University
CARL SIMON, University of Michigan
EVA TARDOS, Cornell University
KAREN VOGTMANN, Cornell University
BIN YU, University of California, Berkeley
Staff
SCOTT WEIDMAN, Director
NEAL GLASSMAN, Senior Program Officer
MICHELLE SCHWALBE, Program Officer
BARBARA WRIGHT, Administrative Assistant
BETH DOLAN, Financial Associate
Preface
When I was asked to chair a committee of mathematical scientists charged with examining the field now with an eye toward how it needs to evolve to produce the best value for the country by 2025, I demurred because I am not a mathematical scientist. The counter was that therefore I would not be biased, could be objective to prevent possible internal politics from “capturing” the report, and would be continuing a tradition of having such committees chaired by nonexperts. The assignment was educational in many ways.
The committee was extraordinary in its makeup, with experts from the core of mathematics as well as from departments of statistics and computer science, from both academia and industry. My eyes were opened to the power of the mathematical sciences today, not only as an intellectual undertaking in their own right but also as the increasingly modern foundation for much of science, engineering, medicine, economics, and business. The increasingly important challenges of deriving knowledge from huge amounts of data, whether numerical or experimental, of simulating complex phenomena accurately, and of dealing with uncertainty intelligently are some of the areas where mathematical scientists have important contributions to make going forward—and the members of this committee know it. They have demonstrated a great capacity to envision an emerging era in which the mathematical sciences underpin much of twenty-first century science, engineering, medicine, industry, and national security. I hope that this report persuades many others to embrace that vision.
While all members of the committee contributed to this report, vice-chair Mark Green, from the University of California at Los Angeles, and
Acknowledgments
This report has been reviewed in draft form by individuals chosen for their diverse perspectives and technical expertise, in accordance with procedures approved by the National Research Council’s Report Review Committee. The purpose of this independent review is to provide candid and critical comments that will assist the institution in making its 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 review comments and draft manuscript remain confidential to protect the integrity of the deliberative process. We wish to thank the following individuals for their review of this report:
Emery Brown, Massachusetts General Hospital and Massachusetts Institute of Technology
Anna Gilbert, University of Michigan
Leslie Greengard, New York University
Yu-Chi Ho, Harvard University
Stephen Robinson, University of Wisconsin
Kenneth Ribet, University of California, Berkeley
Terence Tao, University of California, Los Angeles
Yannis Yortsos, University of Southern California
Bin Yu, University of California, Berkeley
Robert Zimmer, University of Chicago
Although the reviewers listed above have provided many constructive comments and suggestions, they were not asked to endorse the conclusions
or recommendations nor did they see the final draft of the report before its release. The review of this report was overseen by Lawrence D. Brown of the University of Pennsylvania and C. Judson King of the University of California, Berkeley. Appointed by the National Research Council, they were responsible for making certain that an independent examination of this report was carried out in accordance with institutional procedures and that all review comments were carefully considered. Responsibility for the final content of this report rests entirely with the authoring committee and the institution.
The committee also acknowledges the valuable contribution of the following individuals, who provided input at the meetings on which this report is based or by other means:
Theodore T. Allen, Ohio State University
Yali Amit, University of Chicago
Nafees Bin Zafar, DreamWorks Animation
Emery Brown, Massachusetts General Hospital
Robert Bryant, Mathematical Sciences Research Institute
Philip Bucksbaum, Stanford University
Russel Caflisch, University of California, Los Angeles
James Carlson, Clay Mathematics Institute
William Cleveland, Purdue University
Ronald Coifman, Yale University
Peter Constantin, University of Chicago
James Crowley, Society for Industrial and Applied Mathematics
Brenda Dietrich, IBM T.J. Watson Research Center
David Donoho, Stanford University
Cynthia Dwork, Microsoft Research
Lawrence Ein, University of Illinois at Chicago
Charles Fefferman, Princeton University
Robert Fefferman, University of Chicago
John S. Gardenier, Centers for Disease Control and Prevention (ret.)
Scott Guthery, Docent Press
Alfred Hales, Institute for Defense Analyses’ Center for Communications Research, La Jolla
Kathryn B. Hall, Hewlett Packard
James J. Higgins, Kansas State University
Shi Jin, University of Wisconsin
C. Judson King, University of California, Berkeley
William E. Kirwan, University System of Maryland
Bryna Kra, Northwestern University
Deborah Lockhart, National Science Foundation
Dana Mackenzie, mathematics writer
Wen Masters, Office of Naval Research
Donald McClure, American Mathematical Society
Jill Mesirov, Broad Institute
Diane K. Michelson, International Sematech Manufacturing Initiative
Assaf Naor, New York University
Deborah Nolan, University of California, Berkeley
Martin Nowak, Harvard University
Sastry Pantula, National Science Foundation
Colette Patt, University of California, Berkeley
Walter Polansky, Department of Energy
Adrian Raftery, University of Washington
Samuel Rankin, American Mathematical Society
Nancy Reid, University of Toronto
Fadil Santosa, University of Minnesota
Terence Sejnowski, University of California, San Diego
Harry Shum, Microsoft Corporation
James Simons, Renaissance Technologies
Douglas Simpson, University of Illinois at Urbana-Champaign
Hal Stern, University of California, Irvine
Tina Straley, Mathematical Association of America
Terence Tao, University of California, Los Angeles
Richard Taylor, Harvard University
Charles Toll, National Security Agency
Kam Tsui, University of Wisconsin
Gunther Uhlmann, University of Washington
Ron Wasserstein, American Statistical Association
S.-T. Yau, Harvard University
Bin Yu, University of California, Berkeley
Robert Zimmer, University of Chicago
Contents
Nature of the Mathematical Sciences
Everyone Should Care About the Mathematical Sciences
2 VITALITY OF THE MATHEMATICAL SCIENCES
The Topology of Three-Dimensional Spaces
The Mathematical Sciences and Social Networks
Primes in Arithmetic Progression
Inverse Problems: Visibility and Invisibility
The Interplay of Geometry and Theoretical Physics
New Frontiers in Statistical Inference
Economics and Business: Mechanism Design
3 CONNECTIONS BETWEEN THE MATHEMATICAL SCIENCES AND OTHER FIELDS
Broadening the Definition of the Mathematical Sciences
Implications of the Broadening of the Mathematical Sciences
Two Major Drivers of Expansion: Computation and Big Data
Contributions of Mathematical Sciences to Science and Engineering
Contributions of Mathematical Sciences to Industry
Contributions of Mathematical Sciences to National Security
4 IMPORTANT TRENDS IN THE MATHEMATICAL SCIENCES
Increasing Importance of Connections for Mathematical Sciences Research
Innovation in Modes for Scholarly Interactions and Professional Growth
The Mathematical Sciences Should More Thoroughly Embrace Computing
Funding Implications of Increasing Connectivity of the Mathematical Sciences
5 PEOPLE IN THE MATHEMATICAL SCIENCES ENTERPRISE
Changing Demand for the Mathematical Sciences
The Typical Educational Path in the Mathematical Sciences Needs Adjustments
Attracting More Women and Underrepresented Minorities to the Mathematical Sciences
The Critical Role of K-12 Mathematics and Statistics Education
Enrichment for Precollege Students with Clear Talent in Mathematics and Statistics
6 THE CHANGING ACADEMIC CONTEXT