The Mathematical Sciences in 2025

199 Pages·2013·5.54 MB·English

by  Committee on the Mathematical Sciences in 2025, Board on Mathematical Sciences and Their Applications, Division on Engineering and Physical Sciences, National Research Council

The Mathematical Sciences in 2025
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
The Mathematical Sciences in 2025
Committee on the Mathematical Sciences in 2025
Board on Mathematical Sciences and Their Applications
Division on Engineering and Physical Sciences

THE NATIONAL ACADEMIES PRESS
Washington, D.C.
www.nap.edu

Copyright © National Academy of Sciences. All rights reserved.
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
THE NATIONAL ACADEMIES PRESS 500 Fifth Street, NW Washington, DC 20001
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
Additional copies of this report are available from the National Academies Press, 500 Fifth
Street, NW, Keck 360, Washington, D.C. 20001; [phone] or [phone];
http://www.nap.edu.
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
Copyright © National Academy of Sciences. All rights reserved.
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
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.
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. Harvey V. Fineberg 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. Ralph J. Cicerone and Dr. Charles M.
Vest are chair and vice chair, respectively, of the National Research Council.
www.national-academies.org
Copyright © National Academy of Sciences. All rights reserved.
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
Copyright © National Academy of Sciences. All rights reserved.
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
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, Simons Foundation
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
v
Copyright © National Academy of Sciences. All rights reserved.
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
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
vi
Copyright © National Academy of Sciences. All rights reserved.
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
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 NRC staff, headed by Scott
Weidman, worked tirelessly to provide much of the writing and data that gives the report
its coherence, organization, and credibility. I especially thank them, for myself and for
the rest of the committee, for their essential contributions.
Thomas E. Everhart, Chair
vii
Copyright © National Academy of Sciences. All rights reserved.
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
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
viii
Copyright © National Academy of Sciences. All rights reserved.
The Mathematical Sciences in 2025
Prepublication Copy: Subject to Further Editorial Correction
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 of Maryland system
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
ix
Copyright © National Academy of Sciences. All rights reserved.