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

NATIONAL RESEARCH COUNCIL
OF THE NATIONAL ACADEMIES

THE NATIONAL ACADEMIES PRESS

Washington, D.C.

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
International Standard Book Number-10: 0-309-28457-0
Library of Congress Control Number: 2013933839

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.

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.

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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

NRC staff, headed by Scott Weidman, worked tirelessly to provide much of the writing and data that give 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

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

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Contents

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