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Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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Fueling Innovation and Discovery

The Mathematical Sciences
in the 21st Century

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.
www.nap.edu

Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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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.

www.national-academies.org

Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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COMMITTEE ON THE MATHEMATICAL SCIENCES IN 2025

THOMAS E. EVERHART, Chair, California Institute of Technology

MARK L. GREEN, Vice Chair, University of California, Los Angeles

TANYA STYBLO BEDER, SBCC Group, Inc.

JAMES O. BERGER, Duke University

LUIS A. CAFFARELLI, University of Texas at Austin

EMMANUEL J. CANDES, Stanford University

PHILLIP COLELLA, Lawrence Berkeley National Laboratory

DAVID EISENBUD, University of California, Berkeley

PETER WILCOX 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, Director, Board on Mathematical Sciences and Their Applications

DANA MACKENZIE, Mathematics Writer

TOM ARRISON, Senior Staff Officer

MICHELLE SCHWALBE, Associate Program Officer

BARBARA WRIGHT, Administrative Assistant

BOARD ON MATHEMATICAL SCIENCES AND THEIR APPLICATIONS

C. DAVID LEVERMORE, Chair, University of Maryland

TANYA STYBLO BEDER, SBCC Group, Inc.

PATRICIA FLATLEY BRENNAN, University of Wisconsin

GERALD G. BROWN, Naval Postgraduate School

L. ANTHONY COX, JR., Cox Associates, Inc.

BRENDA DIETRICH, IBM Thomas J. Watson Research Center

CONSTANTINE GATSONIS, Brown University

DARRYLL HENDRICKS, UBS Investment Bank

KENNETH L. JUDD, Hoover Institution

DAVID MAIER, Portland State University

JAMES C. McWILLIAMS, University of California, Los Angeles

JUAN C. 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

DONALD G. SAARI, University of California, Irvine

J.B. SILVERS, Case Western Reserve University

GEORGE SUGIHARA, University of California, San Diego

EVA TARDOS, Cornell University

KAREN L. VOGTMANN, Cornell University

BIN YU, University of California, Berkeley

STAFF

SCOTT WEIDMAN, Director

NEAL GLASSMAN, Senior Program Officer

MICHELLE SCHWALBE, Associate Program Officer

BARBARA WRIGHT, Administrative Assistant

BETH DOLAN, Financial Manager

Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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Fueling Innovation and Discovery

The Mathematical Sciences in the 21st Century

Launched in 2010 with funding from the National Science Foundation, the National Academies’ study The Mathematical Sciences in 2025 (MathSci 2025) is a forward-looking assessment of the current state of the mathematical sciences in the United States. The final report of the MathSci 2025 project will be released later in 2012. More information about the project is available at www.nas.edu/mathsci2025.

This publication, Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century, is a separate product being released in advance of the final report. It is based on the committee’s identification of recent advances in the mathematical sciences or advances enabled by mathematical sciences research, drawn from the committee’s assessment of the vitality of the discipline. This report is geared toward general readers who would like to know more about ongoing advances in the mathematical sciences and how these advances are changing our understanding of the world, creating new technologies, and transforming industries.

In selecting the topics for this report, the committee aimed to cover a range of mathematical sciences subfields and areas of impact, choosing topics where information was accessible and where developments could be described in a few pages. While the committee believes that all the topics covered are important and interesting, this publication is not intended to be a comprehensive selection of the most important developments in the mathematical sciences.

The committee worked primarily with mathematics writer Dana Mackenzie to prepare this report. It greatly appreciates his insights and hard work. During late 2010 and 2011, appropriate topics were identified, experts consulted, drafts prepared and revised, and accompanying images compiled. This report contains no committee conclusions or recommendations.

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 Academies’ Report Review Committee. The review of this report was overseen by Samuel Fuller, Analog Devices, Inc. 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 quality and objectivity. The review comments and draft manuscript remain confidential to protect the integrity of the process.

We wish to thank the following individuals for their review of this report:

JOHN BRADY, California Institute of Technology,

JAMES CARLSON, Clay Mathematics Institute,

ANNA GILBERT, University of Michigan,

MARVIN GOLDSTEIN, NASA Glenn Research Center,

RONALD GRAHAM, University of California, San Diego,

JON KETTENRING, Telcordia Technologies, Inc. (retired),

AROGYASWAMI PAULRAJ, Stanford University,

STEVEN STROGATZ, Cornell University,

LARRY WASSERMAN, Carnegie Mellon University,

EUGENE WONG, University of California, Berkeley, and

BIN YU, University of California, Berkeley.

Although the reviewers listed above have provided many constructive comments and suggestions, they were not asked to endorse the content of the report, nor did they see the final draft before its release. Responsibility for the final content of this report rests entirely with the committee and the institution.

Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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Suggested Citation:"Front Matter." National Research Council. 2012. Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century. Washington, DC: The National Academies Press. doi: 10.17226/13373.
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The mathematical sciences are part of everyday life. Modern communication, transportation, science, engineering, technology, medicine, manufacturing, security, and finance all depend on the mathematical sciences. Fueling Innovation and Discovery describes recent advances in the mathematical sciences and advances enabled by mathematical sciences research. It is geared toward general readers who would like to know more about ongoing advances in the mathematical sciences and how these advances are changing our understanding of the world, creating new technologies, and transforming industries.

Although the mathematical sciences are pervasive, they are often invoked without an explicit awareness of their presence. Prepared as part of the study on the Mathematical Sciences in 2025, a broad assessment of the current state of the mathematical sciences in the United States, Fueling Innovation and Discovery presents mathematical sciences advances in an engaging way. The report describes the contributions that mathematical sciences research has made to advance our understanding of the universe and the human genome. It also explores how the mathematical sciences are contributing to healthcare and national security, and the importance of mathematical knowledge and training to a range of industries, such as information technology and entertainment.

Fueling Innovation and Discovery will be of use to policy makers, researchers, business leaders, students, and others interested in learning more about the deep connections between the mathematical sciences and every other aspect of the modern world. To function well in a technologically advanced society, every educated person should be familiar with multiple aspects of the mathematical sciences.

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