Strengthening the Linkages Between the Sciences and the Mathematical Sciences

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Overview

Over three hundred years ago, Galileo is reported to have said, "The laws of nature are written in the language of mathematics." Often mathematics and science go hand in hand, with one helping develop and improve the other. Discoveries in science, for example, open up new advances in statistics, computer science, operations research, and pure and applied mathematics which in turn enabled new practical technologies and advanced entirely new frontiers of science. Despite the interdependency that exists between these two disciplines, cooperation and collaboration between mathematical scientists and scientists have only occurred by chance.

To encourage new collaboration between the mathematical sciences and other fields and to sustain present collaboration, the National Research Council (NRC) formed a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. The goal of the committee was to examine the mechanisms for strengthening interdisciplinary research between mathematical sciences and the sciences, with a strong focus on suggesting the most effective mechanisms of collaboration. Strengthening the Linkages Between the Sciences and the Mathematical Sciences provides the findings and recommendations of the committee as well as case studies of cross-discipline collaboration, the workshop agenda, and federal agencies that provide funding for such collaboration.

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Product Details

  • ISBN-13: 9780309069472
  • Publisher: National Academies Press
  • Publication date: 4/19/2000
  • Pages: 138
  • Product dimensions: 8.30 (w) x 10.80 (h) x 0.40 (d)

Read an Excerpt

STRENGTHENING THE LINKAGES BETWEEN THE SCIENCES AND THE MATHEMATICAL SCIENCES
National Academies Press

Copyright © 2000 National Academy of Sciences
All right reserved.

ISBN: 978-0-309-06947-2



Chapter One

Executive Summary

Mathematics and the sciences have grown up together, repeatedly interacting. Discoveries in science open up new advances in statistics, computer science, operations research, and pure and applied mathematics. These, in turn, enable new practical technologies and advance entirely new frontiers of science. Frequently, however, cooperation and collaboration between mathematical scientists and scientists have come as a result of chance encounters. Often a scientific or technological problem exists for years before a mathematical scientist discovers it and recognizes it as interesting and mathematically tractable. Similarly, scientists have frequently expended energy "inventing" mathematical solutions that existed for decades but were not familiar to them from their training.

To encourage new linkages between the mathematical sciences and other fields and to sustain old linkages, the National Research Council (NRC) constituted a committee representing a broad cross-section of scientists from academia, federal government laboratories, and industry. Its task was to "examine the mechanisms for strengthening interdisciplinary research between the sciences and mathematical sciences, with theprincipal efforts being to suggest what are likely to be the most effective mechanisms for collaboration...."

The committee believes that the benefits to be derived from cross-disciplinary activities linking the mathematical sciences with science and engineering are indeed huge and far reaching. Its recommendations can be found in Chapter 4. The main elements of these recommendations are summarized here.

FUNDING DIRECTIONS

The committee recommends that additional funding be allocated to initiatives that will strengthen existing linkages between the mathematical sciences and other sciences and that will build new linkages.

New resources are required if the nation is to realize the enormous potential of cross-disciplinary fertilization. However, a key premise of the committee's report is that the basic sciences and the mathematical sciences must remain healthy if cross-disciplinary research is to advance. Some disciplines will, accordingly, need additional funds to be capable of developing cross-disciplinary ties. Funding for cross-disciplinary research must not compromise support for basic disciplinary research or for individual investigators.

Chapter 4 contains detailed recommendations to funding agencies that will enhance multidisciplinary activities: support for summer institutes, workshops at existing research centers, and new science and technology centers. The committee also recommends fellowship programs of various types to sustain research scientists in their pursuit of compelling multidisciplinary ideas.

Case studies of math-science research linkages provide compelling evidence for the synergism between science and mathematics. They also elucidate the factors that made these cross-disciplinary efforts possible, as well as the barriers that inhibited them. Appendix A presents the 10 case studies and Chapter 2 discusses the lessons learned from them, with an emphasis on the obstacles to cross-disciplinary collaborations. Some obstacles are resource-related, and it is these obstacles the committee hopes to overcome with its recommendation on funding. Other obstacles are cultural: different disciplines have different goals, philosophies, and languages.

The committee found that many institutions have overcome barriers to cross-disciplinary research despite the obstacles and have flourished. Examples of such programs can also be found in Chapter 2. Moreover we can anticipate even more activity at the interface of mathematics and other fields in the future. Universities with vision are developing, at an increasing pace, new interdisciplinary programs that cut across traditional departmental and college boundaries; such programs are vital to the strategic planning of a university's educational and research mission. Mathematics can, because of its uniquely central role in science and engineering, play an important part in these plans for interdisciplinary growth.

CROSS-DISCIPLINARY INTERACTIONS

The committee recommends that academic institutions take responsibility for implementing vigorous cooperative programs between the sciences and the mathematical sciences.

As the examples show, departments and their faculty can actively pursue cross-disciplinary research opportunities and make changes in the curriculum that will give students cross-disciplinary skills. It is particularly important to develop effective criteria for the evaluation of cross-disciplinary research to ensure that promotion, tenure, and reward mechanisms fully recognize the importance of quality cross-disciplinary research.

OVERSIGHT

The committee recommends that a new standing committee be established with a long-term focus on improving the linkages between the mathematical sciences and other sciences in both academia and industry.

A standing committee would have as its special mission the fostering and nurturing of such linkages by monitoring and evaluating successful initiatives and by communicating its findings to the community. The committee could advise funding agencies on how they might better evaluate cross-disciplinary research, advise private foundations on effective methods for supporting such research, and inform professional societies about multidisciplinary research opportunities and related educational opportunities. Some specific responsibilities for such a committee are suggested in Chapter 4.

(Continues...)



Excerpted from STRENGTHENING THE LINKAGES BETWEEN THE SCIENCES AND THE MATHEMATICAL SCIENCES Copyright © 2000 by National Academy of Sciences. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

Contents

1 Executive Summary....................1
1 Introduction....................5
References....................7
2 Example 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
7 Examples from Molecular Biology....................63
8 Challengers, Barriers, and Rewards in the Transition from Computer Scientist to Computational Biologist....................67
9 Crossbreeding Mathematics and Theoretical Chemistry: Two Tales with DifferentEndings....................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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