National Academies Press: OpenBook
« Previous: Executive Summary
Suggested Citation:"1 Introduction." National Research Council. 2000. Strengthening the Linkages Between the Sciences and the Mathematical Sciences. Washington, DC: The National Academies Press. doi: 10.17226/9813.
×

1
Introduction

Mathematics and the sciences have developed hand in hand as man has sought to understand the physical universe surrounding him. Over three hundred years ago, Galileo is reported to have said, “The laws of nature are written in the language of mathematics.” Nobel laureate Eugene Wigner entitled his Courant lecture “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” (Wigner, 1960). He emphasized that mathematical concepts turn up in entirely unexpected natural applications and that the enormous usefulness of mathematics borders on the mysterious.

Many mathematical applications are not mysterious. Mathematics has developed out of attempts to explain the world around us: for example, the calculus, differential equations, the Fourier series and the Fourier transform, and statistics all arose out of scientific problems. Not only has the application of these methods advanced engineering and the sciences, but the methods have also become an integral part of mathematics. Sometimes, moreover, mathematics gained insights on its own that greatly influenced other fields: the importance of symmetry groups in coding theory, chemistry, and physics and of non-Euclidean and differential geometry in relativity and string theory.

In this report the Committee on Strengthening the Linkages Between the Sciences and the Mathematical Sciences will highlight a few examples (among many) of the effective interaction between mathematics and other fields: the beginning of modern weather prediction, the development of biostatistics, mathematical economics, and biomedical imaging. Behind these dramatic developments lies a vast array of research activities at the interface of mathematics and other disciplines.

With the advent of the computer, linking mathematics and science is even more imperative. Mathematical modeling has become a third investigative approach in many areas of science, providing an important complement to the classical investigative approaches of theory and experimentation. In a number of sciences, modeling and simulation are the only viable complement to theoretical studies, because many problems cannot be addressed experimentally.

Large volumes of quantitative data with increasingly rich structures necessitate new mathematical approaches for their analysis. The evaluation of astronomical, geophysical, agricultural, climate, weather, economic, and genomic data now involves addressing data sets with one million times more data (i.e., tera- and peta-byte data sets) than were previously involved in analysis. The day-to-day experiments in human gene expression now require techniques utilizing concepts not of 3 dimensions but of 600 dimensions.

Suggested Citation:"1 Introduction." National Research Council. 2000. Strengthening the Linkages Between the Sciences and the Mathematical Sciences. Washington, DC: The National Academies Press. doi: 10.17226/9813.
×

Performing large-scale computations on complex systems and visualizing and analyzing the results pose new mathematical problems. The solutions to these problems will require new engineering science developments in computer architectures and communications and visualization systems. Future generations of computers will challenge mathematics even more.1

The need for research linkages is well described in Science, Technology, and the Federal Government: National Goals for a New Era (NAS, NAE, and IOM, 1993):

Traditionally, science has been organized into specific disciplines. However, science, by its nature, is in continual flux. New disciplines emerge at the edges or intersections of existing ones. Old disciplines are transformed by new knowledge and new techniques, while new disciplines draw knowledge and techniques from the old.

Furthermore, many of the problems that scientists are now trying to solve require contributions from more than one discipline. For this interdisciplinary research to succeed, scientists must be able to extend their knowledge to new areas and work effectively as members of teams.

The performers and funders of research must allow these dynamics of science to drive its organization. They must remove barriers to emerging areas of research and encourage permeable institutional structures that allow for the flow of interdisciplinary opportunities.

To encourage new linkages between mathematics and other fields and to sustain old ones, the NRC appointed the committee and gave it the following charge:

 . . . to examine mechanisms for strengthening interdisciplinary research between the sciences and mathematical sciences, with the principal efforts of the committee being to suggest what are likely to be the most effective mechanisms for collaboration, and to implement them through the Internet, widely circulated reports, and other dissemination activities, such as campus workshops convened by committee members [and to] examine implications for education in the sciences and mathematics and suggest changes in graduate training intended to reinforce efforts to strengthen the dialogue among the sciences.

The committee represents a cross-section of scientists and mathematicians from academia, national laboratories, and industry. The members' backgrounds encompass disciplines from the biomedical, life, physical, engineering, and social sciences, and from different mathematical sciences, including statistics and theoretical computer sciences. The methods used by the committee to arrive at the recommendations in this report include the following:

  • Examination of case studies documenting the value of cross-disciplinary work involving mathematical sciences;

  • Personal experience and interviews with peers, administrators, representatives of industry, federal agencies, and private foundations;

1  

 For a few specific examples of research areas ripe for advancement through cross-disciplinary efforts, see the National Science Foundation (NSF) white paper “Mathematics and Science,” by A. Chorin and M. Wright, available from the NSF Division of Mathematical Sciences.

Suggested Citation:"1 Introduction." National Research Council. 2000. Strengthening the Linkages Between the Sciences and the Mathematical Sciences. Washington, DC: The National Academies Press. doi: 10.17226/9813.
×
  • Examination of the mechanisms developed by different institutions to overcome some of the barriers to successful cross-disciplinary work;

  • Consideration of related studies conducted by the NRC, federal agencies, and professional societies since 1980;

  • Consideration of the status of a variety of efforts under way to enhance the opportunities and climate for cross-disciplinary work; and

  • Debate among committee members leading to a consensus on the key issues and recommendations of this report.

The committee focused on the first part of its charge. Although it agreed early in the course of its work that it could not credibly propose meaningful reforms of graduate education, it nonetheless felt that such education is an extremely important topic that needs to be addressed. Top-down dictums meant to apply to all of science and/or mathematics and proposed by a group that by its nature had thin representation from some disciplines and none from others would at best be too general to be meaningful. Each community, discipline, or department responds to a specific set of both national and local needs and must determine for itself the role it should play in its community, in other words, its mission. Each organization's mission will largely determine the steps it can take at the graduate level to enhance cross-disciplinary linkages. Accordingly, this report relies instead on an anecdotal approach to provide ideas and inspiration. Those who recognize the value of cross-disciplinary linkages can use the lessons these anecdotes teach in formulating programs that meet their local needs.

Chapter 2 of this report discusses examples of cross-disciplinary research efforts; it distills those features that seem most likely to foster successful interactions and draws conclusions from them. The chapter also lists the major barriers to cross-disciplinary research. Chapter 3 looks at previous studies relevant to cross-disciplinary interactions and compares the findings and recommendations to the committee's own experience. Chapter 4 details the committee's recommendations. The committee believes the benefits to be accrued from activities linking the mathematical sciences with the other sciences could be huge and far-reaching. Successful linkages benefit both mathematics and science, and society as a whole will be greatly enriched.

Case studies of math-science interactions are presented in Appendix A, and a report on the workshop held by the committee to examine factors enabling and inhibiting cross-disciplinary research is presented in Appendix B. Appendix C gives a brief description of earlier studies that considered how to promote mathematics/science linkages. Appendix D is a beginner's guide to federal funding opportunities for projects linking the sciences and mathematical science. Appendix E lists acronyms and abbreviations.

REFERENCES

National Academy of Sciences (NAS), National Academy of Engineering (NAE), and Institute of Medicine (IOM). Committee on Science, Engineering and Public Policy. 1993. Science, Technology, and the Federal Government: National Goals for a New Era. Washington, D.C.: National Academy Press.

Suggested Citation:"1 Introduction." National Research Council. 2000. Strengthening the Linkages Between the Sciences and the Mathematical Sciences. Washington, DC: The National Academies Press. doi: 10.17226/9813.
×

Wigner, E. 1960. The unreasonable effectiveness of mathematics in the natural sciences. Communications on Pure and Applied Mathematics 13(February):1-14.

Suggested Citation:"1 Introduction." National Research Council. 2000. Strengthening the Linkages Between the Sciences and the Mathematical Sciences. Washington, DC: The National Academies Press. doi: 10.17226/9813.
×
Page 5
Suggested Citation:"1 Introduction." National Research Council. 2000. Strengthening the Linkages Between the Sciences and the Mathematical Sciences. Washington, DC: The National Academies Press. doi: 10.17226/9813.
×
Page 6
Suggested Citation:"1 Introduction." National Research Council. 2000. Strengthening the Linkages Between the Sciences and the Mathematical Sciences. Washington, DC: The National Academies Press. doi: 10.17226/9813.
×
Page 7
Suggested Citation:"1 Introduction." National Research Council. 2000. Strengthening the Linkages Between the Sciences and the Mathematical Sciences. Washington, DC: The National Academies Press. doi: 10.17226/9813.
×
Page 8
Next: 2 Examples of Linkages »
Strengthening the Linkages Between the Sciences and the Mathematical Sciences Get This Book
×
Buy Paperback | $46.00 Buy Ebook | $36.99
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

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.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    Switch between the Original Pages, where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

    « Back Next »
  6. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  7. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  8. ×

    View our suggested citation for this chapter.

    « Back Next »
  9. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!