Excerpt from Summary of The Mathematical Sciences in 2025
National Research Council. 2013. The Mathematical Sciences in 2025. Washington, D.C.: The National Academies Press. 187 pages.
Finding: Mathematical sciences work is becoming an increasingly inte- gral and essential component of a growing array of areas of investigation in biology, medicine, social sciences, business, advanced design, climate, finance, advanced materials, and many more. This work involves the integration of mathematics, statistics, and computation in the broadest sense and the interplay of these areas with areas of potential applica- tion. All of these activities are crucial to economic growth, national competitiveness, and national security, and this fact should inform both the nature and scale of funding for the mathematical sciences as a whole. Education in the mathematical sciences should also reflect this new stature of the field.

Many mathematical scientists remain unaware of the expanding role for their field, and this incognizance will limit the community’s ability to produce broadly trained students and to attract more of them. A community-wide ef-fort to rethink the mathematical sciences curriculum at universities is needed. Mechanisms to connect researchers outside the mathematical sciences with the right mathematical scientists need to be improved and more students need to be attracted to the field to meet the opportunities of the future.

Conclusion: The mathematical sciences have an exciting opportunity to solidify their role as a linchpin of twenty-first century research and technology while maintaining the strength of the core, which is a vital element of the mathematical sciences ecosystem and essential to its future. The enterprise is qualitatively different from the one that pre- vailed during the latter half of the twentieth century, and a different model is emerging—one of a discipline with a much broader reach and greater potential impact. The community is achieving great success within this emerging model, as recounted in this report. But the value of the mathematical sciences to the overall science and engineering enterprise and to the nation would be heightened if the number of mathematical scientists who share the following characteristics could be increased:
  • They are knowledgeable across a broad range of the discipline, beyond their own area(s) of expertise;
  • They communicate well with researchers in other disciplines;
  • They understand the role of the mathematical sciences in the wider world of science, engineering, medicine, defense, and business; and
  • They have some experience with computation.

    It is by no means necessary or even desirable for all mathematical scientists to exhibit these characteristics, but the community should work toward increasing the fraction that does.