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 prevailed 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.

In order to move in these directions, the following will need attention:

•   The culture within the mathematical sciences should evolve to encourage development of the characteristics listed in the Conclusion above.

•   The education of future generations of mathematical scientists, and of all who take mathematical sciences coursework as part of their preparation for science, engineering, and teaching careers, should be reassessed in light of the emerging interplay between the mathematical sciences and many other disciplines.

•   Institutions—for example, funding mechanisms and reward systems—should be adjusted to enable cross-disciplinary careers when they are appropriate.

•   Expectations and reward systems in academic mathematics and statistics departments should be adjusted so as to encourage a broad view of the mathematical sciences and to reward high-quality work in any of its areas.

•   Mechanisms should be created that help connect researchers outside the mathematical sciences with mathematical scientists who could be appropriate collaborators. Funding agencies and academic

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