Recommendation: More professional mathematical scientists should become involved in explaining the nature of the mathematical sciences enterprise and its extraordinary impact on society. Academic departments should find ways to reward such work. Professional societies should expand existing efforts and work with funding entities to create an organizational structure whose goal is to publicize advances in the mathematical sciences.

The market for mathematical sciences talent is now global, and the United States is in danger of losing its global preeminence in the discipline. Other nations are aggressively recruiting U.S.-educated mathematical scientists, especially those who were born in those nations. Whereas for decades the United States has been attracting the best of the world’s mathematical scientists, a reverse brain drain is now a real threat. The policy of encouraging the growth of the U.S.-born mathematical sciences talent pool should continue, but it needs to be supplemented by programs to attract and retain mathematical scientists from around the world, beginning in graduate school and continuing through an expedited visa process for those with strong credentials in the mathematical sciences who seek to establish permanent residence.

The underrepresentation of women and ethnic minorities in mathematics has been a persistent problem for the field. As white males become a smaller fraction of the population, it is even more essential that the mathematical sciences become more successful at attracting and retaining students from across the totality of the population. While there has been progress in the last 10-20 years, the fraction of women and minorities in the mathematical sciences drops with each step up the career ladder. A large number of approaches have been tried to counter this decline, and many appear to be helpful, but this problem still needs attention, and there is no quick solution.

Recommendation: Every academic department in the mathematical sciences should explicitly incorporate recruitment and retention of women and underrepresented groups into the responsibilities of the faculty members in charge of the undergraduate program, graduate program, and faculty hiring and promotion. Resources need to be provided to enable departments to adopt, monitor, and adapt successful recruiting and mentoring programs that have been pioneered at other schools and to find and correct any disincentives that may exist in the department.

While the mathematical sciences enterprise has tremendous responsibilities for educating students across the range of STEM fields, it must also, of course, replenish itself. One successful way to strengthen that part of

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