because of its ability to attract such people, many of whom stay to contribute to U.S. science, technology, and business.

However, as economic and scientific conditions improve in other countries—especially in China and India—it may be more difficult to keep foreign-born graduates in the United States; already, other nations are aggressively recruiting talented individuals, especially those born there but who are now in the United States. Increasingly, there are reports of more Chinese graduate students electing to return to China after their Ph.D. work, and the opportunities for rewarding research careers in the mathematical sciences are improving in China and elsewhere overseas. Publication counts also suggest that other locations are increasingly productive in mathematics. From 1988 through 2003, the number of publications in mathematics worldwide increased by 40 percent—from 9,707 to 15,170— while the number of mathematics publications with at least one U.S. author increased by only 8 percent—from 4,301 to 4,651.11 U.S. policies regarding work visas and immigration are an important factor here, too. A decline in the ability of the United States to attract and retain top international students will have a serious negative effect on U.S. graduate training and on the production of young mathematical scientists to meet the demand of U.S. academic institutions, industry, and government exactly at the time of increasing demand for such people.

To the extent possible, NSF policies should be aligned with the goals of continuing to attract top foreign talent to our shores and inducing talented foreigners, especially those who pass through our educational system, to choose to make their careers here. Policies that encourage the growth of the U.S.-born segment of the mathematical sciences talent pool should clearly continue, but they need to be supplemented by programs to attract and retain mathematical scientists from other countries, especially for graduate school and continuing as feasible into early careers. This goal leads directly to questions about immigration policies, which are, of course, beyond the control of NSF. Mathematical scientists who are concerned about the future vitality of our profession should recognize the important role played by immigration policies and perhaps weigh in on related political discussions.

One particular aspect deserves mention here in connection with the stresses on academic finances: The ratio of federal support to institutional support for graduate students in the mathematical sciences is very low relative to the same ratio for students of other sciences, as shown in Figure 6-1. The support model for graduate students in the mathematical sciences is overly reliant on teaching assistantships, which extends time to degree, and is especially burdensome at a time when the amount that a graduate student in the mathematical sciences must learn is expanding. Overreliance on teaching assistantships is also worrisome because the changing business model for mathematics departments makes this source of support especially vulnerable to cutbacks, as discussed above. As a community, the mathematical sciences must be proactive in shifting this balance, because innovations in the delivery of the classes that support teaching assistants could erode that means of support much faster than the number of research assistantships could ramp up. A first step is for mathematical science researchers to be more aggressive in seeking research assistantships for their students, in recognition of the need for graduate students today to gain more research experience and to lessen departments’ dependency on teaching assistantships.

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11 Derek Hill, Alan I. Rapoport, Rolf F. Lehming, and Robert K. Bell, 2007, Changing U.S. output of scientific articles: 1988-2003. Report 07-320, Appendix Table 2. National Science Foundation, Division of Science Resources Statistics, Arlington, Va.



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