Appendix D
The Mathematical Sciences Since 1998
The nature of higher education in the mathematical sciences is not static. Identifying the impact of the National Science Foundations (NSF’s) Grants for the Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE) program is made more difficult because this nature continued to evolve during the lifetime of the VIGRE program. This appendix looks briefly at how the field has changed since the VIGRE program began.
Federal funding in mathematics, both by the National Science Foundation and by federal agencies in general, continued to grow from 1999 through 2005, the most recent year for which data are available. The NSF’s share of federal funding to academic institutions has oscillated, as shown in Table D1, but it remains the dominant source of funding for the mathematical sciences.
Although the overall amount of federal funding has grown, NSF’s fraction of the total federal obligations to institutions is similar during the VIGRE period and the period prior to the program (see Figure D1). Note that the NSF’s responsibility for graduate student support has gone up from the preVIGRE period to the VIGRE period (VIGRE was established in 1998), as shown in the figure.
The average percentage of support provided by NSF to fulltime graduate students in mathematics and statistics at doctorategranting institutions from 1980 to 1998 was 34 percent of all federal funding. During the 1999 to 2006 period it was 55 percent.
Considering the mechanisms of support that NSF uses with respect to graduate students, there is some growing reliance on teaching assistantships. Comparing Table D2 with Table 23 in Chapter 2, one sees that the percentage of graduate students supported by NSF research assistantships has declined somewhat in the years since the establishment of the VIGRE program, while the fraction of students supported by NSFsponsored teaching assistantships has increased. Of course, most teaching assistantships are provided by universities, so looking at NSF support gives only a partial picture.
Turning from funding to an assessment of the number of students in mathematics and statistics, the committee is pleased to see that the number of fulltime graduate students has grown during the VIGRE period, after falling somewhat from 1992 to 1998, and that the number of students is now higher than at any time since 1980. Figure D2 shows the reversal.
TABLE D1 National Science Foundation (NSF) Share of Federal Funding to Universities and Colleges for Research in the Mathematical Sciences, 19992005 (in thousands of dollars)
Year 
NSF Share 
Total 
Percent 
1999 
84,975 
131,264 
65 
2000 
99,625 
211,490 
47 
2001 
105,251 
169,702 
62 
2002 
142,298 
200,758 
71 
2003 
162,546 
230,156 
71 
2004 
184,037 
322,989 
57 
2005 
185,390 
365,756 
51 
NOTE: Data are collected by NSF from NSF’s “Survey of Federal Funds for Research and Development.” Data contained in the survey are provided by agencies. SOURCE: National Science FoundationNational Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” accessed via WebCASPAR, http://webcaspar.nsf.gov. 
Data from the American Mathematical Society also show a rise in graduate students over the more recent period, as shown in Figure D3.
As Figure D4 shows, the percentage of graduate students in mathematics and statistics who are U.S. citizens or permanent residents has unfortunately not rebounded, although more and more graduate students fall into this category from 2000 to 2006. The percentage of female graduate students, which had been rising between 1980 and 1998, appears to have leveled off. The same is true for underrepresented minorities. This is of concern, and additional research could be directed toward a deeper understanding of changes in the composition of the graduate student body in the mathematical sciences.
TABLE D2 Percentage of National Science Foundation Support for FullTime Graduate Students in Mathematics and Statistics, 19992006, by Mechanism of Support
Year 
Fellowships 
Traineeships 
Research Assistantships 
Teaching Assistantships 
Other Mechanisms of Support 
1999 
24 
4 
68 
2 
2 
2000 
37 
6 
54 
3 
1 
2001 
37 
5 
54 
4 
0 
2002 
33 
4 
59 
3 
1 
2003 
30 
3 
62 
5 
1 
2004 
26 
4 
65 
5 
0 
2005 
26 
1 
63 
9 
1 
2006 
28 
3 
60 
8 
1 
SOURCE: National Science FoundationNational Institutes of Health, “Survey of Graduate Students and Postdoctorates in S&E,” accessed via WebCASPAR, http://webcaspar.nsf.gov. 
AMS data show similar results. The percentage of U.S. citizens among total fulltime graduate students in mathematics dropped from 55 percent in 1998 to 49 percent in 2001, then rose to 56 percent in 2007. The percentage of females has remained flat, ranging between 29 and 32 percent between 1998 and 2007. The percentage of underrepresented minorities has also remained flat—at about 10 percent—from 2003 to 2007 (Phipps et al., 2008b).
Digging a bit deeper into data on graduate study, the committee notes that the median time to degree seems not to have changed much during the first 5 years of the VIGRE program, as noted in Table D3.
TABLE D3 Median Years Elapsed from Bachelor’s to Doctoral Degree in Mathematics, 19992003
Year 
Median Years 
1999 
8.0 
2000 
7.6 
2001 
8.0 
2002 
7.6 
2003 
7.7 
SOURCE: Adapted from NSB (2006), Appendix Table 234. 
Figure D5 looks at degree production in the mathematical sciences. The falling number of bachelor’s degrees awarded from 1980 to 1998 has been reversed since 2001 and is almost back to the peak of degrees awarded in the mid1980s. Likewise, the number of master’s degrees and PhDs awarded has also grown during the VIGRE period.
Turning to doctorates, the committee notes that the percentage of doctorates awarded to U.S. citizens and permanent residents, although rising during the early 1990s, is declining overall, as shown in Figure D6. By contrast, the percentage of female and underrepresented minorities who received doctorates has generally been growing.
Looking at recent doctorates and where they were planning to go after receiving their doctorate, the committee sees similar trends during the VIGRE program (Table D4) and the earlier period represented in Table 25 in Chapter 2. For all years, about onethird of new PhDs in mathematics planned to go directly into a postdoctoral appointment. (Because the total number of PhDs is rising, this translates into more postdoctorals.)
As might be expected given the goals of the VIGRE program, the number of postdoctoral fellows in mathematics and statistics has risen quite a bit since the VIGRE program started, as shown in Figure D7.
Finally, the committee collected some information on VIGRElike activities taking place in recent years in departments that did not receive a VIGRE award. Those data are presented in Table D5.
All of the trends discussed above need to be considered as background or context when assessing the impact of the VIGRE program.
TABLE D4 New Doctorate Recipients with Definite Commitments to Postdoctoral Study or Research, by Broad Field of Doctorate, 19992005
Field of Doctorate 
1999 
2000 
2001 
2002 
2003 
2004 
2005 

Number 

Total recipients with commitments, all fields 
25,975 
26,711 
26,889 
25,984 
26,167 
26,280 
27,383 
Total planning postdoctoral study 
7,090 
6,978 
7,109 
7,195 
7,784 
8,210 
8,786 
Science and engineering, total 
6,485 
6,386 
6,346 
6,445 
6,988 
7,405 
7,952 
Mathematics 
215 
213 
217 
239 
258 
269 
298 

Percentage 

Total planning postdoctoral study 
27 
26 
26 
28 
30 
31 
32 
Science and engineering, total 
39 
38 
37 
40 
43 
45 
45 
Mathematics 
30 
29 
31 
36 
37 
36 
36 
SOURCE: National Science Foundation, Science and Engineering Doctorate Awards, Arlington, Va., various years. 
TABLE D5 “VIGRElike” Activities of Departments That Did Not Receive a VIGRE Award
Topic 
Number 
Outreach to K12 students 
40 
Outreach to K12 teachers 
53 
Summer camps in mathematics/statistics 
30 
Postdoctoral fellowships 
44 
Graduate traineeships 
57 
Undergraduate research experiences 
71 
Mentoring by faculty 
95 
Mentoring of students by postdoctorals or graduates 
31 
Teaching collaborations with other departments outside of mathematics or statistics 
67 
Research collaboration with other departments outside of mathematics or statistics 
92 
Group activities that include undergraduates, graduates, postdoctorals, and faculty 
50 
Other activities 
11 
SOURCE: Committee request for information. Total number of departments responding was 122. 