The following HTML text is provided to enhance online
readability. Many aspects of typography translate only awkwardly to HTML.
Please use the page image
as the authoritative form to ensure accuracy.
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
APPENDIX B
STATISTICAL DATA ON THE FIELD OF MATHEMATICS
This appendix is a collection of some of the data that various members of the panel reviewed before developing conclusions. It provides the available data on education, employment, funding, and papers and citations. Most of the information is available only for the United States, but non-US data, when available, are included.
EDUCATION
Figure B-1 shows how the number of institutions in the United States awarding PhDs in mathematics has grown since 1920. Figure B-2 provides the number of PhDs that these institutions awarded during the same period. The drastic increase in PhDs in the 1960s was probably due to the draft exemption during the Vietnam War. The big increase in degrees granted in the 1980s probably occurred when computer science came into vogue.
Figure B-3 shows how long it took students to attain their degrees and provides the age at which they received their doctorate. Figure B-4 shows how many of those students were foreign citizens, and table 1 in section 5.5 shows the decrease in applications to US PhD programs in mathematics by US and non-US citizens.
Figure B-5 compares the number of first degrees (equivalent to a BS in the United States) in mathematics and computer science in the United States and western Europe. The data were available only for mathematics and computer science combined, and computer science grew rapidly during the period covered, especially in western Europe.
Figure B-6 shows the number of doctoral degrees awarded in natural sciences in Asia, Europe, and the United States in 1992. Mathematics cannot be separated out from these data.
Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole. Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 57
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
APPENDIX B
STATISTICAL DATA ON THE FIELD OF MATHEMATICS
This appendix is a collection of some of the data that various members of the panel reviewed before developing conclusions. It provides the available data on education, employment, funding, and papers and citations. Most of the information is available only for the United States, but non-US data, when available, are included.
EDUCATION
Figure B-1 shows how the number of institutions in the United States awarding PhDs in mathematics has grown since 1920. Figure B-2 provides the number of PhDs that these institutions awarded during the same period. The drastic increase in PhDs in the 1960s was probably due to the draft exemption during the Vietnam War. The big increase in degrees granted in the 1980s probably occurred when computer science came into vogue.
Figure B-3 shows how long it took students to attain their degrees and provides the age at which they received their doctorate. Figure B-4 shows how many of those students were foreign citizens, and table 1 in section 5.5 shows the decrease in applications to US PhD programs in mathematics by US and non-US citizens.
Figure B-5 compares the number of first degrees (equivalent to a BS in the United States) in mathematics and computer science in the United States and western Europe. The data were available only for mathematics and computer science combined, and computer science grew rapidly during the period covered, especially in western Europe.
Figure B-6 shows the number of doctoral degrees awarded in natural sciences in Asia, Europe, and the United States in 1992. Mathematics cannot be separated out from these data.
OCR for page 58
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-1: Number of US institutions awarding PhDs in mathematics, 1920-1995
Source: Analysis conducted by the National Research Council's Office of Scientific and Engineering Personnel for this study.
Figure B-2: Number of PhDs awarded in mathematics in the United States, 1920-1995
Source: Analysis conducted by the National Research Council's Office of Scientific and Engineering Personnel for this study.
OCR for page 59
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-3: Median time to PhD and age at receipt of PhD in mathematics in the United States
Source: COSEPUP 1995.
Figure B-4: Doctoral recipients: total number and US and non-US citizens
Source: AMS 1996.
OCR for page 60
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-5: Number of first degrees in mathematics and computer science
Source: NSF 1996c, p. 34.
Figure B-6: Doctoral degrees in natural-sciences, 1992 Degrees Awarded
Source: NSF 1996c, p. 8.
OCR for page 61
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
EMPLOYMENT
Figure B-7 shows the number of PhD mathematicians employed in the United States from 1973 to 1991. Where they are employed is shown in table B-1, and the type of work they are doing is shown in table B-2.
The data are from the Survey of Doctorate Recipients (SDR). The SDR is a biennial longitudinal survey, dating back to 1973, of research doctorates working in the United States. The survey questionnaire is sent in the spring to a sample of about 50,000. These people are asked a series of demographic and employment-characteristics questions. The response rate for the survey has varied over the years; in the late 1980s it was about 60%. That has been improved during the last 2 survey cycles through the use of second-wave mailings and telephone interviews; in 1995, it was about 85%.
The sample is stratified across 3 variables: field of degree, sex, and a combination variable that includes degree field, sex, handicap status, ethnic group, and nationality of birth. The results of the survey are statistically analyzed to translate the data into weighted numbers for the entire population. From these data, the doctorate workforce in science and engineering can be analyzed across different dimensions by looking at different demographic and employment characteristics and by taking different cohorts. This provides for both longitudinal and timeseries analyses, as shown here.
Of course, differentiating between research and teaching in determining the type of work for faculty is difficult. However it is fruitful to think about the nonresearch and teaching positions that mathematicians are obtaining and how they are changed over time.
Figure 4 in section 5.3.2 shows some of this information graphically. Note how the percentage of mathematicians employed as tenured and tenure-track faculty has declined while the percentage of mathematicians employed in industry has increased. The percentage in government employment has remained stable.
Figure B-8 shows the median salaries for PhD mathematicians and PhD holders in several related fields.
Figure B-9 shows the citizenship of faculty hired in 1991-1992 and figure B-10 the source of their PhDs.
Of particular concern is the unemployment status of new PhDs. Figure B-11 shows the change in unemployment rate for new mathematics PhDs from 1989 to 1996. The salaries of the new PhDs who attained academic employment are shown in figure B-12; the 9-month salaries included data on 102 men and 38 women, and the 12-month salaries included data on 20 men and 7 women.
OCR for page 62
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-7: Number of PhD mathematicians employed in the United States
Source: COSEPUP 1995, p. 153.
OCR for page 63
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Table B-l: Employment Status of PhD Mathematicians in the United States
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
Tenured and tenure-track faculty
9,238
10,332
10,690
10,341
10,936
11,233
11,887
11,627
12,057
12,209
12,779
12,437
Tenured faculty
6,280
6,546
7,458
8,303
8,715
9,124
9,469
9,438
9,80l
10,039
10,386
10,338
Tenure-track faculty
2,958
3,786
3,232
2,038
2,221
2,109
2,418
2,189
2,256
2,170
2,393
2,099
Other academic positions
343
666
779
1,582
1,266
1,592
1,693
1,950
2,313
2,133
1,994
1,788
Postdoctoral appointments-academic
41
73
93
146
102
102
83
264
210
99
105
484
2-yr college faculty
87
183
284
290
275
233
233
245
252
257
454
466
Industry
1,027
1,622
2,064
2,635
3,274
3,350
3,795
4,179
4,355
4,295
4,658
4,886
Federal and other government positions
586
601
719
918
988
887
958
871
965
1,076
1,083
1,045
Self-employed and others
280
448
634
686
855
1,195
989
940
1,177
1,292
1,550
1,597
Postdoctoral appointments-other
31
35
31
30
87
33
47
25
45
19
50
27
Unemployed and seeking employment
161
79
168
66
102
105
86
169
91
62
211
301
Elementary- and high school teachers
22
35
49
52
102
172
130
196
172
192
123
155
Total
11,816
14,074
15,511
16,746
17,987
18,902
19,901
20,466
21,637
21,634
23,007
23,186
Tenured and tenure-track faculty
78.2%
73.4%
68.9%
61.8%
60.8%
59.4%
59.7%
56.8%
55.7%
56.4%
55.5%
53.6%
Tenured faculty
53.1%
46.5%
48.1%
49.6%
48.5%
48.3%
47.6%
46.1%
45.3%
46.4%
45.1%
44.6%
Tenure-track faculty
25.0%
26.9%
20.8%
12.2%
12.3%
11.2%
12.2%
10.7%
10.4%
10.0%
10.4%
9.1%
Other academic positions
2.9%
4.7%
5.0%
9.4%
7.0%
8.4%
8.5%
9.5%
10.7%
9.9%
8.7%
7.7%
Postdoctoral appointments-academic
0.3%
0.5%
0.6%
0.9%
0.6%
0.5%
0.4%
1.3%
1.0%
0.5%
0.5%
2.1%
2-yr college faculty
0.7%
1.3%
1.8%
1.7%
1.5%
1.2%
1.2%
1.2%
1.2%
1.2%
2.0%
2.0%
Industry
8.7%
11.5%
13.3%
15.7%
18.2%
17.7%
19.1%
20.4%
20.1%
19.9%
20.2%
21.1%
Federal and other government positions
5.0%
4.3%
4.6%
5.5%
5.5%
4.7%
4.8%
4.3%
4.5%
5.0%
4.7%
4.5%
Self-employed and others
2.4%
3.2%
4.1%
4.1%
4.8%
6.3%
5.0%
4.6%
5.4%
6.0%
6.7%
6.9%
Postdoctoral appointments-other
0.3%
0.2%
0.2%
0.2%
0.5%
0.2%
0.2%
0.1%
0.2%
0.1%
0.2%
0.1%
Unemployed and seeking employment
1.4%
0.6%
1.1%
0.4%
0.6%
0.6%
0.4%
0.8%
0.4%
0.3%
0.9%
1.3%
Elementary- an high school teachers
0.2%
0.2%
0.3%
0.3%
0.6%
0.9%
0.7%
1.0%
0.8%
0.9%
0.5%
0.7%
Source: Analysis conducted by the National Research Council's Officeof Scientific and Engineering Personnel for this study.
OCR for page 64
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Table B-2: Occupation Status of PhD Mathematicians in the United States
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
Research
2,605
3,100
3,637
4,272
4,483
4,620
5,411
5,409
5,958
6,005
5,848
5,902
Basic research
1,510
1,490
1,662
2,017
1,878
1,924
2,746
3,025
3,270
2,984
2,797
2,836
Applied research
799
919
1,222
1,321
1,588
1,335
1,444
1,799
1,921
2,299
2,676
2,660
Development
296
691
753
934
1,017
1,361
1,221
585
767
722
375
406
Research management
521
631
593
1,160
824
1,059
1,135
1,077
1,156
771
2,300
1,861
Management-other
665
932
1,265
1,357
1,230
1,164
1,660
1,360
1,398
1,438
Teaching
7,454
8,622
8,603
8,601
9,311
9,590
9,460
9,484
9,794
9,161
10,239
10,108
Professional services
37
74
106
136
365
212
226
44
71
169
562
520
Consulting
177
222
232
406
648
763
611
448
629
Computing
794
2,322
2,587
Other work activities, no response
299
414
907
748
927
1,389
1,312
2,547
2,542
2,571
1,525
1,907
Federal support
3,879
3,680
4,000
4,716
4,533
5,853
5,009
7,293
8,189
7,911
4,653
5,507
No federal support, no response
8,015
10,315
11,343
11,964
13,352
12,944
14,806
13,004
13,359
13,661
18,143
17,378
Total
23,652
27,990
30,686
33,360
35,673
37,594
39,630
40,666
43,096
42,481
45,592
45,770
Research
11.0%
11.1%
11.9%
12.8%
12.6%
12.3%
13.7%
13.3%
13.8%
14.1%
12.8%
12.9%
Basic research
6.4%
5.3%
5.4%
6.0%
5.3%
5.1%
6.9%
7.4%
7.6%
7.0%
6.1%
6.2%
Applied research
3.4%
3.3%
4.0%
4.0%
4.5%
3.6%
3.6%
4.4%
4.5%
5.4%
5.9%
5.8%
Development
1.3%
2.5%
2.5%
2.8%
2.9%
3.6%
3.1%
1.4%
1.8%
1.7%
0.8%
0.9%
Research management
2.2%
2.3%
1.9%
3.5%
2.3%
2.8%
2.9%
2.6%
2.7%
1.8%
5.0%
4.1%
Management-other
2.8%
3.3%
4.1%
4.1%
3.4%
3.1%
4.2%
3.3%
3.2%
3.4%
0.0%
0.0%
Teaching
31.5%
30.8%
28.0%
25.8%
26.1%
25.5%
23.9%
23.3%
22.7%
21.6%
22.5%
22.1%
Professional services
0.2%
0.3%
0.3%
0.4%
1.0%
0.6%
0.6%
0.1%
0.2%
0.4%
1.2%
1.1%
Consulting
0.7%
0.8%
0.8%
1.2%
1.8%
2.0%
1.5%
1.1%
1.5%
Computing
1.9%
5.1%
5.7%
Other work activities, no response
1.3%
1.5%
3.0%
2.2%
2.6%
3.7%
3.3%
6.3%
5.9%
6.1%
3.3%
4.2%
Federal support
16.4%
13.1%
13.0%
14.1%
12.7%
15.6%
12.6%
17.9%
19.0%
18.6%
10.2%
12.0%
No federal support, no response
33.9%
36.9%
37.0%
35.9%
37.4%
34.4%
37.4%
32.0%
31.0%
32.2%
39.8%
38.0%
Source: Analysis conducted by the National Research Council's Officeof Scientific and Engineering Personnel for this study.
OCR for page 65
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-8: Median salaries in 1993 of US PhDs who received their degree in 1985-1990,
Source: NSF 1996a, appendix table 5-27.
Figure B-9: Citizenship of full-time mathematics faculty with PhDs hired during 1991-1992 in the United States
Source: AMS 1992, pp. 314-315.
OCR for page 66
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-10: Source of PhDs of full-time mathematics faculty hired during 1991-1992 in the United States
Source: AMS 1992, pp. 314-315.
Figure B-11: Percentage of unemployed new US mathematics PhDs
Source: AMS 1996, 1997c.
OCR for page 67
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-12: Median nine- and twelve-month salaries of new US PhDs for teaching or teaching and research in 1995 dollars
Source: AMS 1996.
FUNDING
The information provided in this section, unless otherwise indicated, is from an analysis conducted by the Joint Policy Board for Mathematics for the American Association for the Advancement of Science. It produces an annual analysis of federal budget data on the field of mathematics.
There are 7 dedicated programs in mathematical sciences at 3 agencies: the Department of Defense (DOD), the Department of Energy (DOE), and the National Science Foundation (NSF). NSF focuses on fundamental research and its vitality, DOD looks on mathematical sciences as a problem-solving technology that can reduce costs in the development and deployment of hardware and software, and DOE and other agencies —such as the Department of Transportation, the Environmental Protection Agency, the National Aeronautics and Space Administration, the National Institutes of Health, and the National Institute of Standards and Technology—maintain mostly-applied mathematics and statistics activities to enable progress in fields related to their missions. All other agencies use applied mathematics and statistics.
Table B-3 shows federal support for academic mathematical-sciences research. Figure B-13 compares the percentage of academic mathematical scientists who have federal support to the percentages in other fields. Federal support for all mathematical research (basic, applied, and development) is shown in figure B-14.
OCR for page 68
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
The NSF Department of Mathematical Sciences (DMS) supports development of mathematical and statistical ideas and techniques, encourages the integration of mathematics with other disciplines, and encourages the diffusion of mathematics into technology. Grants are provided to individual investigators, research institutes, and centers and for shared computing equipment, postdoctoral fellowships, research conferences, and undergraduate programs such as curriculum development.
NSF supports three mathematics institutes--the Institute for Mathematics and its Applications (IMA) at the University of Minneapolis was supported at $1,900,000 and the Mathematical Sciences Research Institute (MSRI) at the University of California, Berkeley was supported at $3,110,000 in FY1996. The IMA nearly matches the NSF support with funds from industry, sponsoring institutions, other agencies, and the University of Minnesota. The MSRI has limited additional support outside the NSF award. In 1998, there will be a recompetition for the location of the institutes in the mathematical sciences. The MSRI and the IMA are under review for “bridging” awards until the new national institutes are established as a result of the recompetition. Since its inception in 1989, the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) at Rutgers University and its staff have received a total of $74 million in science and technology center (STC) and individual-investigator grants, of which NSF support has accounted for 50%. In 1995, total funding was $9.9 million. The STC program is nearing its end, and DIMACS will need to decide soon whether will recompete for NSF STC funds. Other large projects supported by NSF include the Institute for Advanced Studies at $1,333,000 and the National Institute for Statistical Science at $1,068,000 in FY1996.
In DOD, the Air Force Office of Scientific Research supports research in subjects such as optimization, signal-processing, probability and statistics, computational mathematics, and dynamics and control. The Army Research Office focuses on the mathematics of materials science, high-performance computing, stochastic methods in image analysis, and mathematical and computational issues in intelligent manufacturing. The Office of Naval Research supports research in the mathematical subfields of applied analysis, discrete mathematics, numerical analysis, operations research, and probability and statistics. The Defense Advanced Research Projects Agency supports research that facilitates the development of technologies needed to meet future military needs. Of particular interest recently have been mathematical aspects of signal- and image-processing, electromagnetics, modeling and simulation of manufacturing processes, and optimized portable application libraries.
The National Security Agency is the nation's largest employer of mathematical scientists. It has a competitive grants program that supports unclassified academic research in discrete mathematics, algebra, number theory, probability, statistics, and cryptology.
The DOE focuses its R&D support on applied computer and computational mathematics, science and technology.
OCR for page 69
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Table B-3: Federal Support for the Mathematical Sciences, Fiscal Year 1995-1998, in Millions, Current Dollars
OCR for page 70
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-13: Percentages of US academic scientists with federal support, 1993
Source: NSB 1996, appendix table 5-27.
OCR for page 71
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-14a: Federal funding of US mathematical research - academic, 1993-1995 average
Figure B-14b: Federal funding of US mathematical research - all R&D
Key: NSF= National Science Foundation; DOD= Department of Defense; DOE= Department of Energy HHS= Department of Health and Human Services; NASA= National Aeronautics and Space Administration; USDA= Department of Agriculture; DOC= Department of Commerce; DOT= Department of Transportation; DOI= Department of the Interior
Source: NSB 1996.
OCR for page 72
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
PAPERS AND CITATIONS
Two recent reports—one from Australia and the other from the United Kingdom—have analyzed scientific performance on a comparative basis using research-paper production and citation data. As noted in the Australian Bureau of Industry Economics report Australian Science: Performance from Published Papers (1996), there are a number of problems in using such data, including a bias toward roman script and English-language journals; the greater attention paid to papers by renowned authors than to high-quality papers by less-known authors, technical papers, review articles, and recipes with little frontier science; and self-citation and citation circles.
Other problems occur because journal prestige and variation among disciplines is not considered. Time lag is a problem. There can be differential counting or miscounting due to multiple authorship, multiple field allocation, limits on the number of citations by journal, and changes in the number of journals in the field over time. And authors might use the same material with slight elaborations or break up a major article into several minor ones.
Papers “ahead of their time” and research communicated in nonjournal form (such as working papers, scientific equipment, computer programs, and seminar papers) might not be cited. Other outputs (such as teaching, advice to government, commercial research, and scientific services) are not included in bibliometric analyses.
Thus, citation rates measure visibility but not inaccessible work and not necessarily quality.
Figure B-15 shows the percentage of mathematical-research papers published by US authors relative to authors in 4 other countries that have strong mathematics programs. Figure B-16 compares the number of papers produced by US mathematicians with those produced in the European Community.
The UK report The Quality of the UK Science Base (1997) identifies the following as the top countries according to share of world's citations in mathematics:
United States.
United Kingdom.
Germany.
France.
Japan.
Another measure that was used in the UK report is the relative citation impact. The relative citation impact for a country in a particular field is defined as the country's share of the world's citations in the field divided by its share of world publications in the field. It can be thought of as a comparison of a country's citation rate for a particular field with the world's citation rate for the field. A relative citation impact (or rate) higher than 1 shows that the country's citation for the field is higher than the world's. According to the UK report, it is a measure of both the impact and the visibility of a country's research (as disseminated through publications) and gives some indication of the quality of the average paper.
The top countries in mathematics according to the relative citation impact index are
OCR for page 73
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Denmark.
Norway.
UK.
US.
Netherlands.
Figure B-15: Percentage of mathematical-research papers published by US authors
Source: NSB 1996, appendix table 5-31.
OCR for page 74
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH
Figure B-16: Number of mathematical-research papers by US and EC authors, 1981-1996
Source: Institute for Scientific Information, National Science Indicators on Diskette, 1981-1996. Philadelphia, PA.
Items in cart [1]
