Experiments in International Benchmarking of US Research Fields (2000) / Chapter Skim
Currently Skimming:
Attachment I: International Benchmarking of US Mathematics Research
Attachment I: International Benchmarking of US Mathematics Research
Pages 59-126
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 59... ...
ATTACHMENT 1 INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH Pane! on international Benchmarking of US Mathematics Research Committee on Science, Engineering, and Public Policy
|
From page 61... ...
McDONALD, Head, Operations Research Department, GM Research and Development Center, Warren, MI CATHLEEN S MORAWETZ, Professor Emeritus, Courant Institute of Mathematical Sciences, New York University, New York, NY PETER SARNAK, Chair, Department of Mathematics, Princeton University, Princeton, NJ I.M.
|
From page 62... ...
Mathematics Benchmarking Guidance Group MARYE ANNE FOX (Chair) , Vice President for Research, University of Texas at Austin, Austin TX PHILLIP A
|
From page 63... ...
CO NTE NTS EXECUTIVE SUMMARY BACKGROUND SCOPE AND NATURE OF THE PANEL'S EVALUATION RELATIVE POSITION OF US RESEARCH IN MATHEMATICS 3.1 The Discipline, 1-8 3.1.1 Leadership, 1-8 3.1.2 Depth, 1-9 3.2 Mathematics in a Broader Context, 1-10 3.2.1 Science and Engineering, 1-10 3.2.2 Industry, 1-12 3.2.3 Government Laboratories and Agencies, 1-14 3.2.4 Mathematics Education, 1-15 4 FACTORS THAT INFLUENCED PAST US PERFORMANCE IN MATHEMATICS 4.1 Attractiveness to Talent from Outside the United States, 1-17 4.2 Quality and Structure of Graduate Education in Mathematics, 1-18 4.3 Diversity of the US Research Enterprise, 1-18 4.4 Adequate Funding, 1-20 1-1 1-3 1-5 1-8 1-17 I-v
|
From page 64... ...
Tables Report Figure 1: Percentage of mathematics-research papers published by US authors, 1-10 Figure 2: Percentage unemployment among new US PhDs in mathematics, autumn of year shown, 1-23 Figure 3: Number of PhDs produced by US mathematics departments, spring of year shown, 1-24 Figure 4: Employment status of PhD mathematicians in the US, 1-25 Figure 5: Doctoral recipients: total number and US and non-US citizens, 1-26 Figure 6: Percentage of foreign natural-sciences doctoral students in various countries, 1-27 Figure 7: Stay rates percentages of foreign doctoral students who plan to remain in the United States, averaged over 1988-1992, 1-27 Figure 8: Total full-time PhD students in mathematical sciences, 1-28 Table 1: Decrease in applications to PhD programs in mathematics, 1994 to 1996, 1-29 Figure 9: Median salaries in 1993 of US PhDs who received their degrees in 1985-1990, by field, 1-30 1-21 1-33 1-35 1-37 1-43 I-vi
|
From page 65... ...
Contents Figure 10: Percentages of academic scientists with federal support, 1993, 1-31 Figure 11: Percentage increase in federal R&D expenditures at universities and colleges, by field, 1-31 Appendix B Figure B-1: Number of US institutions awarding PhDs in mathematics, 1920-1995, 1-44 Figure B-2: Number of PhDs awarded in mathematics in the United States, 1920-1995, 1-44 Figure B-3: Median time to PhD and age at receipt of PhD in mathematics in the United States, 1-45 Figure B-4: Doctoral recipients: total number of US and Non-US citizens, 1-45 Figure B-5: Number of first degrees in mathematics and computer science, 1-46 Figure B-6: Doctoral degrees in natural-sciences, 1992, 1-46 Figure B-7: Number of PhD mathematicians employed in the United States, 1-47 Table B-1: Employment Status of PhD Mathematicians in the United States, 1-48 Table B-2: Occupation Status of PhD Mathematicians in the United States, 1-49 Figure B-8: Median salaries in 1993 of US PhDs who received their degree in 1985-1990, by field, 1-50 Figure B-9: Citizenship of full-time mathematics faculty with PhDs hired during 1991-1992 in the United States, 1-51 Figure B-10: Source of PhDs of full-time mathematics faculty hired during 1991-1992 in the United States, 1-51 Figure Bell: Percentage of unemployed new US mathematics PhDs, 1-52 Figure B-12: Median nine- and twelve-month salaries of new US PhDs for teaching or teaching and research in 1995 dollars, 1-52 Table B-3: Federal Support for the Mathematical Sciences, Fiscal Year 1995-1998, in Millions, Current Dollars; and in Millions, Constant 1992 Dollars, 1-53 Figure B-13: Percentages of US academic scientists with federal support, 1993, 1-54 Figure B-14a: Federal funding of US mathematical research academic 1993-1995 average, 1-55 Figure B-14b: Federal funding of US mathematical research all R&D, 1-55 Figure B-15: Percentage of mathematical research papers published by US authors, 1-57 Figure B-16: Number of mathematical research papers by US and EC authors, 1981-1996, 1-58 I ..
|
From page 67... ...
Mathematical research is conducted on a very broad front, and seemingly disjointed branches often turn out to be intimately related. · Ideas of abstract mathematics often are crucial ingredients in practical applications.
|
From page 68... ...
· Sustained funding for research from universities and the federal government. The United States continues to attract some of the best graduate students and postdoctoral fellows from all over the world; a substantial portion of active research mathematicians now in the United States come from outside the United States.
|
From page 69... ...
Each panel would consist of researchers in the particular field, researchers in closely related fields, and research users who follow the field, and each panel would include researchers from outside the United States. In late 1996, COSEPUP began an experimental study of the effectiveness and outcome of such panels.
|
From page 70... ...
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH · What is the position of the United States in research in the field relative to that in other regions or countries? · What key factors influence relative US performance in the field?
|
From page 71... ...
. In this report, to conform with the 1992 report Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States, published by the NRC Board on Mathematical Sciences, mathematics broadly includes pure mathematics, applied mathematics, statistics and probability, operations research, and scientific computing.
|
From page 72... ...
The panel has attempted to be as fair and impartial as possible, balancing the points of view of US academic mathematical researchers with views of leading mathematicians from outside the United States, nonmathematical US researchers, and industrial researchers. In addition, the panel was specifically charged not to make recommendations.
|
From page 73... ...
Scope and Nature of the Panel's Evaluation economists, computer scientists, and statisticians. Some Nobel prizes in these fields have been awarded for mathematical work.
|
From page 74... ...
The demographic results of this informal process were remarkably uniform in each subfield and across subfields. In 17 of the 19 subfields, at least half those named are citizens or permanent residents of the United States.
|
From page 75... ...
, attended by about 2,500 mathematical researchers, plenary speakers are chosen by a committee representing mathematics societies from 12 countries or regions, and substantial attention is paid to balancing the plenary speakers among those countries.
|
From page 76... ...
Membership in the societies is a rough measure of sustained interest. 3.2 Mathematics in a Broacier Context As mentioned in section 2, the quality of mathematical research can partly be measured by its effects on closely related activities.
|
From page 77... ...
discusses the need for mathematical research in, for example, number theory and logic to develop and analyze cryptographic techniques guaranteed to remain secure when faced with continuing gains in raw computing power.
|
From page 78... ...
3.2.2 Industry Many large companies in the United States that rely on technical innovation support research and development laboratories that employ PhD mathematicians. In 1995, 21% of doctoral mathematical scientists in the US workforce were employed in private industry a proportion that has steadily increased over the years (see table Bug.
|
From page 79... ...
Within the last few years, there has been a great deal of interest by banks and investment houses in employing mathematicians to use mathematical techniques to model and analyze financial trends (COSEPUP 1995~; financial mathematics depends on a number of recent discoveries and techniques found in mathematics. Attempts to assess precisely the contributions of mathematical research to industrial problems are hindered by the blurring of disciplinary boundaries throughout most of industry (SIAM 1995~.
|
From page 80... ...
Major decreases in defense spending in the UK have led to concomitant reductions in mathematical research in the associated laboratories. Nonmilitary research in government laboratories has been cut; several nondefense laboratories that employed research mathematicians have been privatized and have moved toward commercial, shortterm activities, rather than long-term research.
|
From page 81... ...
Research mathematicians from all sectors of the US higher-education system, including the most-prestigious mathematics departments, are increasingly involved in improving the teaching of mathematics, at every level of education, to both specialists and nonspecialists. "Service teaching" of undergraduate mathematics to nonmajors is the responsibility of mathematics departments in all US universities, and many leading US academic mathematicians regularly teach elementary courses for mathematics nonmajors.
|
From page 82... ...
Mathematics education is a major concern in all other countries of which the panel is aware, but we have only anecdotal data about how research mathematicians elsewhere are involved in education. There is a general concern in Europe (except in France)
|
From page 83... ...
This concentration of immigrants raised the level of US mathematics to the top. Substantial increases in the number of outstanding mathematicians immigrating to the United States for example, from China and the former Soviet Union have also occurred more recently.
|
From page 84... ...
The large number of "baby boom" undergraduates entering colleges and universities in the 1960s and 1970s led to substantial expansion in mathematics departments and graduate programs throughout the United States. One structural aspect of US graduate education in mathematics stands out in comparison with other countries: the much lower level of specialization required to enter a graduate program.
|
From page 85... ...
A somewhat different model is the Courant Institute which is integrated with the mathematics and computer science departments at New York University. Those four and the National Institute of Statistical Sciences have increased awareness of research accomplishments, brought leading and junior researchers together, provided support for postdoctoral students, and created ties between different subfields of mathematics for example, geometry and mathematical physics and between mathematics and industry.
|
From page 86... ...
These have greatly increased the exchange of information through personal discussion in mathematical research over the last two decades. The predominant element in funding of United States mathematics research has been the strong commitment to intellectual excellence by private and public universities.
|
From page 87... ...
However, unemployment among recent PhDs has created tremendous stress on US mathematics during the 1990s. In this section, we identify a variety of current trends positive and negative that are affecting or are likely to affect the relative position of US mathematical research in scientific accomplishments and development of the knowledge base.
|
From page 88... ...
To name just one topic of current interest, mathematical research will be crucial in making sense of massive data sets (NRC 1996c) , particularly when data-gathering happens adaptively in real time; lack of progress in this arena is a recognized impediment to progress in biology, medicine, astronomy, physics, and geosciences.
|
From page 89... ...
The number of PhDs produced by US mathematics departments began to increase in the middle 1980s, rose during the early 1990s, and has shown signs of instability recently, as shown in figure 3 (see section 5.5~. During the same period, the number of academic positions open to new PhDs in mathematics has been shrinking.
|
From page 90... ...
number of positions offered in US mathematics departments to new PhDs fell by 33%; from 1995 to 1996, there was a 6% drop in the number of new PhDs employed by US academic institutions (Davis 1997~. During 1994-1995, there were 240 tenure-track positions for new doctoral recipients in US doctorate-granting departments in the mathematical sciences and 184 non-tenure-track positions.
|
From page 91... ...
Many European governments are actively encouraging nondefense industrial research and development; details about these 60 55 50 40 ° 35 Q Cat 30 25 20 ; ~, ~_ 10 5< ~ ~_,~ / ~ I_ ~ -I ~r 01 ~ -- ~-= ~ ~1 ~5 ~9 ~9~\~ ,~9 ~9 ~9 ~9~ ~9~ ,~9~ ,~9~9 ,~99~ ~99~ ~99~ 0 Tenured faculty ~ Tenure-track faculty · Other academic positions Postdoc appointmentsacademic K 2-yr college faculty · Industry 0 Federal and other government positions Self-employed and others 0 Unemployed and seeking FIGURE 4 Employment status of PhD mathematicians in the US. Source: Analysis conducted by the National Research Council Office of Scientific and Engineering Personnel for this study.
|
From page 92... ...
Furthermore, in every year since 1990, foreign students have received more than half the PhDs awarded in mathematics in the United States. That phenomenon occurs elsewhere, and high proportions of foreign students in the sciences are relatively common in other industrialized countries, especially those with former colonial ties.
|
From page 93... ...
However, the overall picture of "stay rates" for foreign students in all science and engineering fields, as shown in figure 7, suggests that such intentions are widespread and confirms the attractiveness of the United States to foreign talent mentioned in section 4.1. To explore the question further, the panel conducted its own informal survey of 10 highly rated US mathematics departments.
|
From page 94... ...
An online NSF data brief of February 1997 (NSF 1997a) reveals that, among all US doctoral students in the sciences, the largest percentage from 1994 to 1995 occurred in the mathematical sciences and physics, each of which experienced a 6% reduction.
|
From page 95... ...
5.6 Support In section 4.4. we stated that an important underpinning for US success in mathematical research has been sustained support and 1-29
|
From page 96... ...
Figure 9 compares the 1993 median salaries of US PhDs who received their degrees in 1985-1990 in mathematics, computer science chemistry, physics/astronomy, and electrical engineering. One might reasonably conclude that mathematics PhDs have less-favorable salary prospects than other science PhDs.
|
From page 97... ...
On the basis of current dollars in the actual FY1996 and estimated FY1997 budgets, the Divi 12 10 8 6 a)
|
From page 98... ...
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH sion of Mathematical Sciences at the National Science Foundation experienced growth of 7.1%. Overall Department of Defense spending on mathematical sciences decreased by 12.3% and overall Department of Energy spending on mathematical sciences remained flat.
|
From page 99... ...
As recognition of the importance of mathematics in interdisciplinary research grows, opportunities will expand for collaborations that enrich other sciences and mathematics. The panel believes that the future relative position of the United States in interdisciplinary mathematical research depends in large part on the effectiveness with which these opportunities are realized.
|
From page 100... ...
A key factor in this cultivation is the quality of mathematics education in K-12 and college. 6.4 Support for Mc~thematical Research The most important safeguard of US preeminence in mathematical research and in all the sciences is the flourishing of both private and state research universities.
|
From page 101... ...
AMS (American Mathematical Society)
|
From page 102... ...
. Mathematical Research in Materials Science.
|
From page 103... ...
Before taking his current positions, he was director of the Courant Institute of Mathematical Sciences (1972-1980) and director of the AEC Computing and Applied Mathematics Center (1964-1972)
|
From page 104... ...
He has pioneered industrial and applied mathematics cooperation in France as cofounder of Institut National de Recherche en Informatique et en Automatique (INRIA) and as president of the French Space Agency.
|
From page 105... ...
, the international Frederic Esser Nemmers Prize in Mathematics of Northwestern University (1994) and the Brouwer Golden Medal of the Royal Society and Mathematical Society of the Netherlands for work in number theory (1987~.
|
From page 106... ...
She was president of the American Mathematical Society during 1995-1996 and is a member of the Mathematical Association of America, and the Society for Industrial and Applied Mathematics and a fellow of the American Association for the Advancement of Science. She received her BA (1945)
|
From page 107... ...
He is a member of the Council of the National Academy of Sciences, the Governing Board of the National Research Council, the American Academy of Arts and Sciences, the American Mathematical Society (vice president, 1970-1972) , the American Physical Society, and the American Philosophical Society.
|
From page 108... ...
. He held positions in the Environmental Protection Agency, the US Regulatory Council, and the Office of Management and Budget before coming to the National Academy of Sciences in 1981.
|
From page 109... ...
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.
|
From page 110... ...
1 2,000 1 0,000 8,000 6,000 4,000 2,000 O 1 920- 1 926- 1 936 1 925 1 935 1 945 1 946- 1 956- 1 965- 1 976- 1 986 1955 1965 1975 1985 1995 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.
|
From page 111... ...
1 995-1 996 1 990-1 991 1 985-1 986 1 980-1 981 1 975-1 976 0 150 300 450 600 750 900 1,050 1,200 1,350 Number of Recipients O US Citizens Non-US Citizens O Total Number of Recipients FIGURE B-4 Doctoral recipients: total number of US and non-US citizens. Source: AMS 1996.
|
From page 112... ...
Mathematics cannot be separated out from these data. EMPLOYMENT Figure B-7 shows the number of PhD mathematicians employed in the United States from 1973 to 1991.
|
From page 113... ...
8. 26,000 24,000 22,000 20,000 18,000 16,000 ~,14,000 z12,000 1 0,000 8,000 6,000 4,000 2,000 O 1973 1975 1979 1 983 1 987 1 991 1993 1 995 Year FIGURE B-7 Number of PhD mathematicians employed in the United States.
|
From page 116... ...
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.
|
From page 117... ...
U.S. 74% FIGURE B-10 Source of PhDs of full-time mathematics faculty hired during 1991-1992 in the United States.
|
From page 118... ...
INTERNATIONAL BENCHMARKING OF US MATHEMATICS RESEARCH 16 14 12 10 8 6 4 / \ \ \ O 1989-1990 1990-1991 1991-1992 1 992-1993 1 993-1 994 1 994-1 995 1995-1996 ~Fall ~Spring FIGURE Bell Percentage of unemployed new US mathematics PhDs. Source: AMS 1996, 1997c.
|
From page 119... ...
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)
|
From page 120... ...
79.25 79.80 82.76 3.71% 83.93 1.4% Other MPS 2.23 3.64 4.44 1.99% 4.33 -2.5% Department of Defenseb 71.92 70.34 60.19 -16.86% 63.68 5.8% AFOSR 16.26 15.20 15.18 -0.13% 14.80 -2.5% ARO 13.94 13.65 11.54 -18.28% 12.98 12.5% DARPA 19.51 20.84 17.31 -20.39% 19.38 12.0% NSA 2.32 2.27 1.86 -22.04% 1.82 -2.5% OUR 19.88 18.38 14.29 -28.62% 14.00 2.9% Department of Energy 14.59 14.56 14.20 -2.54% 13.84 -2.5% University support 5.76 5.00 4.44 -12.61% 4.33 -2.5% National laboratories 8.83 9.55 9.77 2.30% 9.52 -2.5% TOTAL, All Agencies 167.99 168.34 161.59 -4.18% 165.78 2.6% a Column added by authors of this report. b The FY1998 budgets for DOD's mathematical programs are estimates based on DOD's overall budget request for basic research.
|
From page 121... ...
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.
|
From page 122... ...
~ HHS 3% \ DOD 42% DOI 1% 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.
|
From page 123... ...
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.
|
From page 124... ...
4,000 ~ ~ 3,800wO 3,600 ~ <~' 3~400 ~ Q 3,200 ~ ~ 3,000 ~ Z 2,8002,600 ~ 2,400 ~ 2,200 ~ 2.000 ~ ~ / ~. _ - ~ T T 1 I r T 1 [ T T 1 I r T 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 ~EC Papers ~US Papers FIGURE B-16 Number of mathematical-research papers by US and EC authors.
|
From page 125... ...
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)
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.