National Academies Press: OpenBook

International Benchmarking of US Mathematics Research (1997)

Chapter: APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS

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Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
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Figure 10: Percentages of academic scientists with federal support, 1993

Source: NSB 1996, appendix table 5-27.

Figure 11: Percentage increase in federal R&D expenditures at universities and colleges, by field

Source: NSF 1997b, table 1 and discussions with NSF staff.

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
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Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

6

LIKELY FUTURE RELATIVE POSITION OF US MATHEMATICS

The current trends described in section 5 are obviously mixed. This section summarizes our best estimate about the future relative position of US mathematical research. *

6.1. Intellectual Quality

As already stressed in section 5.1., the field is full of new results, new methods, new points of view, and new problems. Because the United States is preeminent, mathematics in the United States is likely in the near term to retain its dominant position in the world. In the long term, however, some of this momentum might be lost, depending on how we rise to new challenges and potentially damaging developments described below.

6.2 Interdisciplinary Research

Notable successes in interdisciplinary research (see section 3.2.1. and section 3.2.2.) have made this aspect of US mathematical research of preeminent importance today—although not uniformly throughout the United States. 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. As observed in section 5.2 and section 5.3.2, governments, universities, and industry in other countries are actively supporting mechanisms that encourage interdisciplinary research. The United States must pay serious attention to this issue.

6.3. US Graduate Education in Mathematics

The panel is especially concerned about the potential erosion of the US research base because of a decrease in the number of graduate students at leading universities. The trends discussed in section 5.4 imply that the future position of US mathematics is likely to depend increasingly on graduate students and postdoctoral fellows from other countries; this makes our preeminence precarious if jobs in their countries of origin become more attractive to foreign students or if changes in immigration laws close the United States doors to non-native mathematicians. In addition, there is a dearth of minority-group members in mathematics. The panel believes that the United States must cultivate its own mathematical talent to retain its leading stature in mathematical research. A key factor in this cultivation is the quality of

*

Many of these issues are discussed in a National Research Council report (NRC 1997).

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
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mathematics education in K-12 and college.

6.4. Support for Mathematical 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. Some of the stresses faced today by US research universities are described by the Council on Competitiveness as “facing a funding squeeze and growing, often contradictory, demands” (Council on Competitiveness 1996, p. 21). The research universities respond to this squeeze in part by reducing staff size. This situation affects mathematics because research universities provide a stable base, both financial and professional (see section 4.4). The current trend toward hiring temporary faculty discussed in section 5.3.1 is a prime indication that US universities might provide much less of that support in the future.

Today the research universities are the major instruments in the United States for research and development that fuel high technologies, an extremely important part of the US economy. Mathematics has prospered in part because it plays an important role in this research. But the research enterprise is at risk if the support for research universities continues to decline.

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

7

REFERENCES

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AMS (American Mathematical Society) . “Recent Trends in Graduate Admissions in Mathematics Departments” , Notices of the AMS , February 1997a .

AMS (American Mathematical Society) . “A Survey of Four-Year and University Mathematics in Fall 1995: A Hiatus in Both Enrollment and Faculty Increases” , Notices of the AMS , September 1997b .

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Askey, Richard . “The Japanese University Entrance Examinations in Mathematics” , FOCUS Newsletter , Mathematics Association of America , vol. 13, no. 1 , 1993 .

Chen, L.Q. , B. Fultz , J.W. Cahn , J.R. Manning , J.E. Morral , J. Simmons , eds. Mathematics of Microstructure Evolution. The Minerals, Metals, and Materials Society , Warrendale, PA , and Society for Industrial and Applied Mathematics , Philadelphia, PA , 1996 .

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COSEPUP (Committee on Science, Engineering, and Public Policy) . Reshaping the Graduate Education of Scientists and Engineers. Washington, D.C. : National Academy Press , 1995 .

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
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COSEPUP (Committee on Science, Engineering, and Public Policy) . An Assessment of the National Science Foundation's Science and Technology Program. Washington, D.C. : National Academy Press , 1996 .

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ED (U.S. Department of Education) . Pursuing Excellence, NCES 97-198. National Center for Education Statistics . Washington, D.C. : U.S. Government Printing Office , 1996 .

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NRC (National Research Council) . Calculating the Secrets of Life: Applications of the Mathematical Sciences to Molecular Biology. Washington, D.C. : National Academy Press , 1995b .

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NRC (National Research Council) . Research-Doctorate Programs in the United States: Continuity and Change. Washington, D.C. : National Academy Press , 1995d .

NRC (National Research Council) . Cryptography's Role in Securing the Information Society. Washington, D.C. : National Academy Press , 1996a .

NRC (National Research Council) . Mathematics and Physics of Emerging Biomedical Imaging. Washington, D.C. : National Academy Press , 1996b .

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
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NRC (National Research Council) . Massive Data Sets: Proceedings of a Workshop. Washington, D.C. : National Academy Press , 1996c .

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NSB (National Science Board) . Science and Engineering Indicators - 1996. Arlington, VA : National Science Foundation , 1996 .

NSF (National Science Foundation) . Characteristics of Doctoral Scientists and Engineers in the United States, 1993. NSF 96-302 . Arlington, VA : National Science Foundation , 1996a .

NSF (National Science Foundation) . Women, Minorities, and Persons with Disabilities in Science and Engineering: 1996. NSF 96-311 . Arlington VA : National Science Foundation , 1996b .

NSF (National Science Foundation) . Human Resources for Science & Technology: The European Region. NSF 96-316 . Arlington, VA : National Science Foundation , 1996c .

NSF (National Science Foundation) . Data Brief . 97-303 . Arlington, VA : National Science Foundation , February 7, 1997a .

NSF (National Science Foundation) . Data Brief . 97-304 . Arlington, VA : National Science Foundation , March 7, 1997b .

NSF (National Science Foundation) . Knowledge and Distributed Intelligence . See World Wide Web documents at http://www.nsf.gov.

NSF (National Science Foundation) . 1995 Graduate Student Survey . Available at http://www.nsf.gov.

SIAM (Society for Industrial and Applied Mathematics) . Mathematics in Industry. Philadelphia : SIAM , 1995 .

SIAM (Society for Industrial and Applied Mathematics) . “Mathematics meets film animation in Kansas City community lecture ” , SIAM News , vol. 29, no. 7 , 1996 .

United Kingdom Office of Science and Technology . The Quality of the UK Science Base. London, UK : Department of Trade and Industry , March 1997 .

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
This page in the original is blank.
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

APPENDIX A

PANEL AND STAFF BIOGRAPHICAL INFORMATION

Committee on Science, Engineering, and Public Policy

International Benchmarking of US Mathematics Research Panel

Peter D. Lax [NAS*] (Chair) is professor of mathematics and director of the Courant Mathematics and Computer Lab at New York University. 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), both at NYU. He is a National Medal of Science awardee, former president of the American Mathematical Society (AMS), and a former National Science Board member. He has extensive experience as a lecturer overseas, particularly in Germany, France, and the United Kingdom as well as being a foreign member of the French, Chinese, Hungarian, and Russian academies of sciences. He is a member of the American Philosophical Society. Dr. Lax has received many honorary degrees, the Wolf Prize (1987), the National Academy of Sciences Prize in Applied Mathematics (1983), the Norbert Wiener Prize of AMS and the Society for Industrial and Applied Mathematics (1975), the Chauvenet Prize of the Mathematical Association of America (1974), and the Steele Prize of AMS (1992).

Michael F. Atiyah [NAS-F] is director of the Isaac Newton Institute for Mathematical Sciences in Cambridge, England, and president of the Royal Society (1990-1995). He has recently retired as master of Trinity College, Cambridge. Before this, he was a Royal Society research professor and fellow of St. Catherine's College, Oxford (1973-1990). He has served as professor of mathematics at the Institute for Advanced Study in the United States (1969-1972) and Savilian Professor of Geometry at University of Oxford (1963-1969). He attended Victoria College in Cairo and received his BA (1952) and PhD (1955) from the University of Cambridge. Sir Michael is a member of many academies of sciences. He holds many honorary doctorates and several honorary fellowships. Sir Michael has been a member of the Executive Committee of the International Mathematical Union (1966-1974), president of the London Mathematical Society (1975-1977), president of the Mathematical Association (1981-1982), member of the Science and Engineering Research Council (1984-1989), member of the Council of the Royal Society (1973-1974), vice-president of the Royal Society (1984-1985), and chairman of the European Mathematical Council (1978-1990). He received the Fields Medal in 1966.

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

Spencer J. Bloch [NAS] is professor of mathematics at the University of Chicago. He was an instructor, lecturer, and assistant professor at Princeton (1971-1974) and an associate professor at the University of Michigan (1974-1976). Dr. Bloch has done pioneering work in the application of higher algebraic K theory to algebraic geometry, particularly in problems related to algebraic cycles, and is regarded as the world's leader in this field. His work has firmly established higher K theory as a fundamental tool in algebraic geometry. Dr. Bloch received his BA at Harvard (1966) and his PhD from Columbia (1971).

Joseph B. Keller [NAS] is professor of mathematics and mechanical engineering (emeritus) at Stanford University. Before this, he was at Courant Institute of Mathematical Sciences, New York University (1948-1979), where he received his PhD in mathematics (1948). He is a foreign member of the Royal Society and was honorary professor of mathematical sciences at the University of Cambridge. He is a recipient of the Wolf Prize (1997), the Frederick E. Nemmers Prize (1996), the National Academy of Sciences Award in Applied Mathematics and Numerical Analysis (1995), the National Medal of Science (1988), the Timoshenko Medal (1984), the Eringen Medal (1981), and the von Karman Prize (1979). He was von Neumann Lecturer (1983) and Gibbs Lecturer of the American Mathematical Society (1977).

Jacques-Louis Lions [NAS-F] is professor at the College de France in Paris and president of the French Academy of Sciences. He has contributed fundamental research in nonlinear partial differential equations, including homogenization and control. He has trained an entire generation of modern applied mathematicians in France. 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. In addition, he is a former president and secretary of the International Mathematical Union.

Yuri I. Manin is a member (since 1993) and director (since 1995) of the Max Planck Institute for Mathematics. He is also leading researcher of the Steklov Mathematical Institute of the Russian Academy of Sciences (since 1960, now in absentia.) In 1965-1992, he was professor of algebra at Moscow University and held various visiting professorships, in particular at Harvard University, Columbia University, and the Massachusetts Institute of Technology. He is a member of the Academy of Sciences, Russia, the Royal Society of Sciences of the Netherlands, the Academia Europaea, the Max-Planck-Gesellschaft, the Gottingen Academy of Sciences Class of Physics and Mathematics, and the Pontificia Academia Scientiarum. He won the Lenin Prize for work in algebraic geometry (1967), 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).

Rudolph A. Marcus [NAS] is A.A. Noyes Professor of Chemistry at the California Institute of Technology. He is also an honorary professor at Fudan University in Shanghai, China, and at the Institute of Chemistry in the Chinese Academy of Sciences in Beijing. Dr. Marcus holds an honorary fellowship at University College of the University of Oxford and was Linnett Visiting Professor of Chemistry at the University of Cambridge. He previously held positions at the University of North Carolina, the Polytechnic Institute of Brooklyn, the Courant Institute of Mathematical Sciences of New York University, the University of Illinois, the University of

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

Oxford, and the California Institute of Technology. Dr. Marcus received his BSc (1943) and PhD (1946) in chemistry from McGill University in Montreal, Canada. He is a fellow of the National Academy of Sciences, the American Academy of Arts and Sciences, the Royal Society of Chemistry, and the Royal Society of Canada, and he is a member of the Royal Society, the International Academy of Quantum Molecular Science, the American Philosophical Society, the American Association for the Advancement of Science, the American Chemical Society, and the American Physical Society. Dr. Marcus received the Nobel prize in chemistry in 1992.

Gary C. McDonald is head of the Operations Research Department at the General Motors Research and Development Center. Before this, he was head of the mathematics department at the center (1983-1992). He is also adjunct professor of mathematics at Oakland University. Dr. McDonald started as associate senior research mathematician at General Motors in 1969 and has held the positions of senior research mathematician (1972-1976) and assistant department head (1976-1983). He received his BA (1964) from St. Mary's College and his MS (1966) and PhD (1969) from Purdue University. He is a fellow of the Institute of Mathematical Statistics, the American Statistical Association, and the American Association for the Advancement of Science.

Cathleen S. Morawetz [NAS] is professor emeritus at the Courant Institute of Mathematical Sciences of New York University. She has been with the institute since starting as a research associate (1952). She held positions as assistant professor (1957-1960), associate professor (1960-1965), professor (1965-present), and chairman (1981-84) Department of Mathematics, associate director (1978-1981), deputy director (1981-1984), and director (1984-1988). Dr. Morawetz was a trustee of the Alfred P. Sloan Foundation (1980-1984) and a member of the National Research Council's Board on Mathematical Sciences. 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 the University of Toronto, her MS (1946) from the Massachusetts Institute of Technology, and her PhD (1951) from New York University.

Peter Sarnak is chairman of the Department of Mathematics at Princeton University. Before this, he was the H. Fine Professor (1995-1996). He has also been professor at Stanford University (1987-1991), the Sherman Fairchild Distinguished Scholar at the California Institute of Technology (1989), a fellow at the Institute of Advanced Studies at Hebrew University (1987-1988), and assistant and associate professor at the Courant Institute of Mathematical Sciences of New York University (1980-1983). Dr. Sarnak received his BSc (1974) from the University of Witwatersrand in South Africa and his PhD (1980) from Stanford University. He is a member of the American Academy of Arts and Sciences and was a Sloan fellow (1983-1985) and presidential young investigator (1985-1990).

I.M. Singer [NAS] is Institute Professor at the Massachusetts Institute of Technology (MIT). His research has been in the fields of index theory/manifold invariants/elliptic analysis, differential geometry, functional analysis, and operator theory. He has been teaching calculus intermittently between 1949 and 1997. He received the AMS Bocher Memorial Prize (1969), the National

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

Medal of Science (1983), the Wigner Medal (1988), and the AMS Award for Public Service (1993). He was chairman of the National Academy of Sciences Committee on Science and Public Policy (1973-1978) and was with the White House Science Council from 1982 to 1988. Dr. Singer received his BS (1944) from the University of Michigan and his MS (1948) and PhD (1950) in mathematics from the University of Chicago. 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.

Margaret H. Wright [NAE] is a Distinguished Member of Technical Staff at Bell Laboratories, Lucent Technologies. Before joining Bell Laboratories she worked in the Department of Operations Research at Stanford University (1976-1988). Dr. Wright holds a BS in mathematics, and MS and PhD degrees in computer science, from Stanford University. She served as president of the Society for Industrial and Applied Mathematics during 1995-1996. Her research involves theory and algorithms for optimization and linear algebra, scientific computing, and solution of real-world optimization problems.

STAFF

Deborah D. Stine is the study director and associate director of the Committee on Science, Engineering, and Public Policy (COSEPUP). She has been working on various projects throughout the National Academy of Sciences complex since 1989. She received a National Research Council group award for her first study for COSEPUP on policy implications of greenhouse warming and a Commission on Life Sciences staff citation for her work in risk assessment and management. Other studies have addressed graduate education, responsible conduct of research, careers in science and engineering, environmental remediation, the national biological survey, and corporate environmental stewardship. She holds a bachelor's degree in mechanical and environmental engineering from the University of California, Irvine; a master's degree in business administration; and a PhD in public administration, specializing in policy analysis, from the American University. Before coming to the Academy, she was a mathematician for the Air Force, an air-pollution engineer for the state of Texas, and an air-issues manager for the Chemical Manufacturers Association.

John R. Tucker has been director of the Board on Mathematical Sciences (BMS) since 1994. He earned degrees in mathematics at Washington College (BA) and George Washington University (Mphil and PhD). He has worked as a researcher with Chi Associates, Inc., and an assistant professor of mathematics at Virginia Commonwealth University and Mary Washington College. He joined the National Research Council in 1989 as program officer for the BMS and advanced to senior program officer in 1993. His interests include nonlinear dynamics, order and disorder, mixing processes, and mathematical developments in biology and medicine.

Lawrence E. McCray is executive director of the Committee on Science, Engineering, and Public Policy (COSEPUP). 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. He has directed Academy studies in carcinogenic risk assessment,

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

export controls, nuclear winter, and federal science budgeting. A Fulbright scholar in 1968, he received the Schattschneider award in 1972 from the American Political Science Association for the best dissertation in American government and politics. In 1987, he received the National Research Council staff award. He joined COSEPUP in 1988 as executive director and since 1994 has served concurrently as the director of the NRC Policy Division.

Patrick P. Sevcik is research associate with the Committee on Science, Engineering, and Public Policy (COSEPUP). He works on a variety of projects for COSEPUP, the Policy Division (PD), and the PD Office of Special Projects, assisting Deborah Stine and Lawrence McCray. Before coming to the National Research Council in 1993, he was an assistant program officer with the International Republican Institute from 1990 to 1993, working on democracy development, primarily in central and eastern Europe. He has held positions at the White House in the Office of Political Affairs (1989-1990) and on Capitol Hill (1987-1988) in the office of Representative John DioGuardi (R-NY). During that time, he also held concurrent positions in several Slovak-American organizations. He holds a BA in international affairs, with an emphasis on Soviet and Eastern European studies, from the George Washington University. He has also studied Russian language and culture at the Leningrad Polytechnic Institute in Leningrad.

*

NAS Member of the National Academy of Sciences

NAS-F Foreign member of the National Academy of Sciences

NAE Member of the National Academy of Engineering

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
This page in the original is blank.
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

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.

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

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.

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

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.

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×

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.

Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
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Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
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Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
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Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
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Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
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Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 48
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 49
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 50
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 51
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 52
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
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Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
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Page 54
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
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Page 55
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 56
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 57
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 58
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
×
Page 59
Suggested Citation:"APPENDIX B STATISTICAL DATA ON THE FIELD OF MATHEMATICS." National Academy of Sciences, National Academy of Engineering, and Institute of Medicine. 1997. International Benchmarking of US Mathematics Research. Washington, DC: The National Academies Press. doi: 10.17226/9089.
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Page 60
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