Appendix C

Basic Data about the U.S. Mathematical Sciences

CURRENT AND RECENT FUNDING FOR THE MATHEMATICAL SCIENCES

In order to provide a picture of the financial support for the mathematical sciences, this appendix gives an overview of federal funding and two private funding sources. Much of this funding supports not only research per se but also most of the research associateships and postdoctoral fellowships that prepare the next generation of researchers. A fraction of the federal funding supports workshops, research institutes, and other mechanisms that enable sharing of results and community interactions. Additional research funding for academic researchers is available from a variety of sources—universities, states, foundations, industry, and programs that primarily fund other science and engineering disciplines. In addition, a good deal of mathematical sciences research is carried out and supported in industry and in government laboratories. Researchers who perform mathematical sciences work in private corporations may not be labeled as “mathematician” or “statistician,” so it is difficult to characterize the magnitude of that component of the mathematical sciences research enterprise. This report does not attempt to do so, but estimates do exist.1

Federal Funding for the Mathematical Sciences

Federal extramural funding for the mathematical sciences has increased in recent years. Four main governmental agencies and their suborganizations

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1 Chapter 4 presents some information about the mathematical sciences in industry.



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Appendix C Basic Data about the U.S. Mathematical Sciences CURRENT AND RECENT FUNDING FOR THE MATHEMATICAL SCIENCES In order to provide a picture of the financial support for the math- ematical sciences, this appendix gives an overview of federal funding and two private funding sources. Much of this funding supports not only re- search per se but also most of the research associateships and postdoctoral fellow­hips that prepare the next generation of researchers. A fraction of s the federal funding supports workshops, research institutes, and other mechanisms that enable sharing of results and community interactions. Additional research funding for academic researchers is available from a variety of sources—universities, states, foundations, industry, and programs that primarily fund other science and engineering disciplines. In addition, a good deal of mathematical sciences research is carried out and supported in industry and in government laboratories. Researchers who perform mathematical sciences work in private corporations may not be labeled as “mathematician” or “statistician,” so it is difficult to characterize the mag- nitude of that component of the mathematical sciences research enterprise. This report does not attempt to do so, but estimates do exist.1 Federal Funding for the Mathematical Sciences Federal extramural funding for the mathematical sciences has increased in recent years. Four main governmental agencies and their suborganiza- 1  Chapter 4 presents some information about the mathematical sciences in industry. 163

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164 APPENDIX C tions typically fund the mathematical sciences through extramural grants (Table C-1): • National Science Foundation (NSF), • Department of Defense (DOD), — ir Force Office of Scientific Research (AFOSR), A — rmy Research Office (ARO), A — efense Advanced Research Projects Agency (DARPA), D — ational Security Agency (NSA), N — ffice of Naval Research (ONR), O • National Institutes of Health (NIH), — ational Institute of General Medical Sciences (NIGMS), N — ational Institute of Biomedical Imaging and Bioengineering N (NIBIB), and • Department of Energy (DOE), — wo programs of the Office of Advanced Scientific Computer T Research (ASCR): Applied Mathematics and Scientific Discovery Through Advanced Computing (SciDAC) NSF is consistently the largest single supporter of the mathematical sciences, and it is the sole federal agency that devotes a significant amount of funding to areas of core mathematics. (NSA’s extramural program is focused on core mathematics, but it is quite small.) Private Sector Mathematical Sciences Funding The Simons Foundation is a relatively new source of funding for the mathematical sciences and is becoming a major source of support. The Simons Foundation Program for Mathematics and the Physical Sciences f ­ocuses on “the theoretical sciences radiating from Mathematics: in par- ticular, the fields of Mathematics, Theoretical Computer Science and Theo- retical Physics.”2 In 2009, the Simons Foundation launched a program to provide an estimated $40 million annually for research in mathematics and theoretical aspects of physical science that relate to mathematics. Much of this initial money went to fund 68 postdoctoral positions at 46 universities. The Simons Foundation will also be funding 40 U.S. and Canadian academic researchers every year as part of the Simons Fellows program, which is intended to increase the opportunity for research leaves from classroom teaching and academic administration and to extend sabbatical leaves to last for a full academic year. At a smaller scale, individual grants of 2 The Simons Foundation, “Mathematics and the Physical Sciences.” Available at https:// simonsfoundation.org/mathematics-physical-sciences. Accessed July 12, 2011.

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APPENDIX C 165 TABLE C-1  Federal Funding for the Mathematical Sciences (millions of dollars) 2012 2005 2006 2007 2008 2009 ARRAa 2010 2011 Estimate NSF                DMS 200 200 206 212 225 97 245 240 238             DOD  AFOSR 30 32 35 37 45 0 52 58 47  ARO 10 14 14 12 13 0 12 16 16  DARPA 19 16 26 19 21 0 12 16 28  NSA 4 4 4 4 4 0 7 6 6  ONR 14 13 14 14 23 0 20 22 24 Total DOD 77 79 93 85 104 0 103 118 121                 DOE   Applied Math 30 32 33 32 45 0 44 46 46  SciDAC 0 3 42 54 60 0 50 53 44 Total DOE 30 36 75 86 105 0 94 99 90               NIH  NIGMS 35 38 45 45 47 0 50  —  —  NIBIB 38 39 38 38 38 0 39  —  — Total NIH 73 77 83 83 85 0 89  —  — Total 380 391 456 466 519 97 531 457 449 NOTE: Budget information is approximate and has been derived from agency documents and AMS staff conversations with agency program managers and representatives. According to the author of the AMS reports, Samuel M. Rankin, III, in a personal communication on October 31, 2011, the amounts shown here for NIH are apparently dominated by intramural funding within NIH and therefore overstate the funds available for the broader community, while the totals shown for DOE include a large amount of funding awarded to researchers at DOE national laboratories. Other amounts in this table are extramural funds. This compila- tion does not capture some mathematical sciences research carried out in the Department of Commerce at the Census Bureau and the National Institute of Technology. aAmerican Recovery and Reinvestment Act of 2009. SOURCE: Samuel M. Rankin, III, Mathematical sciences in the FY2011 budget. Notices of the AMS 57(8):988-991; ———, Mathematical sciences in the FY2010 budget. Notices of the AMS 56(8): 1285-1288; ———, Mathematical sciences in the FY2009 budget. Notices of the AMS 55(7): 809-812; ———, Mathematical sciences in the FY2008 budget. Notices of the AMS 54(7): 872-875; and ———, Mathematical sciences in the FY2007 budget, Notices of the AMS 53(6): 682-685. Data for 2012 and revised 2010 and 2011 data from personal com- munication with Samuel M. Rankin III on October 3, 2012.

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166 APPENDIX C no more than $7,000 are available specifically to defray expenses (such as travel) associated with collaborations. Other mathematical funding comes in the form of Math+X grants, which offer matching endowment grants (up to $1.5 million) to universities to create new tenured Chairs to be shared equally between a department of mathematics and another science or en- gineering department. The Math+X grants also support one postdoctoral researcher and two graduate students (totaling up to $325,000 annually). Finally, the foundation is funding a new institute for the theory of comput- ing, supported at $6 million annually for up to 10 years. The Clay Mathematics Institute (CMI), another privately funded orga- nization, aims to stimulate and disseminate mathematics research. CMI sup- ports individual research mathematicians at various stages in their careers and organizes conferences, workshops, and an annual summer school.3 Finally, the American Institute of Mathematics (AIM) is partially funded by private funds from the Fry Foundation, with additional fund- ing from NSF. The goal of AIM is to expand the frontiers of mathematical knowledge through focused research projects, sponsored conferences, and the development of an online mathematics library.4 SOURCES OF FEDERAL FINANCIAL SUPPORT National Science Foundation The NSF is the primary federal funder of mathematical sciences research and the only one that provides significant extramural support for core fields. The focal point in NSF for the mathematical sciences is the Division of Mathematical Sciences (DMS), which supports the following programs: • Algebra and Number Theory, • Analysis, • Applied Mathematics, • Combinatorials, • Computational Mathematics, • Foundations, • Geometric Analysis, • Mathematical Biology, • Probability and Statistics, and • Topology. 3  The Clay Mathematics Institute, “About the Clay Mathematics Institute.” Available at http://www.claymath.org/about/. Accessed August 18, 2011. 4  American Institute of Mathematics, “About AIM.” Available at http://www.aimath.org/ about/. Accessed August 18, 2011.

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APPENDIX C 167 Other DMS funding opportunities include special research programs, training programs (such as research experiences for undergraduates, re- search training groups, and postdoctoral research fellowships), career devel­ opment programs, and institutes. The fraction of research proposals to DMS that received funding was 35 percent in 2007, 31 percent in 2008, and 37 percent in 2009. DMS received approximately 2,200 proposals per year between 2005 and 2008, with a bump up to 2,300 in 2009 when funding from the federal stimulus program (ARRA) supplemented NSF funds. DMS made approximately 680 awards each year in 2005, 2006, and 2007. In 2008, the total number of awards was 770, and in 2009 it was 840. The median award size in 2008 was $61,000. Department of Defense The Department of Defense (DOD) provides extramural funding for the mathematical sciences primarily through five organizations: AFOSR, ARO, DARPA, NSA, and ONR.5 In aggregate, DOD is the second-largest federal funder of extramural mathematical sciences research. It also sup- ports in-house R&D in the mathematical sciences, especially at the NSA, the Air Force Research Laboratory (AFRL), and Naval Research Labora- tory (NRL). In particular, NSA is often said to be the largest employer of mathematicians in the United States. Details of these in-house research programs are not readily available, and they are not always clustered a ­ ccording to academic disciplines, so the following discussion covers only the extramural programs. AFOSR accounts for the largest continued funding within DOD, as seen in Table C-1. The majority of AFOSR support for the mathemati- cal sciences comes from the Mathematics, Information, and Life Sciences directorate. Mathematical science areas of particular interest to this di- rectorate are collective behavior and sociocultural modeling; complex networks; computational mathematics; dynamics and control; science of information, computation, and fusion; information operations and security; mathematical modeling of cognition and decision; optimiza- tion and discrete mathematics; robust computational intelligence; and systems and software. 5  Many arms of the DOD make use of advances in the mathematical sciences. For example, the Army Research Laboratory and the Air Force Research Laboratory have some collabora- tions (including funding) with mathematical science researchers, the National Geospatial- Intelligence Agency supports some academic research in the mathematical sciences, and several offices in the Pentagon are strongly connected with operations research. But, generally speaking, these sources of support are not formalized in ongoing extramural programs, and they are not captured in Table C-1.

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168 APPENDIX C ARO’s extramural program for the mathematical sciences is modest by comparison. It funds research in four areas: probability and statistics, modeling of complex systems, numerical analysis, and biomathematics. The majority of ONR research in the mathematical sciences comes from the Command, Control, Communications, Computers, Intelligence, Surveillance, and Reconnaissance (C4ISR) Department. This department is partitioned into three divisions: Mathematics, Computers, and Information Research; Electronics, Sensors, and Network Research; and Appli­ ations c and Transitions. The first of these divisions focuses on research in ap- plied computational analysis, command and control, image analysis and understanding, data analysis and understanding, information integration, intelligent and autonomous systems, mathematical optimization, signal processing, and software and computing systems. The Electronics, Sensors, and Network Research Division focuses on research in communications and networking analysis, signal processing, and a number of non­ athematical m areas. The Applications and Transitions Division broadly focuses on pro- grams in surface and aerospace surveillance, communications, and elec- tronic combat. Much of the funding for mathematical sciences within DARPA comes from the Defense Sciences Office (DSO). DSO’s mathematics program has an applied and computational mathematics component, which includes applica- tions such as signal and image processing, biology, materials, sensing, and design of complex systems. The mathematics program also has a fundamental mathematics component, which focuses on exploring selected core areas with the potential for being relevant to future applications. These fundamental areas include topological and geometric methods, extracting knowledge from data, and new approaches to connecting key areas of mathematics. NSA has a very large in-house program in mathematical sciences re- search. Its extramural program is small but important because it is one of the few non-NSF sources of funding for areas of core mathematics, offering grants for unclassified research in algebra, number theory, discrete math- ematics, probability, and statistics. There is also a research grants program, which offers funding to beginning, midlevel, and senior researchers. In addition, MSP funds conferences, workshops, special situation proposals, and sabbatical programs for mathematicians, statisticians, and computer scientists. Department of Energy The Applied Mathematics program at DOE’s Office of Advanced Sci- entific Computing Research (ASCR) supports basic research leading to fundamental mathematical advances and computational breakthroughs rel- evant to DOE missions. Applied Mathematics research supports efforts to

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APPENDIX C 169 develop robust mathematical models, algorithms, and numerical software for enabling predictive scientific simulations of DOE-relevant complex sys- tems. Research includes numerical methods for solving ordinary and par- tial differential equations, multiscale and multiphysics modeling, analysis and simulation, numerical methods for solving large systems of linear and nonlinear equations, optimization, uncertainty quantification, and analy- sis of large-scale data. The program addresses foundational, algorithmic, and extreme-scale mathematical challenges. Currently, approximately two- thirds of the funding supports DOE national laboratory researchers and one-third supports academic and industry researchers. In addition, ASCR’s SciDAC program supports development of math- ematical methodologies, algorithms, libraries, and software for achieving portability and interoperability to accelerate the use of high-performance computing for DOE science. National Institutes of Health Several of the 27 institutes and centers (ICs) that comprise the NIH support the development of methodology and novel applications in math- ematics, computing, and statistics applied to biological, biomedical, and behavioral research. Institutes that have shown particular interest in these areas are the National Institute of General Medical Sciences (NIGMS), the National Institute of Biomedical Imaging and Biomedical Engineering (NIBIB), the National Cancer Institute (NCI), and the National Human G ­ enome Research Institute (NHGRI). NIGMS, in partnership with NSF/ DMS, administers a Math-Biology Initiative that helps to make opportuni- ties available to a broad range of the mathematical sciences community. The NIBIB focuses on applications of importance to imaging technologies and bio­ ngineering. Only the extramural funding from NIGMS and NIBIB e is captured in Table C-1. Several NIH institutes, such as NCI, conduct significant amounts of in-house research in biostatistics, scientific computing, and computational biology, among other areas. These intramural programs are not captured in Table C-1. In addition, some other parts of the Department of Health and Human Services (NIH’s parent organization), such as the Agency for Healthcare Research and Quality, support some extramural research in the mathematical sciences. BASIC DATA ABOUT THE MATHEMATICAL SCIENCES POSTSECONDARY PIPELINE The number of undergraduate degrees granted by mathematics and statis­ tics departments in the United States annually over the period

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170 APPENDIX C 2006-2010 has been roughly 24,000.6 In 2010, 43 percent of these degrees were awarded to women and nearly half were from departments granting a baccalaureate degree only. Master’s degrees in the mathematical sciences are similarly tracked. Between 2006 and 2010, more than 4,000 such degrees were granted, with approximately 40 percent going to females.7 Doctoral degrees in mathemat- ics are on the rise, reaching 1,653 new Ph.D.s for 2010-2011. Figure C-1 gives a breakdown of the 2010-2011 degrees by department type.8 Fig- ure C-2 shows the trends in annual data by department type for the 2001- 2002 to 2010-2011 academic years. Of the total doctorate degrees granted in 2010-2011, 49 percent of the recipients were U.S. citizens and 32 percent of the recipients were female. Figure C-3 gives some information about em- ployment for new Ph.D. recipients from academic year 2010-2011. While most new Ph.D.s enter academic positions (including postdoctoral study at universities and research institutes), some 19 percent reported employment with government, business, or industry. Finally, Figures C-4, C-5, and C-6 present basic data about the ethnic composition of mathematical science students at various postsecondary levels. 6  American Mathematical Society, 2010, Annual Survey of the Mathematical Sciences (AMS- ASA-IMS-MAA-SIAM); Supplementary Tables UD.1 and UD.2. Available at http://www.ams. org/profession/data/annual-survey/2010Survey-DepartmentalProfile-Supp-TableUD1-2.pdf . 7  Ibid., Section on Master’s Degrees Awarded. Supplementary Tables MD.1 and MD.2. 8  Richard Cleary, James W. Maxwell, and Colleen Rose, 2012, Report on the 2010-2011 new doctoral recipients. Notices of the AMS, 58(8):1083-1093. Available at http://www.ams. org/notices/201208/rtx120801083p.pdf.

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APPENDIX C 171 FIGURE C-1 Number and percentage of doctoral degrees awarded by depart- ment grouping in the mathematical sciences (1,653 total; between July 1, 2010, Figure C-1 and June 30, 2011). Group I is composed of departments with scores in the 3.00-5.00 range according to rankings from the National Research Council. Group I Bitmapped Public and Group I Private are Group I departments at public institutions and pri- vate institutions, respectively. Group II is composed of 56 departments with scores in the 2.00-2.99 range. Group III contains the remaining U.S. departments reporting a doctoral program, including a number of departments not included in the 1995 ranking of program faculty. Group IV contains U.S. departments (or programs) of statistics, biostatistics, and biometrics reporting a doctoral program. Group Va con- sists of departments of applied mathematics/applied science. SOURCE: R. Cleary, J.W. Maxwell, and C. Rose, 2012, Report on the 2010-2011 new doctoral recipi- ents. Notices of the AMS 59(8):1083-1093, Figure A.1. Available at http://www. ams.org/notices/201208/rtx20801083p.pdf.

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172 APPENDIX C Group I (Pu) Group I (Pr) Group II Group III Group Va Group VI* 500 450 400 350 300 250 200 150 100 50 0 2001-02 2002-03 2003-04 2004-05 2005-06 2006-07 2007-08 2008-09 2009-10 2010-11 * The increase shown in Group VI is due in part to the increase in response rate FIGURE C-2  Number and percentage of doctoral degrees awarded by department grouping in the mathematical sciences. The increase shown in Group IV is due in part to the increase in response rate. SOURCE: R. Cleary, J.W. Maxwell, and C. Rose, 2012, Report on the 2010-2011 new doctoral recipients. Notices of the AMS 59(8):1083-1093, Figure A.2. Available at http://www.ams.org/profession/ C-2 New data/annual-survey/2011Survey-NewDoctorates-Report.pdf. Employeed in Postdoctoral Positions Employeed in Other Positions Groups I-III & Va 255 105 Group IV 40 33 M, B, & 2-Yr 15 227 Other Academic 73 67 Research Institutes 33 27 Government & Business/Industry 27 289 Non-U.S. Employer 142 81 0 50 100 150 200 250 300 350 FIGURE C-3  Number and percentage of doctoral degrees awarded by department grouping in the mathematical sciences (1,653 total; between July 1, 2010, and June 30, 2011). SOURCE: R. Cleary, J.W. Maxwell, and C. Rose, 2012, Report on the Figure C-3 2010-2011 New Doctoral Recipients. Notices of the AMS 59(8):1083-1093, Figure E.5. Available at http://www.ams.org/notices/201208/rtx120801083p.pdf.

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APPENDIX C 173 American Indian/ Non-resident alien Alaska NaƟve 6% 1% Asian/Pacific Islander 10% Hispanic 6% Black 5% White 72% FIGURE C-4  Bachelor’s degrees in mathematics and statistics conferred by degree- granting institutions, by race/ethnicity: 2010-2011. SOURCE: National Center for Education Statistics (NCES). Available at http://nces.ed.gov/programs/digest/ d12/ tables/dt12_301.asp, Table 300. Figure C-4 White Non-resident alien 45% 38% Two or more races 1% Black American Indian/ Asian/Pacific 3% Hispanic Alaska NaƟve Islander 4% 0% 9% FIGURE C-5  Master’s degrees in mathematics and statistics conferred by degree- granting institutions, by race/ethnicity, 2010-2011, SOURCE: Available at http:// Figure C-5 nces.ed.gov/programs/digest/d12/tables/dt12_304.asp, Table 304.

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174 APPENDIX C White Non-resident 43% alien 47% Two or more races Black 0% 2% American Indian/ Alaska NaƟve 0% Hispanic Asian/Pacific 2% Islander 6% FIGURE C-6  Doctorates in mathematics and statistics conferred by degree-granting institutions, by race/ethnicity, 2010-2011. SOURCE: Available at http://nces.ed.gov/ Figure C-6 programs/digest/d12/tables/dt12_307.asp,Table 307.