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Reports Assess U.S. Standing in Mathematics

Within the past year, two major reports have been ing the use of science in service to society, and issued that attempt to assess the international achieving excellence in education. standing of U.S. mathematical sciences research. While the two reports have many similarities, The reports are part of an effort by the federal gov- they are strikingly different in tone and outlook. ernment to plan more coherently and more strate- In fact, the NSF report does not even mention the gically its support of scientific research. NAS report even though the latter had been out for The first report, “International Benchmarking of six months by the time the NSF report was com- U.S. Mathematics Research”, was issued in October pleted. Bland and dry, as most Academy publica- 1997 by the Committee on Science, Engineering, tions are, the NAS report may have suffered from and Public Policy (COSEPUP) of the National Acad- the fact that the panel producing it was instructed emy of Sciences (NAS). It comes in response to the not to make any recommendations. The NSF panel, 1993 COSEPUP report, “Science, Technology, and by contrast, was charged with making specific rec- the Federal Government: National Goals for a New ommendations to the Foundation. Consequently, Era”, which outlined a methodology for making de- the NSF report is more opinionated and forceful, as well as longer and more detailed. cisions about federal spending on research. The Both reports conclude that the U.S. is the world first step in the methodology is to assess where leader in mathematical sciences research. Among the U.S. stands in comparison to its international the evidence offered for this conclusion is the fact peers in various scientific areas. Mathematics was that U.S.-based mathematicians write about 40 the first field for which such a comparison was percent of all research articles in the subject and done; an NAS benchmarking report of materials claim a healthy share of international honors, such science was released in April. as prizes and invitations to speak at major meet- The second mathematics report, issued by the ings like the International Congress of Math- National Science Foundation (NSF), is called “Re- ematicians. Despite these signs of success, the port of the Senior Assessment Panel of the In- NSF report says that mathematicians in the U.S. suf- ternational Assessment of the U.S. Mathematical fer from a sense of “low morale” not found among Sciences”. The NSF purposely chose as panelists in- their counterparts in Western Europe and the Pa- dividuals who had not recently received funding cific Rim. When it comes to promoting the use of from the Foundation. Issued in March 1998, the re- mathematics outside the field, the U.S. is not doing port was produced in compliance with the Gov- much better than its peers: The NSF report states ernment Performance and Results Act (GPRA), bluntly, “Communication between mathematical which requires federal agencies to set strategic scientists and other scientists is poor the world goals and evaluate their progress toward those over.” In mathematics education, the reports say goals. The NSF’s goals call for upholding the U.S. that the U.S. is clearly the leader at the Ph.D. level, position of world leadership in research, promot- attracting talented students from all over the world.

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Both reports say that mathematics in the U.S. is Report of the Senior Assessment Panel of the International strong, but warn that this strength is “fragile”. Assessment of the U.S. Mathematical Sciences, National Science One of the reasons given for this fragility is the Foundation, March 1998. decline in federal support for mathematics; iron- Available on the World Wide Web at: http://www. ically, the NAS report counts good federal sup- nsf.gov/cgi-bin/getpub?nsf9895/ and http:// port in the past as one of the factors that has www.nsf.gov/pubs/1998/nsf9895/nsf9895.htm. made mathematics in the U.S. so strong. One of the Available upon request from: Division of Mathematical Sci- main themes of the NSF report is that federal sup- ences, National Science Foundation, Room 1025, 4201 Wilson port for graduate students and young researchers Boulevard, Arlington, VA 22230; telephone 703-306-1870. in mathematics is far below that for their coun- terparts in the physical and biological sciences. The Panel Members emphasis on federal support is secondary in the Lt. General William E. Odom (retired) (chair) NAS report, which says that the predominant fac- Hudson Institute, USA tor contributing to the strength of U.S. mathematics has been the support of private and public uni- E. F. Infante (convener of panel) versities. In fact, in its closing sentences the NAS Vanderbilt University, USA report states: “The most important safeguard of U.S. preeminence in mathematical research—and Huzihiro Araki in all the sciences—is the flourishing of both pri- Science University of Tokyo, Japan vate and state research universities.” The NSF report suggests that the low level of fed- Tanya S. Beder eral support for young people in mathematics has Capital Market Risk Advisors, USA induced talented undergraduates to enter other fields, leading to an overall decline in recent years Marsha J. Berger in enrollments in U.S. Ph.D. programs in math- Courant Institute of Mathematical Sciences, USA ematics. The NAS report presents data showing that U.S. mathematics Ph.D.s have lower median salaries Lennart A. E. Carleson than those in other sciences and engineering. Also Royal Institute of Technology, Sweden contributing to the lack of appeal of mathematics is the anemic academic job market, coupled with Albert M. Erisman the perception that a career in academia is the Boeing Company, USA only path open to a mathematics Ph.D. According to the NSF report, this is a misperception: “With a Mikhael Gromov reorientation of curriculum and of employment ex- Institut des Hautes Études Scientifiques, France pectations, possibilities for a career outside acad- emia are very bright for mathematically talented Darryl D. Holm and well-trained individuals.” Los Alamos National Laboratory, USA The NSF report hammers away at the notion that mathematics must be open to taking on math- Shirley Strum Kenny ematical problems that arise in other fields of sci- State University of New York, Stony Brook, USA ence, in industry, and in society. Academic math- ematicians come in for some criticism for being Maria Klawe “insufficiently connected” to users of mathemat- University of British Columbia, Canada ics, though the division of universities into de- partments, the rigidity of funding agencies, and Hanspeter Kraft lack of support from industry also take some of University of Basel, Switzerland the blame. In its recommendations the report states that the NSF’s objective should be to build an aca- Donald W. Marquardt demic mathematical sciences community “that is Donald W. Marquardt and Associates, USA both intellectually distinguished and relevant to so- ciety,” noting that the inclusion of societal rele- Sir H. Peter F. Swinnerton-Dyer vance is an “important shift in emphasis” for the Isaac Newton Institute, United Kingdom Foundation. More specifically, the report recom- mends that the NSF “promote interactions between George Whitesides university-based mathematical scientists and users Harvard University, USA of mathematics in industry, government, and uni- versities.” The report makes it clear that the NSF has the clout to influence mathematics in the di- rections recommended. After presenting a graph that shows that the NSF holds the purse strings on

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International Benchmarking of U.S. Mathematical Research, about 60 percent of all federal funds for math- Committee on Science, Engineering, and Public Policy, Na- ematics research (with the remainder scattered tional Academy of Sciences, 1997. among six other agencies with varying missions), Available on the World Wide Web at: http:// the report notes that the Foundation has “high www2.nas.edu/cosepup/. leverage in enforcing change.” Order from: National Academy Press, 2101 Constitution Av- Some of the most intriguing material in the NSF enue, NW, Washington, DC 20418; telephone 1-800-624-6242 report appears in the appendices. One is a piece or 202-224-3313 (in the Washington metropolitan area). called “Possible Trends in the Coming Decades”, by Mikhael Gromov; it is reproduced in the “Forum” Panel Members column of this issue of the Notices. Another ap- pendix contains an assessment of U.S. standing in Peter D. Lax (chair) various subfields of mathematics. For example, Courant Institute of Mathematical Sciences, USA the assessment of algebraic geometry and number theory states that leadership in algebraic geome- Sir Michael F. Atiyah try is shared by the U.S., Japan, and Western Eu- University of Cambridge, United Kingdom rope, “with the United States having the most ac- tive researchers.” It comments that in the U.S., Spencer J. Bloch computational algebraic geometry “lacks depth, University of Chicago, USA and leadership is held by the Europeans.” It also notes that number theory is dominated by several Joseph B. Keller “grand challenges,” among them the Riemann Hy- Stanford University, USA pothesis (RH). “There is renewed activity in RH,” the appendix says, “but probably not at the depth Jacques-Louis Lions needed.” There are similar evaluations of eight Collège de France other subfields: foundations, algebra and combi- natorics, topology and geometric analysis, analy- Yuri I. Manin sis, probability, applied mathematics, computa- Max-Planck-Institut für Mathematik, Germany tional mathematics, and statistics. —Allyn Jackson Rudolph A. Marcus California Institute of Technology, USA

Gary C. McDonald GM Research and Development Center, USA

Cathleen S. Morawetz Courant Institute of Mathematical Sciences, USA

Peter Sarnak Princeton University, USA

I. M. Singer Massachusetts Institute of Technology, USA

Margaret H. Wright Bell Laboratories, Lucent Technologies, USA

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