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O- Federal Support of Research The general history of federal support of scientific research has already been clearly traced in an earlier report of the National Academy of Sciences.4t For the mathematical sciences, the period since World War II is of special importance. During this postwar period, federal support of mathematical research and graduate edu- cation has grown significantly, stimulating and keeping pace with the general growth in American mathematical activity; and during this period the United States has moved into a position of world leadership in mathematical research (see Chapter 1~. LEVEL AND SOURCES OF SUPPORT The principal government-wide analysis of federal research obli- gations is contained in the National Science Foundation series, Federal Funds for Research, Development, and Other Scientific Activities.2 The figures below were obtained from Volumes IV-XV of this series. As Table 12 shows, eight agencies are currently the key federal contributors to support of research, both basic and applied, in the mathematical sciences. At this point we make a distinction between basic and applied research. For the mathematical sciences, this is not at all the dis- tinction between core mathematics and applied mathematical sci- ences. Research is basic or applied according to whether it is inner- directed or mission-oriented. Although he does not use the term "inner directed," Brooks has given a clear discussion of this idea in a 163

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164 TABLE 12 Federal Obligations for Research Sciences Level and Forms of Support in the Mathematical MILLIONS OF DOLLARS AGENCY 1960 1962 19641966 National Science Foundation 3.8 7.4 11.414.9 Army 2.7 5.5 8.38.6 Navy 6.9 16.3 26.226.5 Air Force 5.0 10.4 20.433.2 DoD-wide Agencies 6.4 14.419.2 Atomic Energy Commission 3.2 4.1 5.16.5 National Aeronautics and Space Administration 1.0 17.2 6.37.6 National Institutes of Health 0.1 0.1 2.64.3 All Others 0.9 1.6 3.34.1 TOTALS 23.6 69.0 98.0 124.9 recent article in Science.40 Research is basic, or inner-directed, when the choices made by the researcher in the course of the research are "influenced almost entirely by the conceptual structure of the sub- ject rather than by the ultimate utility of the results." As Brooks goes on to point out, it is perfectly consistent with this conception for the subject of a basic research to have utility and for the research to be funded with this in mind. Thus inner-directed research includes work in both core mathematics and applied mathematics. Examples of basic research in applied mathematics are studies in the mathe- matical theory of linguistics, dynamical systems and their astro- nomical applications, and the theory of rotating fluids for the under- standing of geophysical phenomena. The amounts shown in Table 19 are for the support of both basic and applied research. The over-all figures in reference 2 indi- cate that for 1966 the $125 million in federal obligations for mathe- matical-sciences research was almost equally split between basic and applied research; about $62.5 million went to basic research. Accord- ing to a study made by F. J. Weyl for our Panel on Level and Forms of Support, however, certain of these figures are of uncertain re- liability, so that a conservative total of $46.5 million for basic- research support in 1966 seems closer to the facts. A complete tabu- lation of the amounts obligated by various federal agencies for sup- port of basic research in the mathematical sciences is shown in

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Fecleral Support of Research 165 Table 13 along Title the basic-research percentage of total research obligations. Table 13, especially the percentage comparison with Table 12, demonstrates the striking growth of the applied-research effort in the mathematical sciences, based on the use that can now be made of mathematical modes of analysis together with modern computing equipment. When it comes to interpreting the dollar amounts in Table 13, it must be kept ire mind that they neither coincide with nor entirely include the totals allocated for mathematical research to universities. In the budgets of the military services, about 85 percent of the amount allocated to basic mathematical research is spent in universities. In the case of the other five key agencies, less is known about any further breakdown of the reported figures. Returning to Table 12, it had been our hope to extract in the first instance all "large" projects, say $500,000 or more in fiscal year 1966, and to specifically identify them, especially those which, although of predominantly mathematical nature, serve primarily research objectives in other disciplines. Next, we had hoped to break out of the residue the amounts allocated to in-house mathematical activity. It would have been our aim, anally, to show how the re TABLE 13 Basic-Research Amounts and Percentagesa 1960 1962 1964 1966 AGENCY AMT. ~AMT.% AMT. ~AMT. ~ NSF 3~8 100 7.4100 11.4 100 14.9 100 Army 2.? 81 2.647 2.9 35 2.4 28 Navy 4.8 70 4.698 6.7 26 5.9 22 Air Force 2.0 40 3.029 b.4 26 6.2 19 DOD Agencies - 0 [14.1] [98] t16.0] tea] AEC 2.8 88 3.995 4.9 96 6.3 97 NASA 1.0 100 [0.7]p4] 5.4 86 7.0 92 NIH 0.1 100 0.1100 0.8 31 2.? 51 All Others 0.3 33 0.425 1.2 36 1.6 40 TOTALS 17.0 72 22.032 38.7 40 46.5 37 :22.7]tag] [52.8] [54] ~62.~] [50] c Figures in square brackets are of uncertain reliability and therefore omitted from the unbracketed totals. The minimum in percentage of basic research shown as occurring in 1962 may be due to some artifact of the data, such as reclassification.

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166 Level and Forms of Support mainder is divided among the five major categories: core mathe- matics, physical mathematics, mathematical statistics, computer science, and the pioneering of mathematical methods in new areas, especially the biological and behavioral sciences. This has turned out to be impossible. In no agency does there exist a central focus for maintaining an overview regarding its entire commitment to mathematical-sciences research. The study made for our Panel on Level and Forms of Support estimates that in fiscal year 1964 approximately $45 million were allocated by the federal government to mathematical-sciences re- search at universities, $16 million going to contract research centers and $29 million for academic research. The $16 million involves such organizations as Argonne National Laboratory, Lincoln Lab- oratory, Lawrence Radiation Laboratory, and Los Alamos Scientific Laboratory. The $29 million certainly includes almost the entire $11.4 million of the National Science Foundation. Adding also the approximately 85 percent of the $15.1 million in the Army, Navy, and Air Force budgets for basic mathematical-sciences research ($12.4 million), there is a remainder of $5 million, which must have been contributed by the AEC (perhaps about $3 million), NASA, and NIH (approximately $1 million each). Comparable amounts in fiscal year 1966 might be roughly estimated as not less than 10 percent and not more than 15 percent higher, suggesting a total current allo- cation to academic research in the mathematical sciences in the neighborhood of $35 million. A slightly higher growth rate- approximately 18 percent has held in recent years for PhD produc- tion (see The Doctorate in the Mathematical Sciences, page 138) and for the closely correlated support of core research areas (see The Core, page 197~. Undoubtedly, substantial apportionments for research in the mathematical sciences are made by the key agencies, other than the AEC and the NSF (which have no in-house laboratories), to intra- mural research activities. In the Army alone, this accounts for about $5 million of its total $8.6 million spent for mathematical- sciences research in fiscal year 1966. Of this amount only $1 million is under the central management of the headquarters staff of the Army Research Once in the Office of the Director of Research and Development. A comparable amount is probably distributed in the laboratories of the Navy, and somewhat less in the Air Force. Once the contributions of NIH and NASA have been added to these items and combined with the mathematical research funds obligated by

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Federal Support of Research 167 the remaining agencies, something like a total of $15 million may be accounted for. THE ROLE OF THE MISSION-ORIENTED AGENCIES The mission-oriented agencies concerned with the mathematical sciences are the agencies listed in Table 12, excluding the National Science Foundation. In this connection, two points need emphasis. First, although it is not ordinarily classed as a mission-oriented agency, the National Science Foundation itself has a very definite mission in the promotion and support of basic research and edu- cation in the sciences (see reference 41, page 46~. Second, though they are not as yet extensively concerned with the mathematical sciences, mission-oriented agencies other than those listed in Table 12 will likely become so in the near future. This applies especially to agencies whose missions lie in urban development, environmental control, transportation, education, and related concerns. A great deal of credit for the rise of the United States, during the 1950's, to a position of world pre-eminence in mathematical research is due to the vision and policies of mission-oriented agencies within the federal government, and above all those of the Depart- ment of Defense. In fact, in the critical period immediately follow- ing World War II it was a newly formed mission-oriented agency- the Once of Naval Research that pioneered in developing con- tract machinery appropriate for federal support of scientific re- search in universities. This, together with the grant mechanisms being evolved at about the same time by the National Institutes of Health, has led to the extremely fruitful project-grant mode of federal research support (see reference 41, Chapter III). From the outset, ONR had a clear conception of the value of supporting basic research ("free rather than directed") and "maintaining contact with the most imaginative people in science" (reference 41, page 37~. A mission-oriented agency supporting research in the mathe- matical sciences as part of its research and development program will do so for the sake of the following major objectives: 1. The development and use of mathematical techniques, as well as the training of mathematical scientists in the fields, at the level, and in the numbers that its mission requires

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168 Level and Forms of Support Decisions of sponsorship therefore reflect an interest in particular subject-matter fields. Of course, such expectations of mission-related usefulness cannot be put on a project-by-project basis but are attached to a coherent program effort over a reasonable time. Thus, $300,000 knowledgeably invested for five to seven years in research on nonlinear ordinary differential equations will make a difference in the designing of guidance and control servos of more versatile performance. How much difference it will make, how much more difference might be made by each additional 5100,000 so invested, or whether the entire amount would do better in some other area depends on such factors as the field, the people, and the problems. To raise and, no matter how imperfectly, to answer such questions is properly the concern of the research administrator. 2. Marshaling, when and as needed, the contributions that can be made to its mission by the sum total of the mathematical sciences, both as a body of accumulated knowledge and as a community of concerned and experienced scholars Assuring the sponsor of prompt alerting and cogent advice on matters of importance to his affairs has long been recognized as an important part of research support, especially in the mathematical sciences, where the areas to be covered are generally extensive, while the manpower that can be allocated in-house is limited. 3. The contributions that the agency can make by opening up the most challenging problems that it faces for work by the research community Manifold patterns of communication are being utilized for bring- ing the open scientific problems of research-sponsoring agencies before the mathematical-sciences community. Joint meetings, prob- lem workshops, and special program activities aimed at "coupling" are all being tried, in part to get the word out and in part to create opportunities for outstanding mathematicians to influence, when and as they may choose, the extension of mathematical modes of thinking in areas of science and technology currently of national concern. We note that support of basic research by agencies with specific applied missions results in multiple sources of support, a condition

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Federal Support of Research 169 that has proved beneficial for the advance of all sciences and in particular for the mathematical ones. It is not always realized how large a fraction of federal support of the mathematical sciences in recent years has come from the mission-oriented agencies. Table 13 shows that during the period 1960 to 1966 approximately 70 percent of the federal support of basic mathematical research has been contributed by the mission- oriented agencies, that is, by the listed agencies other than the National Science Foundation. The amounts and percentages for specific years are given in Table 14. TABLE 14 Amount and Percentage of Federal Support of Basic Mathematical Research Contributed by Missior~-Oriented Agencies 1960 1962 1964 1966 Amount ($ millions) 13.2 14.6 27.3 31.6 Percentage 78 66 71 68 The mission-oriented agencies have always had a mandate (clari- fied in the President's Executive Order 10521 of March 17, 1954, as noted in reference 41, page 49) to engage in support of basic mathe- matical research in areas closely related to their missions; and, in- deed, Table 14 indicates that this support has grown at an average annual rate of approximately 15 percent during the period 1960- 1966. During the same period, however, a computation using figures from Tables 12 and 13 shows that support of applied mathematical research by the mission-oriented agencies has grown at an average annual rate of over 50 percent. Undoubtedly, work involving expen- sive computer systems accounts for a large fraction of this phe- nomenal growth, but this is still impressive documentation of the rapidly increasing use of the mathematical sciences by these mis . . - slon-or~entec . agencies. Provided it is understood that basic research in the mathematical sciences includes basic research in computer science, which involves expensive equipment, we feel that it makes sense to recommend that future support of such basic research by the mission-oriented agencies grow in proportion to these agencies' utilization of the knowledge and techniques of the mathematical sciences. We also find it appropriate that these agencies, who are themselves con- sumers of mathematically trained personnel and who benefit from

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170 Level and Forms of Support the high level of science and technology that depends on advanced mathematical training, should continue to participate in the sup- port of this training. Furthermore, we believe that these agencies can continue to find value in contact with first-rate academic mathematical scientists, and that, conversely, these scientists can receive valuable intellectual stimulus as well as financial support from mission-oriented agencies. In particular, the mission-oriented agencies would profit from supporting more postdoctoral research associates. Some further observations and recommendations in this general direction are made in the discussion of support by industrial and government laboratories in Chapter 13. Finally, we emphasize once more that in the future comparable recommendations may be expected to apply not only to the mission-oriented agencies of Table 12 but also to federal agencies concerned with such matters as urban development, education, environmental pollution, and natural resources. FORMS OF SUPPORT This Committee is aware that authoritative voices have proposed very radical changes in the whole federal system for supporting academic research and university education, abandoning the present forms of support in favor of direct federal subsidies to universities. COSRIMS felt that a discussion of this problem lay outside its com- petence. The fact that we do not mention this possibility in our report should not be taken as evidence that we either oppose or support it. It is self-evident that any thorough discussion of such a radical change of the present system would have to take account of the problems of the mathematical sciences. Currently federal support of basic mathematical-science research in institutions of higher learning, estimated above at about $35 million in fiscal 1966, assumes a variety of forms. The principal forms have been individual or group projects, conferences, depart- mental or block grants, and institutional grants (especially the NSF Science Development Program). The Project System Project support has been by far the largest single item, and the one that we consider to be most important, for research advance.

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Federal Support of Research 171 According to estimates computed for us by the CBMS Survey Com- mittee directly from the grant lists of funding agencies, project sup- port of basic mathematical research in universities accounted for something over $20 million in fiscal year 1966. This was primarily for "inner-directed" projects involving only occasional, and usually very minor, allowances for computers and other equipment. Responses to the CBMS Graduate Questionnaire (reference 16, Volume II) indicate that grants of this sort provided support for the summer research activities of over 900 senior investigators (associate and full professors) and over 500 younger ones (assistant professors, instructors, and research associates), as well as academic-year sup- port (usually only partial) for about 240 senior investigators and over 1 no Nicer ones. In addition. they provided stipends for approximately 750 graduate research assistants, proportionately more of the graduate students in applied mathematics, computer science, and statistics being supported in this way. (Proportionately more in core mathematics are supported as teaching assistants.) Also included were small but important allowances for travel and for publication costs incidental to the projects supported. The project system of research support is thoroughly discussed and evaluated in a 1964 report by the Committee on Science and Public Policy of the National Academy of Sciences (reference 41, Chapter VII) . That report recommends (page 77) that for the foreseeable future, the major emphasis in the federal government's support of basic research in science in institutions of higher learning should continue to be given to the project system. We strongly endorse this recommendation. Mathematical research of high quality has resulted from the project system, especially through its use of panels of peers in assessing mathematical scien- tists and their research. This system has also stimulated the greatest expansion of graduate mathematical education at those institutions best qualified to give it. A point that deserves emphasis is the relative inexpensiveness of "project support per tenure research grantee" for the mathematical sciences as compared with the physical sciences. The primary Sensors for this is, of course, easily understood: project grants in the mathe- matical sciences, even as recently as 1966, involved little in the way of computer or other equipment costs, whereas equipment costs for the physical sciences in the recent years have ranged from relatively modest, as in the case of chemistry and solid-state physics, to ex

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172 Liege! and Forms of Sup/?ort tremely high, as in the case of elementary-particle physics and as- tronomy. It for the mathematical sciences in 1966 we take the total of project support, slightly over 520 million, and divide this by the number of tenure researchers on project grants, approximately 920, we obtain a little over $22,000 as the project support per tenure re- search investigator (TRI). ___1 _ ~. r ~- (It must be understood, of course, that only a traction of this amount actually pays for the services of the TR} himself typically approximately $5,000, primarily for support of summer research activities. The rest goes for such things as sup- port of junior researchers, research associates, and research assist- ants; for travel and publication costs; for clerical materials and services; and above all-actually-for indirect costs or overhead.) For comparison, Physics: Survey and Outlook,42 pages 103 and 108, concludes that for physics in 1963 "annual research support per active faculty investigator" could be conservatively estimated at $60,000 and conservatively projected to 1966 at approximately $67,000. Actually, the discrepancy between the physics and mathe- matical-sciences figures may be much greater than this comparison of S67,000 with $22,000 suggests, since "active faculty investigators" in the physics computation appears to have included junior as well as senior researchers, and perhaps even those not on grants at all. We checked the above mathematical-sciences figure of $22,000 on a university-by-university basis for some 15 universities. While there was a fair spread in the results, the average was very close to this $22,000 figure, and the spread was considerably less than where both junior researchers and tenure researchers were taken into account. We therefore suggest that "project support per tenure research investigator" is a reasonably stable figure to use in projecting grant support on a demographic basis. For the future, however, direct costs for equipment primarily computer costs) promise to be distinctly higher in mathem~tirnl miens rPcP~rrh At the cams `;~^ :~:~_. ~. ~^^-- EVE ~^ 044 ~ ~11 ~.~CI 1 11L 1 ~ I I 1 1 ~ ~ ~ ~ ~ ~ ~ ~! ~ costs for salaries and stipends promise to be higher too, as will be costs for research assistants, if the recommendations below concern- ing numbers of research assistants are followed. As a result, we be- lieve that for the future the $22,000 average figure will prove to be unrealistically low and that a figure approaching $30,000 will more nearly answer to the increased needs. We recognize that there have been objectionable features in the # For computer science itself. the corresponding average cost is estimated to be near $60,000 per TR! per year (see Computer Science, page 205).

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Federal Support of Research 173 operation of the project system. Its advisory panels have not always been sufficiently responsive to the newer areas of research, and the system has sometimes failed to meet effectively the needs of young investigators at less-distinguished universities and at liberal arts col- leges. To help offset these disadvantages we suggest that evaluating panels should include representatives of new areas of mathematical research (in both core mathematics and applied fields), that younger investigators not at leading universities should be included in the projects of senior people at such universities, and that the projects should provide for travel funds adequate to maintain contact be- tween the senior mathematicians and such younger men. We also have some specific new proposals to make regarding the support of young investigators (see the discussion of postdoctoral teaching fel- lowships in the section on Postdoctoral Research Education, page 182~. Overhead, a sizable item in project budgets, amounted in fiscal 1966 to perhaps 30 percent of gross direct costs. Recent changes in accounting procedures have, however, already begun to increase this proportion and appear certain to increase it to over 40 percent within the next few years. Actually, the effect of new cost-sharing requirements has been a shift in the allocation of the overhead burden from the experimental to the theoretical sciences, where the primary budgetary items are salaries. Unless compensating upward adjustments are made in the total funds available to these theoretical fields, the effect will be an increasingly serious net loss to research support. This effect is already beginning to be felt in the mathe . matlcal sciences. Departmental Grants Here we shall consider department-level grants, conceived of as a more or less indefinitely renewable mode of sustaining research ac- tivities within a department. (In the succeeding subsection we shall consider developmental grants, including grants at the department level, intended to initiate a development but not to sustain it in- definitely.) There are advantages of simplicity and flexibility in department- level grants generally, as a supplement or partial alternative to project grants. Awhile agreeing that departmental grants can be given only after a department has attained a minimal level of excellence, we recognize that such grants may be particularly appropriate for

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174 Level and Forms of Support small departments, provided there is substantial agreement among the department faculty that this type of support is desirable, and we recommend that this type of grant be tried on an experimental basis. In order to have the desired flexibility, these departmental grants should approximate as closely as possible, in character, the relatively unrestricted grants-in-aid that have been made by private foundations. Such grants should run for about three years and should include some support of younger mathematicians, travel, graduate research assistants, and publication costs. The same prin- ciple of departmental grants should apply to developing and sus- taining the efforts of strong or excellent departments if they wish to extend their activities to include new areas of research. For ex- ample, if a department of mathematics is already excellent in pure mathematics and in applied mathematics in the physical sciences, a grant in applied mathematics for the social sciences might be made available. Developmental Block and Area Grants Over recent years, various types of developmental block and area grants have been made. The most important federal program in this direction has been the National Science Foundation Science Development Program. Announced in the spring of 1964, this pro- gram had made 17 awards to universities by the end of fiscal 1966. Of these, 10 involved the mathematical sciences directly though not in uniform ways or to a uniform extent. Individual grants, made for three-year periods, tended to average fairly close to $4 million, but the mathematical-science percentages of these grants varied all the way from 4.3 percent to 31 percent. In total, the mathematical- science parts of these 10 grants amounted to some $4.7 million, the major portion of it awarded within fiscal 1966. In the fall of 1966s the Science Development Program was broadened to include, in addition to the original University Science Development Program, a Departmental Science Development Program at the graduate level and a College Science Improvement Program for primarily under- graduate institutions. Our Panel on New Centers has made a special study and evalu- ation of the NSF university development grants affecting the mathe- matical sciences. Queries by the Panel to recipient institutions con- firm that the major use to which the mathematical portions of these grants have been put, or are planned to be put, is the procurement

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Federal Support of Research 175 of high-quality research faculty. Other uses of the grants include library improvement, computer installations, fellowships, salary increases, and the provision or improvement of administrative and clerical services. Among recipients of the university development grants there are institutions in which a serious effort in coordinating the develop- ment of the mathematical sciences with that of other scientific dis- ciplines has been successfully fostered by the grant. Indeed, we feel that such mathematical sciences as computer science and statistics are by their very nature especially well adapted to interdisciplinary grants. On the other hand, in the cases of two institutions, the awarding of strongly interdisciplinary grants led to considerable friction between the mathematics department and the other depart- ments involved, and the outcome was on the whole detrimental to the development of mathematics in these institutions. For this reason especially, we welcome the broadening of the NSF Science Development Program to include a departmental program and feel that the added flexibility thus introduced will prove particularly valuable to departments of mathematics. Concurring with our Panel on New Centers, we do not wish to take a stand relative to geographical considerations in the estab- lishment or development of new centers. We feel that geographical considerations transcend the mathematical sciences as such and are concerned with more general questions of policy that will not be resolved by any simple formula. We do, however, wish to identify and comment on three types of possibilities relating to geographical . considerations. One of these possibilities is the development of new centers in close proximity to existing major centers. Assuming the proper departmental and administrative conditions for the development of an important new center, a university near one or more existing major centers should find the recruitment of the proper type of new faculty relatively easy. This is particularly true of junior faculty members who want to be in frequent contact with important con- tributors to research and who want to be able to attend seminars and colloquia at the nearby major centers. The payoff in positive influence in the geographical area of the new center is correspond- ingly less, however, since the area already has top-level mathematical activity. Second, there is the possibility of developing new centers in large metropolitan areas without existing major centers. It seems self

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176 revel and Forms of Support evident that the longer-range scientific effort of the country will be enhanced by the deliberate development of important scientific and mathematical centers in those larger metropolitan areas that have not developed their own major educational centers. Here, assum- ing the proper departmental and administrative conditions, it should be possible in a somewhat longer period of time to develop important new mathematical centers that, in turn, should tend to improve the education and scientific activity in the given metro- politan area. The payoff should be greater but the task harder than in areas close to existing centers. A third possibility is the creation of new centers in educationally underdeveloped larger geographical areas. The problem of creating major new centers in such areas is greatly complicated by the gen- eral educational level and the apparent relative unattractiveness of such areas for top-level younger mathematicians. Such consider- ations extend not only to schools for the children of mathematicians but to the university and graduate-level recruitment of talented students. Whereas the difficulties of major improvement are the greatest, the payoff for success is the greatest in important side effects on the whole educational process in a large area. It seems likely that support for the development of several nearby centers in a given geographical area may be an effective way to accelerate the desired growth process and make recruiting of talented younger mathematicians easier. Advantage should be taken of improved socio-economic conditions when these are present. The NSF Science Development Program has sometimes been de- scribed as aimed at creating "new centers of excellence." As far as departments of mathematics are concerned, this program has in practice aimed mainly at raising them to the "strong" level, rather than the "distinguished" one, in the rating of Cartter's study,32 page 66. The nine departments classified by Cartter as distinguished are responsible for the education of a disproportionately large num- ber of American research mathematicians (see Appendix E, Table E-3), and it is certainly in the national interest to increase the num- ber of such departments. We caution, however, against the idea that money in itself is sufficient to create such new centers of excellence. There are two striking examples of universally recognized, excellent departments of mathematics that could not have been created except for massive infusion of federal funds. These are the Mathematics Department at Stanford University and the Courant Institute at New York University. In both cases, however, there were unusual

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Federal Support of Research 177 circumstances; a strong nucleus of first-rate mathematicians was already attached to these institutions at the very beginning of their activities. It does not seem likely that similar opportunities, which in these instances resulted from political conditions in Europe in the 1930's, will be repeated in the near future. TIME AND EFFORT REPORTING Prominent members of the mathematics community have expressed strong concern to us arid to the Division of Mathematical Sciences of the National Research Council about the unreasonableness and the dangers of recent requirements of faculty "time and effort re- portirlg" in connection with university cost-sharing on project grants. We realize that this is a matter affecting the entire scientific community and not just mathematicians; however, research in the mathematical sciences differs, in its independence of place and tools, from research in other sciences. We feel that a statement from us may be useful both to federal agencies and to university administra tions. If a university is to share salary costs as its required contribution to a project, it certainly has an obligation to provide evidence that it has actually contributed its share. It must, however, take care that it does this in a way that does not corrode the traditional re- lationship between the professor and the university. Mathematical research (in common with research in such fields as theoretical physics) is not tied to a laboratory, a library, or an office. A mathematical scientist, once immersed in a problem, finds himself thinking about it at all sorts of odd moments; the duration and internality of his research work cannot be measured quantita- tively. Neither he nor, indeed, any professor can distinguish pre- cisely between the research and educational aspects of, for example, a conference with a graduate student. Consequently, a report in # Since this section was written, the Bureau of the Budget has, in response to the opposition of virtually all universities and many federal administrators as well, dropped most of its time and effort reporting requirements for university pro- fessorial staff See "~{Tort Reporting: Government Drops Much-Criticized Paper- work," Science, 160, 1323 (June 21, 1968) i. We feel, however, that the present clear statement of the mathematical community's position on the matter may still be of value, as a cautionary reminder of the issues of integrity and univer- sity-professor relations involved.

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178 [eves and Forms of support definite quantitative terms of a scientist's allocation of his time to various activities over a short period (a month or a quarter) is im- possible to give honestly and meaningfully; this impossibility is particularly acute for a mathematical scientist. To impose a require- ment that is impossible of honest fulfillment is to undermine the u-ac~ona~ anct essential relation of mutual trust and good faith between the scientist and his university. An acceptable arrangement must recognize that in many univer- sities a professor's salary is not paid exclusively for his teaching but in large part for his research on problems of his own choosing. Furthermore, no sharp line can be drawn between the part of this research that is performed with outside support and the part that ~ ~ . ~ ~ . Is performed as part of the professor's general obligation to the university. We therefore urge that federal fiscal offices and university busi- ness officers work with the academic research community to develop accounting requirements, appropriate to each individual university and discipline, that will provide proper information in a way that will preserve the integrity of the scientific community. We also note the following resolution passed by the Council of the American Mathematical Society meeting in Toronto on August 29, 1967: The Council of the American Mathematical Society urges responsible uni- versity officers to take immediate action to have Time and Effort Reports and similar documents pertaining to faculty members' time eliminated, be- cause it considers that such documents are incompatible with academic life and work. The Council reiterates the traditional view that teaching and research are inseparable, and that accounting procedures in universities must take account of their unitary character.