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3 FUNDING OPPORTUNITIES Discussion under this topic encompasses how to motivate faculty to apply for grants, both as individuals and through cooperative efforts; some extraordinary sources of grants, including equipment andfacilities grants; and how to enhance cross-disciplinary collaboration and research. LOVE S LAB ORS WON: NONCONVENTIONAL FUNDING FOR THE MATHEMATICAL SCIENCES James Glimm (Organizer), State University of New York, Stony Brook OUTSIDE FUNDING Daniel Goren~tein, Rutgers University DEVEEOPMENT GRANTS Calvin C. Moore, University of California 25

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FUNDING OPPORTUNITIES . LOVE S LABORS WON: NONCONVENTIONAL FUNDING FOR THE MATHEMATICAL SCIENCES James Glimm State University of New York, Stony Brook "Love's Labors Won" was chosen as the title for this presentation to remind you that this is not a discussion of how to apply for a grant. It is really a discussion of how to win a grant. We assume that you are familiar with the process for obtaining support from the National Science Foundation. Here we are considering the complement of the National Science Foundation/Division of Mathematical Sciences. The winning of a grant begins, of course, with the submission of a proposal. So we will consider the ingredients of a good proposal. First, a good proposal should contain quality science. I will not attempt to advise you on that issue. Second, the proposed project should have realistic goals and potential applications. The list of goals should include objectives that can be achieved in one to three years. Longer-range goals may also be included. A third ingredient of a good proposal is political support. For example, there may be a technology transfer component to the proposal. In this case, political support means that one has identified a user group and the proposal contains a mechanism by which the user may interact with the new science as it is created. That support could be expressed in the form of letters from the potential users. Stronger support consists of letters from potential purchasers of the new science who pledge to contribute to the support of the effort. Finally, the requested level of funding must be realistic. This includes the proposal itself and the costs of actions that might be based on the proposal. These ingredients for a good proposal were set forth by a member of the New York State legislative staff at a symposium I attended on studies of water quality on Long Island. However, Here are some lessons there for mathematicians, also. So, how does one win a nonconventional grant? Knowledge of the program is a key ingredient. Each program has goals, people, and program officers. It is essential that a grant applicant have this information. Additionally, nonconventional grants usually require cooperation with other disciplines. Often mathematics is only a part of the project. The reputation of the proposer is also important. This is related to the quality of the science involved. Finally, successful nonconventional proposals usually have some level of cost sharing from various areas, including the university, the state, the community, and the private sector. I will close with a brief checklist of things to do in preparing for the submission of a nonconventional grant proposal. . 1. Make an inventory of your opportunities. What are the local industries? What are the technical problems of local industries? Invite the technical staff to have informal discussions with faculty and students so that you can determine the mathemati- cal aspects of their problems. Try to place a student on the staff. What are the local governmental laboratories? (Use the same approach as above.) 27

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CHAFING TO MATHEMATICAL SCIENCES DEPARTMENT OF TO 1990S What are the strong technology and science departments in your university? What kind of mathema- tics do they use? What courses do they teach? Is there a possibility of joint Ph.D. theses? What are the existing contacts from your department? What are the areas of mathematical strength in your department? What are the potential applications of these areas? Based on these strengths, can contacts be created? What are the important problems? Where does technology fit in? What mathematics is involved? 2. Identify funding programs. University Governmental (state, local, and federal) Industrial Private Begin with small-scale internal resources. Seminar Key visitors/technical conference Cross-disciplinary students 4. Look for promising problems. Establish a research program. Establish interdisciplinary collaboration. Learn the subject from the viewpoint of other disciplines. Pre-review proposals. 28

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FUNDING OPPORTUNITIES OUTSIDE FUNDING Daniel Gorenstein Rutgers University I speak in three distinct capacities: first, as a former department chair, then as a member for many years of a university committee concerned with priorities in research and graduate education, and finally as the director of the new NSF Science and Technology Center in Discrete Mathematics and Theoretical Computer Science (DIMACS). Let me say first that I have found that, given any reasonable expectation of success, mathematicians are sufficiently self-motivated to apply for individual research grants. However, especially but not exclusively, the problem is rather the preparation of an effective research proposal. As chair, I wrote up a detailed set of guidelines. I then critically read drafts of the proposals of junior faculty (and any senior faculty who asked for my opinion). On a number of occasions, I got the faculty member to give me a lecture about the proposal so that I could determine what he/she was really after. I like to think that in at least a few cases, my help made the difference between being funded or not. This job need not be limited to the chair, but could be assigned to any experienced grant-getter in the department. In my committee member role, I looked for ways of increasing faculty incentives to apply for grants. As I said, this is not so important in mathematics with respect to individual grants, but is important in other fields, especially the experimental sciences, and also in interdisciplinary or unusual types of grants. Rutgers instituted a policy of a return of a percentage of overhead to the department. This gave departments a strong interest in having their faculty seek outside funding. Other areas where the committee affected university policy on research grants included (a) the total percentage of allowable summer salary (up to 3/9 for someone having more than one grant), (b) reduced teaching for faculty with academic year support, (c) tuition remission for graduate students, and (d) reduction in university overhead rates (included as part of the university cost-sharing) in connection with unusual grants that often have programmatic funding limitations. My own feeling is that, in the end, such incentives normally play only a marginal role in who seeks external funding and who gets support. In most cases, the inner drive of the faculty member and the merit of the proposal itself are the dominant factors. We come now to extraordinary type grants. Certainly the grant to DIMACS (as our center is called) falls in this category. I can describe how the center works in any amount of detail you would like to hear, but in these comments I would prefer to focus on what was involved in putting together a successful proposal. It goes without saying that without the existing scientific strength in the four participating institutions Rutgers, Princeton, Bell Labs, and Bellcore-no amount of effort would have availed. But with only 11 centers funded out of 322 proposals received, this was a necessary but far from sufficient condition for success. The NSF solicitation request stressed four things: 1. Proposed centers should be primarily research-oriented. 2. It should involve university-industrial cooperation to strengthen U.S. competitiveness. 3. The proposal should include a significant educational component. 4. It should also include a "knowledge transfer" component to ensure that the fruits of the center's research be widely disseminated. 29

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CHAIRING TO MATHEMATICAL SCJENCES DEPARTMENT OF TO 1990S I have no doubt that the ultimate success of the Rutgers proposal was in part a result of the considerable effort made to meet these requirements: first, by involving both Bell Labs and Bellcore as participating institutions along with Princeton and Rutgers; second, by designing research programs that struck a balance between basic research and possible industrial applications; and third, by including in our educational component two pre-college programs of foundational material: one for high school mathematics teachers, the other for high school students with mathematical ability and interest. Now comes the task of turning this written proposal into a living reality. With four distinct partners, each in its own geographical location and each with its own rules of operations and organization (and with the Center's independent of lice space still a few months off), this has not been easy to achieve. Nevertheless, even though we have been in full operation for only a very short period, I believe we are on our way to implementing the proposal effectively. ADDENDUM: PREPARATION OF NSF PROPOSALS Over the years, I have had a lot of dealings with NSF proposals. At first, I was primarily a reviewer, but in recent years, I have helped some of the junior faculty with the preparation of their proposals. This was done more or less on an ad hoc basis someone would ask me to look over a proposal, and I would make some suggestions for improving it. Or I would go over referees' reports with someone who did not get funded the previous year to see if the criticisms that were leveled against the last proposal could be avoided this time around. This year I decided to be a little more systematic about it, and I have just read through all proposals from junior faculty who either were not funded last year or are new members of our department, with a view to helping them improve their proposals. (I would be happy to do the same for any senior faculty member, but feel it is out of place for me to do that on my own initiative.) I have been struck all along by the uniformity of criticism which I tend to make of the proposals I read. It therefore seems a good idea for me to detail some of the general ideas that I have about NSF proposals and the NSF itself. That is the purpose of this memorandum. Perhaps these comments will be useful to senior faculty as well, and so I am distributing them to the department as a whole for whatever it is worth. 1. Quality of the proposal versus quality of the individual I believe mathematicians have a misconception about the weight that the NSF assigns to the quality of the actual proposal that is submitted. I know many whose proposals are only a page long sometimes less just a bare statement of the problems. The assumption is that they are really "good enough" mathematicians to get funded if they simply sign their names to the proposal. The fact is that this is true in many cases; but it primarily applies to outstanding, well-established mathematicians. An individual who falls only slightly below this level puts himself/herself in jeopardy by submitting such a proposal. Once a referee criticizes an actual proposal, even if he says fine things about the person, it makes it much more difficult to get funded. As far as I can tell, the NSF goes only on the basis of its referee's reports; that is the sole criterion it uses (at least of ficially) in reaching its decisions. Having had many one-page and one- paragraph proposals to review over the years, I can assure you that it is often a strain on the reviewer to evaluate such a proposal. One has to guess what was in the proposer's mind, and many times the reviewer is unwilling to make that guess the same way as the proposer. I know specific cases of leading mathematicians whose proposals were criticized and, as a result, were not funded. Short proposals often suffer from vagueness. Without sufficient detail, it is not always clear what the 30

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FUNDING OPPORTUN1T~S proposer really has in mind. The proposer very often leaves out essential aspects of the proposal, assuming that they are implicit in what he has written, whereas, in fact, a common criticism by NSF reviewers is that a proposal is "vague." If one will contrast what goes on in other fields, one will see at once the difference in attitudes toward proposalpreparation. Iknow many cases where the preparation oftheproposal takes amonth, orlonger, of really hard work on the part of the proposer. The NSF has just issued new guidelines on lengths of proposals: a maximum of 15 pages. Presumably they had been getting proposals of 75 pages or even longer, but l5 pages is not the same as 1 page! For ajunior faculty member, these comments are important. Of course, don't get the idea from this that individuals are not also judged by reviewers. Certainly a reviewer may comment on someone's abilities, past accomplishments, or lack thereof, sometimes favorably, other times very harshly. But this is something over which one has no control. It is not clear how anything one puts into a specific proposal can influence a reviewer's judgment of an individual's stature in the field. 2. Significance of the proposal Most of the `'junior" proposals I have read make little or no attempt to put the problems in any kind of general context and rarely indicate the impact of a positive (or partial) solution on other problems. It is just taken for granted that the reviewer, being an expert in the field, understands all this, and will assume that the proposer does as well. Hence it is presumptuous-perhaps even patronizing for the proposer to elaborate the full significance of the problem area But the reality is the exact opposite the reviewer, in general, will not make any such assumption about what the proposer knows, particularly if he doesn't know the proposer at all, and maybe even if he does. Another problem is that the reviewer may well have a totally different opinion as to what is "significant" than the proposer has. Maybe no matter what the proposer writes, the reviewer will not regard it as an important problem (and perhaps he'll be right), but if the proposer makes a strong case as to why he's planning to work on this particular problem, he may influence (or at least temper) the reviewer's judgment of its significance. Believe me, for a reviewer to write that "this problem is not very significant" is usually the kiss of death. In applied mathematics, especially in interdisciplinary areas, the difficulties are compounded, for one can't even go on the assumption that the reviewer is, in fact, an expert in the field. NSF has much more trouble finding appropriate referees in such areas than in well-established clear-cut fields such as "classical harmonic analysis" or "group theory." So a great deal of thought has to go into this aspect of the proposal. In this connection, it is possible for a proposer to suggest to the NSF a list of potential reviewers. 3. The likelihood of success I find that this represents one of the weakest parts of the proposals I read. Many individuals content themselves with a precise statement of the problems to be attacked and the results obtained so far toward their solution. That is appropriate for a paper, but totally off the mark for an NSF proposal. Well, I should modify this. If one has a reasonably substantial record of having solved problems in the past, it may be entirely sufficient to write the proposal in this way. The referee will most likely assume that the individual has the capability of solving the problem, or at least obtaining something worthwhile on it. But again, one is taking a gamble. I know specific cases in my own field in which the reviewers, despite the clear significance of the problems, were unable to decide from the proposal whether the individuals had any ideas as to how to solve them. These were middle- level junior people of very high ability, but they did not get funded. It is easy to propose to work on the Riemann 31

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CHAD{TNG TO MATHEMATICAL SCIENCES DEPARTMENT OF TO 1990S hypothesis, but I guarantee that despite its significance, not many of us would get funded in that direction! I think that an essential ingredient of any proposal (especially for junior faculty) is to explain in some intuitive way what one has in mind. I know that mathematicians, being such an honest group, are reluctant to make claims about what might or might not work on a given problem. But it's not a question of learning how to "exaggerate." What is required here is an explanation of the techniques you plan to use, why you think they have a chance of working, including special cases that you may have solved, examples that you may have worked out already, partial results you may already have obtained, etc. One componentofareviewer's evaluation will almost certainly be his judgment of We proposer's chance of success. Moreover, the question of "success" is extremely important to the NSF. In examining how the NSF goes about justifying its funding from Congress, one will discover a very detailed discussion (in general terms, of course, for Congress) of specific problems that have been solved on NSF grants. For example, last year's mathematics request to Congress referred specifically to Sims and Leon's construction of the "baby monster." 4. Summary A good proposal should include the following items: a. Sufficient detail. b. The significance of the project, and c. Justification for thinking problems can be solved. 32

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FUNDING OPPORTUNIT~S DEVELOPMEN r GRANTS Calvin C. Moore University of California Based on experiences at the Mathematical Sciences Research Institute at Berkeley and in university administration as a vice president, I would like to share with you some ideas about funding opportunities and strategies. But first I will discuss the general situation in our profession. Ph.D. production in the mathematical sciences in the United States has declined steadily to approximately 750 per year. The most alarming part of this number is that half of these degrees are being earned by students who are not U.S. citizens. There is a general view that we are not renewing the profession at the necessary rate. We cannot continue to rely on foreign students because of the increasing opportunities these students will have as opportunities and funding for research increase in their home countries. Currently, we are able to induce a large number of these students to remain here and contribute to the profession. I am happy to say that the most recent data indicate at least a bottoming out of the decrease in the proportion of U.S. mathematical sciences Ph.D. degrees earned by U.S. citizens. Perhaps this is the beginning of a turnabout. However, we have a very serious problem. There is a need to renew the profession, not only in the mathematical sciences, but in all disciplines. For example, the University of California, all campuses, will need to hire 10,200 faculty in the next 16 years. The recent book by Bowen and Sosa, Prospects for Faculty in the Arts and Sciences, paints a similar picture nationwide. Additionally, the NSF has projections of the doubling of the need for terminal degree holders in science and engineering. The NSF also projects that the current level of production will fall short by a factor of 50 percent. The report Wor1fforce 2000 2 indicates that of the total additions to the work force through the year 2000, only 15 percent will be white males. This has enormous implications. It means that we will have to capitalize on the talents of women and minorities to a far greater degree than before. In the past one spoke of affirmative action programs as a rationale based on social justice. Now the rationale is much wider; it is a matter of survival. In brief, I am sketching a human resource problem of major proportions that must tee addressed at all levels, from kindergarten through postdoctoral years. Given this situation, there are excellent opportunities for funding. I would like to suggest to you a certain type of proposal that has certain analogies with the mathematics institute proposal. I call these, for lack of a better term, development grants. This kind of proposal would have a number of components, including graduate student support, postdoctoral support, and considerable attention to undergraduate programs to increase the flow of students into graduate school. Also, special attention would be given to enhancing the participation of women and minorities. The most important component is a well-thought-out plan. In other words, the proposal would be for a type of mathematics institute within a department. Bowen, W.G., and J.A. Sosa, Prospectsfor Faculty in the arts and Sciences (Princeton University Press, Princeton, N.J., 1989). 2 Johnston, W.B., and A.E. Packer, Wor~orce 200kWork and Workers for the 21st Century (Hudson Institute, Indianapolis, Ind., June 1987). 33

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CHAFING THE MATHEMATICAL SCIENCES DEPARTMENT OF THE 1990S Recall that the mathematics institutes have as one of their primary missions the training of postdoctoral fellows, that is, providing a research experience for them in a rich atmosphere of senior investigators and a flow of ideas that would enhance their career potential. That is a human resource program at the postdoctoral level. The proposals I am discussing would be for human resource development at all levels. Precedents for this exist in the National Science Foundation, in the Computer Sciences Division and in the Biological and Behavioral Sciences Division. The prospects for the funding of such proposals are enhanced if the application clearly states the kinds of resources the department is willing to contribute to the project. These grants address human resource issues. My reading is that such proposals would resonate with current thinking in the federal government, especially at the NSF. According to Dr. Judith Sunley, there is a set-aside in the Division of Mathematical Sciences of the NSF for proposals that address increasing the participation of . . . women and minorities. The NSF has proposed to issue a rather remarkable document, Important Notice 107. This notice adds requirements to ordinary grant proposals. Specifically, each proposal must include a statement specifying the potential of the proposed research to contribute to the education and development of human resources in science and engineering at the postdoctoral, graduate, and undergraduate levels. This statement may include, but is not limited to, the role of the research in student training, course preparation, and seminars, particularly for undergraduates. Special effectiveness or achievement in the area of producing professional scientists and engineers from groups currently underrepresented should be described. This statement is set forth in a document that applies to all proposals submitted to the NSF after it becomes effective. It is a clear signal of a change in the reward structure. It addresses a problem that was discussed earlier today: How do we convince faculty to devote their energies to issues that go beyond research and include human resource development? The NSF has taken an important step. Research proposals are required to address these issues and combine them with research. 34

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FUNDING OPPOR~N1TIES QUESTION-AND-ANSWER SESSION PARTICIPANT: I noticed that two of you mentioned the fact that our graduate students are the best means of technological transfer. I would like to amend that. They should be, but they are not. It is clear that we have the best research establishment in mathematical sciences in the world; yet we have one of the poorest technological transfer establishments in the world. I suggest, as a possible solution to this, that a portion of the graduate programs in mathematical sciences should be changed to address that issue. DR. GLIMM: Graduate students are the best means of technology transfer if they are transferred. However, in many cases they pursue academic careers. I think you are raising the following questions: Should our graduate education be broader? Should we expect a certain fraction of our students to have industrial laboratory careers and an appropriate education? Affirmative answers to these questions would assure that the technology would be transferred through those students. Perhaps we were neglecting that kind of employment consideration in . . c eslgn~ng our programs. DR. GORENSTEIN: For a certain percentage of students, that is very appropriate. Maybe we have neglected it. But there is still core mathematics. The best way to train people for that is to let them prove theorems. I don't know the proper balance. PARTICIPANT: Technology transfer has happened more in statistics than in core mathematics. One of the reasons is that, historically, statistics has recruited into graduate programs students with undergraduate careers in application areas. These persons pursue careers in industry and government more than mathematicians do. It is not easy for statistics to recruit these people; I am sure it is more difficult for mathematics to achieve, but that appears to be a source of technology transfer people. PARTICIPANT: I was struck by Dr. Gorenstein's comment about departments at Rutgers getting a return of indirect costs. I have the task of trying to elevate the level of funding in my department. I am curious as to what fraction of indirect costs comes back to a typical mathematics department. PARTICIPANT: About 5 percent. PARTICIPANT: The University of Maryland gives back 25 percent. DR. GLIMM: In addition to the routine recovery, I think unusual situations sometimes allow for a larger recovery. PARTICIPANT: Just a comment to follow up-that is not the sole measure of how well a department does. Many universities reward departments that bring in a lot of money in other ways. They may increase their basic budgets, for example. We get 30 percent return, but our basic budget is about one-quarter or less of what we need to operate. So it is just a matter of how the money is passed to the department. 35

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CHASING TO MATHEMATICAL SCIENCES DEPARTMENT OF TO 1990S DR. GORENSTEIN: Princeton University gives back zero. However, from my experience, the computer science department is treated very well atPrinceton. Every faculty member has a secretary. So one mustexamine the way in which a university operates vis-a-vis the department. PARTICIPANT: I know that in hiring senior faculty members, particularly in the physical sciences, it is becoming more common for administrations to agree to return a fraction of grant overhead generated by that person as start-up costs. It seems to me that if one is hiring a very strong faculty member in mathematics, one could get the same kind of agreement for start-up costs from the dean that the physics chair is getting for his people. DR. MOORE: The issue of start-up costs is a concern from the perspective of provosts and vice presidents. It is, on average, $100,000. That is averaged over all fields, including the humanities. For senior people in the physical sciences, it can go as high as $1 million. This is a form of subsidy to those departments. You are quite right that mathematics departments have not entered into the sweepstakes to the degree that they might. 36